3.2.2. What is a good model?¶
In science and engineering we often end up in situations where we want to infer (or learn) a quantitative model \(M\) for a given set of sample points \(\boldsymbol{X} \in [x_1, x_2,\dots x_N]\).
-As we will see repeatedely in these lectures, we could try to fit these data points to a model given by a +
As we will see repeatedly in these lectures, we could try to fit these data points to a model given by a straight line, or if we wish to be more sophisticated to a more complex function.
The reason for inferring such a model is that it serves many useful purposes. On the one hand, the model can reveal information encoded in the data or underlying mechanisms from which the data were generated. For instance, we could discover important -corelations that relate interesting physics interpretations.
+correlations that relate interesting physics interpretations.In addition, it can simplify the representation of the given data set and help us in making predictions about future data samples.
A first important consideration to keep in mind is that inferring the correct model @@ -843,7 +843,7 @@ y = 10x+0.01 \times N(0,1),
where \(x\) is defined as before. Does the fit look better? Indeed, by reducing the role of the noise given by the normal distribution we see immediately that our linear prediction seemingly reproduces better the training -set. However, this testing ‘by the eye’ is obviouly not satisfactory in the +set. However, this testing ‘by the eye’ is obviously not satisfactory in the long run. Here we have only defined the training data and our model, and have not discussed a more rigorous approach to the cost function.
We need more rigorous criteria in defining whether we have succeeded or @@ -957,13 +957,13 @@ example of the functionality of Scikit-Learn.
The intercept alpha:
- [2.02408959]
+ [2.03523311]
Coefficient beta :
- [[4.92811987]]
-Mean squared error: 0.25
-Variance score: 0.89
+ [[4.99498108]]
+Mean squared error: 0.27
+Variance score: 0.87
Mean squared log error: 0.01
-Mean absolute error: 0.39
+Mean absolute error: 0.41
@@ -1063,7 +1063,7 @@ a linear \(x\)-dependence we s
-0.005
+0.00499999999999999
This is given by the Singular Value Decomposition (SVD) algorithm, perhaps the most powerful linear algebra algorithm. The SVD provides a numerically stable matrix decomposition that is used in a large -swath oc applications and the decomposition is always stable +swath of applications and the decomposition is always stable numerically.
In machine learning it plays a central role in dealing with for
example design matrices that may be near singular or singular.
@@ -565,7 +565,7 @@ when the matrix \(\boldsymbol{X}\)\(\boldsymbol{X}\)
may be linearly dependent, normally referred to as super-collinearity.
This means that the matrix may be rank deficient and it is basically impossible to
-to model the data using linear regression. As an example, consider the matrix
\[\begin{split}
\begin{align*}
@@ -585,7 +585,7 @@ to model the data using linear regression. As an example, consider the matrix\(\mathbf{X}\) is equal to the number
-of linearly independent columns. In this particular case the matrix has rank 2.
+of linearly independent columns. In this particular case the matrix has rank 1.
Super-collinearity of an \((n \times p)\)-dimensional design matrix \(\mathbf{X}\) implies that the inverse of the matrix \(\boldsymbol{X}^T\boldsymbol{X}\) (the matrix we need to invert to solve the linear regression equations) is non-invertible. If we have a square matrix that does not have an inverse, we say this matrix singular. The example here demonstrates this
@@ -613,7 +613,7 @@ This is equivalent to saying that the matrix \(\boldsymbol{X}^T\boldsymbol{X}\) and we cannot find the parameters (estimators) \(\beta_i\).
-The estimators are only well-defined if \((\boldsymbol{X}^{T}\boldsymbol{X})^{-1}\) exits.
+The estimators are only well-defined if \((\boldsymbol{X}^{T}\boldsymbol{X})\) can be inverted.
This is more likely to happen when the matrix \(\boldsymbol{X}\) is high-dimensional. In this case it is likely to encounter a situation where
the regression parameters \(\beta_i\) cannot be estimated.
A cheap ad hoc approach is simply to add a small diagonal component to the matrix to invert, that is we change
@@ -625,7 +625,7 @@ the regression parameters \(\beta_i\)4.3. Basic math of the SVD¶
-From standard linear algebra we know that a square matrix \(\boldsymbol{X}\) can be diagonalized if and only it is +
From standard linear algebra we know that a square matrix \(\boldsymbol{X}\) can be diagonalized if and only if it is a so-called normal matrix, that is if \(\boldsymbol{X}\in {\mathbb{R}}^{n\times n}\) we have \(\boldsymbol{X}\boldsymbol{X}^T=\boldsymbol{X}^T\boldsymbol{X}\) or if \(\boldsymbol{X}\in {\mathbb{C}}^{n\times n}\) we have \(\boldsymbol{X}\boldsymbol{X}^{\dagger}=\boldsymbol{X}^{\dagger}\boldsymbol{X}\). The matrix has then a set of eigenpairs
@@ -813,7 +813,6 @@ The simple answer is to use the linear algebra function for the pseudoinverse, t return np.matmul(V,np.matmul(invD,UT)) -#X = np.array([ [1.0, -1.0, 2.0], [1.0, 0.0, 1.0], [1.0, 2.0, -1.0], [1.0, 1.0, 0.0] ]) # Non-singular square matrix X = np.array( [ [1,2,3],[2,4,5],[3,5,6]]) print(X) @@ -849,7 +848,7 @@ test VT rectangular matrices where the number of rows and columns are not equal.It is also called the the Moore-Penrose Inverse after two independent discoverers of the method or the Generalized Inverse. It is used for the calculation of the inverse for singular or near singular matrices and for rectangular matrices.
-Using the SVD we can obtain the pseudoinverse of a matrix \(\boldsymbol{A}\) (labeled here as \(\boldsymbol{A}_{\mathrm{PI}}\)
+Using the SVD we can obtain the pseudoinverse (PI) of a matrix \(\boldsymbol{A}\) (labeled here as \(\boldsymbol{A}_{\mathrm{PI}}\)
\[
\boldsymbol{A}_{\mathrm{PI}}= \boldsymbol{V}\boldsymbol{D}_{\mathrm{PI}}\boldsymbol{U}^T,
@@ -919,7 +918,7 @@ x_{n-1,0} & x_{n-1,1} & x_{n-1,2}& \dots & \dots x_{n-1,p-1}\\
\boldsymbol{X}=\boldsymbol{U}\boldsymbol{\Sigma}\boldsymbol{V}^T,
\]
where \(\boldsymbol{U}\) is an orthogonal matrix of dimension \(n\times n\), meaning that \(\boldsymbol{U}\boldsymbol{U}^T=\boldsymbol{U}^T\boldsymbol{U}=\boldsymbol{I}_n\). Here \(\boldsymbol{I}_n\) is the unit matrix of dimension \(n \times n\).
-Similarly, \(\boldsymbol{V}\) is an orthogonal matrix of dimension \(p\times p\), meaning that \(\boldsymbol{V}\boldsymbol{V}^T=\boldsymbol{V}^T\boldsymbol{V}=\boldsymbol{I}_p\). Here \(\boldsymbol{I}_n\) is the unit matrix of dimension \(p \times p\).
+Similarly, \(\boldsymbol{V}\) is an orthogonal matrix of dimension \(p\times p\), meaning that \(\boldsymbol{V}\boldsymbol{V}^T=\boldsymbol{V}^T\boldsymbol{V}=\boldsymbol{I}_p\). Here \(\boldsymbol{I}_p\) is the unit matrix of dimension \(p \times p\).
Finally \(\boldsymbol{\Sigma}\) contains the singular values \(\sigma_i\). This matrix has dimension \(n\times p\) and the singular values \(\sigma_i\) are all positive. The non-zero values are ordered in descending order, that is
\[
@@ -1057,7 +1056,7 @@ function, that is we have
\[
\frac{\partial^2 C(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}^T\partial \boldsymbol{\beta}} =\frac{2}{n}\boldsymbol{X}^T\boldsymbol{X}.
\]
-This quantity defines was what is called the Hessian matrix (the second derivative of a function we want to optimize).
+This quantity defines what is called the Hessian matrix (the second derivative of the cost function we want to optimize).
The Hessian matrix plays an important role and is defined in this course as
\[
@@ -1148,7 +1147,7 @@ We can rewrite the design/feature matrix in terms of its column vectors as
\boldsymbol{x}_i^T = \begin{bmatrix}x_{0,i} & x_{1,i} & x_{2,i}& \dots & \dots x_{n-1,i}\end{bmatrix}.
\]
With these definitions, we can now rewrite our \(2\times 2\) -correlation/covariance matrix in terms of a moe general design/feature +correlation/covariance matrix in terms of a more general design/feature matrix \(\boldsymbol{X}\in {\mathbb{R}}^{n\times p}\). This leads to a \(p\times p\) covariance matrix for the vectors \(\boldsymbol{x}_i\) with \(i=0,1,\dots,p-1\)
@@ -1207,10 +1206,10 @@ covariance matrix through the np.linalg.eig() function.
-
@@ -1247,10 +1246,10 @@ a more brute force way. Here we scale the mean values for each column of the des
0.04413933503955871
-4.12330280229368
-[[0.80162359 2.38222896]
- [2.38222896 8.12167821]]
+-0.08873443359350565
+3.7851533175757255
+[[ 0.98248312 3.05483267]
+ [ 3.05483267 10.24784064]]
-
@@ -1259,7 +1258,7 @@ a more brute force way. Here we scale the mean values for each column of the des
should be and that the matrix is symmetric. Furthermore, diagonalizing
this matrix we easily see that it is a positive definite matrix.
0.06786925114666595
-1.9635449873404844
-[[1. 0.65522261]
- [0.65522261 1. ]]
+0.07858099596662704
+2.071920625289855
+[[1. 0.71822416]
+ [0.71822416 1. ]]
The above procedure with numpy can be made more compact if we use pandas.
-We whow here how we can set up the correlation matrix using pandas, as done in this simple code
+We know here how we can set up the correlation matrix using pandas, as done in this simple code
import numpy as np
@@ -1280,30 +1279,30 @@ this matrix we easily see that it is a positive definite matrix.
-
@@ -1360,37 +1359,37 @@ this matrix we easily see that it is a positive definite matrix.
@@ -1668,7 +1667,7 @@ C(\boldsymbol{X},\boldsymbol{\beta})=\left\{(\boldsymbol{y}-\boldsymbol{X}\bolds
-
-
-
- 7.11. Using Autograd with OLS
+
+ 7.11. Replace or not
+
+
+
+
+ 7.12. Using Autograd
+
+
+
+
+ 7.13. Same code but now with momentum gradient descent
+
+
+
+
+ 7.14. Including Stochastic Gradient Descent with Autograd
+
+
+ 7.15. Introducing JAX
+
+
@@ -502,22 +517,37 @@ const thebe_selector_output = ".output, .cell_output"
-
- 7.11. Using Autograd with OLS
+
+ 7.11. Replace or not
+
+
+
+
+ 7.12. Using Autograd
+
+
+
+
+ 7.13. Same code but now with momentum gradient descent
+
+
+
+
+ 7.14. Including Stochastic Gradient Descent with Autograd
+
+
+ 7.15. Introducing JAX
+
+
@@ -735,7 +765,18 @@ connecting \(x\) and The convex subsets of \(\mathbb{R}\) are the intervals of
\(\mathbb{R}\). Examples of convex sets of \(\mathbb{R}^2\) are the
regular polygons (triangles, rectangles, pentagons, etc…).
-
[[-0.27091656 -1.29083183]
- [ 0.31980301 0.87495119]
- [-0.10835935 1.61413333]
- [ 0.5188328 2.80380438]
- [-0.04996008 -1.95742107]
- [ 1.19432526 2.68719389]
- [ 0.19710439 1.35590603]
- [-0.23857423 -2.50104946]
- [-0.94054854 -2.09034902]
- [-0.62170669 -1.49633743]]
+[[ -2.84861838 -10.07337358]
+ [ 0.53938383 2.59445979]
+ [ -0.40980089 -0.48871288]
+ [ 0.05834332 -0.39384255]
+ [ 2.25385387 7.58112299]
+ [ 0.68246434 2.46650488]
+ [ -0.25366775 -1.97047717]
+ [ 0.79081838 2.03807267]
+ [ -0.06150169 -0.57109235]
+ [ -0.75127504 -1.18266178]]
+ 0 1
+0 -2.848618 -10.073374
+1 0.539384 2.594460
+2 -0.409801 -0.488713
+3 0.058343 -0.393843
+4 2.253854 7.581123
+5 0.682464 2.466505
+6 -0.253668 -1.970477
+7 0.790818 2.038073
+8 -0.061502 -0.571092
+9 -0.751275 -1.182662
0 1
-0 -0.270917 -1.290832
-1 0.319803 0.874951
-2 -0.108359 1.614133
-3 0.518833 2.803804
-4 -0.049960 -1.957421
-5 1.194325 2.687194
-6 0.197104 1.355906
-7 -0.238574 -2.501049
-8 -0.940549 -2.090349
-9 -0.621707 -1.496337
- 0 1
-0 1.000000 0.800615
-1 0.800615 1.000000
+0 1.000000 0.984525
+1 0.984525 1.000000
0 1 2 3 4 5 6 7 \
0 0.0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
-1 0.0 0.084006 0.079882 0.084682 0.084092 0.083417 0.076315 0.076097
-2 0.0 0.079882 0.077644 0.078542 0.078962 0.079424 0.069534 0.069977
-3 0.0 0.084682 0.078542 0.090649 0.088758 0.086665 0.085105 0.084008
-4 0.0 0.084092 0.078962 0.088758 0.087573 0.086250 0.082424 0.081832
-5 0.0 0.083417 0.079424 0.086665 0.086250 0.085776 0.079486 0.079438
-6 0.0 0.076315 0.069534 0.085105 0.082424 0.079486 0.082288 0.080588
-7 0.0 0.076097 0.069977 0.084008 0.081832 0.079438 0.080588 0.079264
-8 0.0 0.076022 0.070618 0.082990 0.081357 0.079553 0.078908 0.077986
-9 0.0 0.076079 0.071460 0.082027 0.080984 0.079823 0.077219 0.076729
-10 0.0 0.068075 0.061188 0.078143 0.075043 0.071666 0.077200 0.075149
-11 0.0 0.067712 0.061308 0.077144 0.074420 0.071445 0.075770 0.074006
-12 0.0 0.067499 0.061604 0.076264 0.073938 0.071388 0.074418 0.072955
-13 0.0 0.067443 0.062089 0.075498 0.073597 0.071505 0.073134 0.071991
-14 0.0 0.067547 0.062777 0.074845 0.073400 0.071804 0.071908 0.071106
+1 0.0 0.090241 0.082140 0.090564 0.084086 0.078082 0.082282 0.076619
+2 0.0 0.082140 0.075227 0.083102 0.077428 0.072150 0.075982 0.070945
+3 0.0 0.090564 0.083102 0.096893 0.090268 0.084107 0.091647 0.085571
+4 0.0 0.084086 0.077428 0.090268 0.084286 0.078707 0.085655 0.080120
+5 0.0 0.078082 0.072150 0.084107 0.078707 0.073657 0.080061 0.075020
+6 0.0 0.082282 0.075982 0.091647 0.085655 0.080061 0.089082 0.083380
+7 0.0 0.076619 0.070945 0.085571 0.080120 0.075020 0.083380 0.078158
+8 0.0 0.071394 0.066284 0.079944 0.074984 0.070333 0.078082 0.073299
+9 0.0 0.066569 0.061966 0.074729 0.070216 0.065973 0.073159 0.068776
+10 0.0 0.073831 0.068541 0.084523 0.079224 0.074258 0.083779 0.078587
+11 0.0 0.068867 0.064081 0.079021 0.074183 0.069640 0.078484 0.073716
+12 0.0 0.064284 0.059952 0.073925 0.069506 0.065349 0.073567 0.069187
+13 0.0 0.060048 0.056127 0.069202 0.065165 0.061359 0.068999 0.064974
+14 0.0 0.056131 0.052581 0.064823 0.061133 0.057648 0.064753 0.061054
8 9 10 11 12 13 14
0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
-1 0.076022 0.076079 0.068075 0.067712 0.067499 0.067443 0.067547
-2 0.070618 0.071460 0.061188 0.061308 0.061604 0.062089 0.062777
-3 0.082990 0.082027 0.078143 0.077144 0.076264 0.075498 0.074845
-4 0.081357 0.080984 0.075043 0.074420 0.073938 0.073597 0.073400
-5 0.079553 0.079823 0.071666 0.071445 0.071388 0.071505 0.071804
-6 0.078908 0.077219 0.077200 0.075770 0.074418 0.073134 0.071908
-7 0.077986 0.076729 0.075149 0.074006 0.072955 0.071991 0.071106
-8 0.077140 0.076349 0.073080 0.072240 0.071510 0.070887 0.070370
-9 0.076349 0.076066 0.070961 0.070443 0.070056 0.069801 0.069681
-10 0.073080 0.070961 0.073601 0.071922 0.070288 0.068689 0.067110
-11 0.072240 0.070443 0.071922 0.070466 0.069065 0.067709 0.066388
-12 0.071510 0.070056 0.070288 0.069065 0.067907 0.066808 0.065761
-13 0.070887 0.069801 0.068689 0.067709 0.066808 0.065983 0.065228
-14 0.070370 0.069681 0.067110 0.066388 0.065761 0.065228 0.064787
+1 0.071394 0.066569 0.073831 0.068867 0.064284 0.060048 0.056131
+2 0.066284 0.061966 0.068541 0.064081 0.059952 0.056127 0.052581
+3 0.079944 0.074729 0.084523 0.079021 0.073925 0.069202 0.064823
+4 0.074984 0.070216 0.079224 0.074183 0.069506 0.065165 0.061133
+5 0.070333 0.065973 0.074258 0.069640 0.065349 0.061359 0.057648
+6 0.078082 0.073159 0.083779 0.078484 0.073567 0.068999 0.064753
+7 0.073299 0.068776 0.078587 0.073716 0.069187 0.064974 0.061054
+8 0.068841 0.064684 0.073750 0.069268 0.065095 0.061209 0.057588
+9 0.064684 0.060863 0.069242 0.065118 0.061272 0.057686 0.054340
+10 0.073750 0.069242 0.079948 0.075028 0.070450 0.066189 0.062220
+11 0.069268 0.065118 0.075028 0.070494 0.066270 0.062333 0.058663
+12 0.065095 0.061272 0.070450 0.066270 0.062370 0.058732 0.055337
+13 0.061209 0.057686 0.066189 0.062333 0.058732 0.055369 0.052227
+14 0.057588 0.054340 0.062220 0.058663 0.055337 0.052227 0.049318
This equation does not lead to a nice analytical equation as in Ridge regression or ordinary least squares. This equation can however be solved by using standard convex optimization algorithms using for example the Python package CVXOPT. We will discuss this later.
Let us assume that our design matrix is given by unit (identity) matrix, that is a square diagonal matrix with ones only along the diagonal. In this case we have an equal number of rows and columns \(n=p\).
-Our model approximation is just \(\tilde{\boldsymbol{y}}=\boldsymbol{\beta}\) and the mean squared error and thereby the cost function for ordinary least sqquares (OLS) is then (we drop the term \(1/n\))
+Our model approximation is just \(\tilde{\boldsymbol{y}}=\boldsymbol{\beta}\) and the mean squared error and thereby the cost function for ordinary least squares (OLS) is then (we drop the term \(1/n\))
\[
C(\boldsymbol{\beta})=\sum_{i=0}^{p-1}(y_i-\beta_i)^2,
@@ -1706,7 +1705,7 @@ C(\boldsymbol{\beta})=\sum_{i=0}^{p-1}(y_i-\beta_i)^2+\lambda\sum_{i=0}^{p-1}\ve
0 &\mathrm{if} & \vert y_i\vert\le \frac{\lambda}{2}\end{array}\right.\\.
\end{split}\]
Plotting these results (figure in handwritten notes for week 36) shows clearly that Lasso regression suppresses (sets to zero) values of \(\beta_i\) for specific values of \(\lambda\). Ridge regression reduces on the other hand the values of \(\beta_i\) as function of \(\lambda\).
-As another examples, +
As another example, let us assume we have a data set with outputs/targets given by the vector
\[\begin{split}
@@ -1878,12 +1877,12 @@ Training MSE for OLS
We see here that we reach a plateau for the Ridge results. Writing out the coefficients \(\boldsymbol{\beta}\), we that they are getting smaller and smaller and our error stabilizes since the predicted values of \(\tilde{\boldsymbol{y}}\) approach zero.
+We see here that we reach a plateau for the Ridge results. Writing out the coefficients \(\boldsymbol{\beta}\), we observe that they are getting smaller and smaller and our error stabilizes since the predicted values of \(\tilde{\boldsymbol{y}}\) approach zero.
This happens also for Lasso regression, as seen from the next code output. The difference is that Lasso shrinks the values of \(\beta\) to zero at a much earlier stage and the results flatten out. We see that Lasso gives also an excellent fit for small values of \(\lambda\) and -shows rthe best performance of the three regression methods.
+shows the best performance of the three regression methods.import os
@@ -2426,7 +2425,7 @@ We define this distribution as
p(y_i, \boldsymbol{X}\vert\boldsymbol{\beta})=\frac{1}{\sqrt{2\pi\sigma^2}}\exp{\left[-\frac{(y_i-\boldsymbol{X}_{i,*}\boldsymbol{\beta})^2}{2\sigma^2}\right]},
\]which reads as finding the likelihood of an event \(y_i\) with the input variables \(\boldsymbol{X}\) given the parameters (to be determined) \(\boldsymbol{\beta}\).
-Since these events are assumed to be independent and identicall distributed we can build the probability distribution function (PDF) for all possible event \(\boldsymbol{y}\) as the product of the single events, that is we have
+Since these events are assumed to be independent and identically distributed we can build the probability distribution function (PDF) for all possible event \(\boldsymbol{y}\) as the product of the single events, that is we have
\[
p(\boldsymbol{y},\boldsymbol{X}\vert\boldsymbol{\beta})=\prod_{i=0}^{n-1}\frac{1}{\sqrt{2\pi\sigma^2}}\exp{\left[-\frac{(y_i-\boldsymbol{X}_{i,*}\boldsymbol{\beta})^2}{2\sigma^2}\right]}=\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta}).
@@ -2497,7 +2496,7 @@ p(X \cup Y)= p(X)+p(Y)-p(X \cap Y).
The product rule (aka joint probability) is given by
\[
-p(X \cup Y)= p(X,Y)= p(X\vert Y)p(Y)=p(Y\vert X)p(X),
+p(X \cap Y)= p(X,Y)= p(X\vert Y)p(Y)=p(Y\vert X)p(X),
\]
where we read \(p(X\vert Y)\) as the likelihood of obtaining \(X\) given \(Y\).
If we have independent events then \(p(X,Y)=p(X)p(Y)\).
@@ -2973,7 +2972,7 @@ parameters \(\beta_j\) as func noise. Here we recommend to use \(\sigma^2=1\) as variance for the added noise (which follows a normal distribution with mean value zero). Comment your results. If you have a large noise term, do the parameters \(\beta_j\) vary more as function -model complexity? And what about their variance? +of model complexity? And what about their variance?4.14. Linking Bayes’ Theorem with Ridge and Lasso Regression¶
@@ -3002,7 +3001,7 @@ p(\boldsymbol{\beta}\vert\boldsymbol{D}). \[ p(\boldsymbol{\beta}\vert\boldsymbol{D})\propto p(\boldsymbol{D}\vert\boldsymbol{\beta})p(\boldsymbol{\beta}). \]We have a model for \(p(\boldsymbol{D}\vert\boldsymbol{\beta})\) but need one for the prior \(p(\boldsymbol{\beta}\)!
+We have a model for \(p(\boldsymbol{D}\vert\boldsymbol{\beta})\) but need one for the prior \(p(\boldsymbol{\beta})\)!
With the posterior probability defined by a likelihood which we have already modeled and an unknown prior, we are now ready to make additional models for the prior.
@@ -3047,12 +3046,12 @@ logarithm of the posterior probability and leaving out the constants terms that do not depend on \(\beta\), we have
\[
-C(\boldsymbol{\beta}=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}+\frac{1}{\tau}\vert\vert\boldsymbol{\beta}\vert\vert_1,
+C(\boldsymbol{\beta})=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}+\frac{1}{\tau}\vert\vert\boldsymbol{\beta}\vert\vert_1,
\]
and replacing \(1/\tau\) with \(\lambda\) we have
\[
-C(\boldsymbol{\beta}=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}+\lambda\vert\vert\boldsymbol{\beta}\vert\vert_1,
+C(\boldsymbol{\beta})=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}+\lambda\vert\vert\boldsymbol{\beta}\vert\vert_1,
\]
which is our Lasso cost function!
Plotting these prior functions shows us that we can use the parameter diff --git a/doc/LectureNotes/_build/html/chapteroptimization.html b/doc/LectureNotes/_build/html/chapteroptimization.html index d0ce220cc..15b97e436 100644 --- a/doc/LectureNotes/_build/html/chapteroptimization.html +++ b/doc/LectureNotes/_build/html/chapteroptimization.html @@ -389,22 +389,37 @@ const thebe_selector_output = ".output, .cell_output"
Convex function: Let \(X \subset \mathbb{R}^n\) be a convex set. Assume that the function \(f: X \rightarrow \mathbb{R}\) is continuous, then \(f\) is said to be convex if $\(f(tx_1 + (1-t)x_2) \leq tf(x_1) + (1-t)f(x_2) \)\( for all \)x_1, x_2 \in X\( and for all \)t \in [0,1]\(. If \)\leq\( is replaced with a strict inequaltiy in the definition, we demand \)x_1 \neq x_2\( and \)t\in(0,1)\( then \)f\( is said to be strictly convex. For a single variable function, convexity means that if you draw a straight line connecting \)f(x_1)\( and \)f(x_2)\(, the value of the function on the interval \)[x_1,x_2]$ is always below the line as illustrated below.
+Convex function: Let \(X \subset \mathbb{R}^n\) be a convex +set. Assume that the function \(f: X \rightarrow \mathbb{R}\) is +continuous, then \(f\) is said to be convex if +\(f(tx_1 + (1-t)x_2) \leq tf(x_1) + (1-t)f(x_2)\) +for all +\(x_1, x_2 \in X\) and for all \(t \in [0,1]\).
+If \(\leq\) is replaced with a strict inequality in the +definition, we demand \(x_1 \neq x_2\) and \(t\in(0,1)\) then \(f\) is said +to be strictly convex. For a single variable function, convexity means +that if you draw a straight line connecting \(f(x_1)\) and \(f(x_2)\), the +value of the function on the interval \([x_1,x_2]\) is always below the +line as discussed below.
In the following we state first and second-order conditions which
ensures convexity of a function \(f\). We write \(D_f\) to denote the
domain of \(f\), i.e the subset of \(R^n\) where \(f\) is defined. For more
@@ -746,7 +787,7 @@ all \(x\) in the domain of
Second order condition.
@@ -899,11 +940,11 @@ which equals
-
-
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94582/483257001.py:18: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_96694/483257001.py:18: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().
ax = fig.gca(projection="3d")
-<mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x128ee8850>
+<mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x11db14850>
@@ -961,7 +1002,7 @@ which equals
-[<matplotlib.lines.Line2D at 0x12946f2e0>]
+[<matplotlib.lines.Line2D at 0x11e09b370>]
@@ -1218,11 +1259,11 @@ when \(||\nabla_\beta C(\beta_k) || \
-[0.34158665 3.94915262]
-[[3.97117751]
- [3.11850274]]
-[[3.97117751]
- [3.11850274]]
+[0.2831603 4.55553537]
+[[3.91511388]
+ [3.13030182]]
+[[3.91511388]
+ [3.13030182]]
@@ -1251,9 +1292,9 @@ when \(||\nabla_\beta C(\beta_k) || \
-[[4.40754621]
- [2.78752269]]
-[4.37713991] [2.77711437]
+[[4.1509778 ]
+ [2.92461411]]
+[4.13288373] [2.92817032]
@@ -1324,10 +1365,10 @@ C_{\text{ridge}}(\beta) = \frac{1}{n}||X\beta -\mathbf{y}||^2 + \lambda ||\beta|
-[[3.94107596]
- [2.96620033]]
-[[3.96670977]
- [2.94212937]]
+[[4.0795449 ]
+ [2.86893619]]
+[[4.04785727]
+ [2.89298533]]
@@ -1577,15 +1618,15 @@ function.
Own inversion
-[[3.95446837]
- [3.16961682]]
-Eigenvalues of Hessian Matrix:[0.31447174 4.32459186]
+[[4.41170104]
+ [2.6431453 ]]
+Eigenvalues of Hessian Matrix:[0.31228042 4.55571665]
theta from own gd
-[[3.95446837]
- [3.16961682]]
+[[4.41170104]
+ [2.6431453 ]]
theta from own sdg
-[[3.91682433]
- [3.13655438]]
+[[4.39272691]
+ [2.63430285]]
@@ -2302,8 +2343,15 @@ which also computed the dot product can be used:
-
-7.11. Using Autograd with OLS¶
+
+7.11. Replace or not¶
+In the above code, we have use replacement in setting up the
+mini-batches. The discussion
+here may be
+useful.
+
+
+7.12. Using Autograd¶
We conclude the part on optmization by showing how we can make codes
for linear regression and logistic regression using autograd. The
first example shows results with ordinary leats squares.
@@ -2362,8 +2410,117 @@ first example shows results with ordinary leats squares.
+
+
+7.13. Same code but now with momentum gradient descent¶
+
+
+# Using Autograd to calculate gradients for OLS
+from random import random, seed
+import numpy as np
+import autograd.numpy as np
+import matplotlib.pyplot as plt
+from autograd import grad
+
+def CostOLS(beta):
+ return (1.0/n)*np.sum((y-X @ beta)**2)
+
+n = 100
+x = 2*np.random.rand(n,1)
+y = 4+3*x#+np.random.randn(n,1)
+
+X = np.c_[np.ones((n,1)), x]
+XT_X = X.T @ X
+theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)
+print("Own inversion")
+print(theta_linreg)
+# Hessian matrix
+H = (2.0/n)* XT_X
+EigValues, EigVectors = np.linalg.eig(H)
+print(f"Eigenvalues of Hessian Matrix:{EigValues}")
+
+theta = np.random.randn(2,1)
+eta = 1.0/np.max(EigValues)
+Niterations = 30
+
+# define the gradient
+training_gradient = grad(CostOLS)
+
+for iter in range(Niterations):
+ gradients = training_gradient(theta)
+ theta -= eta*gradients
+ print(iter,gradients[0],gradients[1])
+print("theta from own gd")
+print(theta)
+
+# Now improve with momentum gradient descent
+change = 0.0
+delta_momentum = 0.3
+for iter in range(Niterations):
+ # calculate gradient
+ gradients = training_gradient(theta)
+ # calculate update
+ new_change = eta*gradients+delta_momentum*change
+ # take a step
+ theta -= new_change
+ # save the change
+ change = new_change
+ print(iter,gradients[0],gradients[1])
+print("theta from own gd wth momentum")
+print(theta)
+
+
+
+
+We note indeed a considerable increase in efficiency here, we less iterations needed.
+However, if we can invert the Hessian matrix, this is the preferred approach, as shown in the example here.
+
+
+# Using Newton's method
+from random import random, seed
+import numpy as np
+import autograd.numpy as np
+import matplotlib.pyplot as plt
+from autograd import grad
+
+def CostOLS(beta):
+ return (1.0/n)*np.sum((y-X @ beta)**2)
+
+n = 100
+x = 2*np.random.rand(n,1)
+y = 4+3*x+np.random.randn(n,1)
+
+X = np.c_[np.ones((n,1)), x]
+XT_X = X.T @ X
+beta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)
+print("Own inversion")
+print(beta_linreg)
+# Hessian matrix
+H = (2.0/n)* XT_X
+# Note that here the Hessian does not depend on the parameters beta
+invH = np.linalg.pinv(H)
+EigValues, EigVectors = np.linalg.eig(H)
+print(f"Eigenvalues of Hessian Matrix:{EigValues}")
+
+beta = np.random.randn(2,1)
+Niterations = 5
+
+# define the gradient
+training_gradient = grad(CostOLS)
+
+for iter in range(Niterations):
+ gradients = training_gradient(beta)
+ beta -= invH @ gradients
+ print(iter,gradients[0],gradients[1])
+print("beta from own Newton code")
+print(beta)
+
+
+
+
+
-7.11.1. Including Stochastic Gradient Descent with Autograd¶
+7.14. Including Stochastic Gradient Descent with Autograd¶
In this code we include the stochastic gradient descent approach discussed above. Note here that we specify which argument we are taking the derivative with respect to when using autograd.
@@ -2444,48 +2601,230 @@ first example shows results with ordinary leats squares.
-
-
diff --git a/doc/LectureNotes/_build/html/searchindex.js b/doc/LectureNotes/_build/html/searchindex.js
index 5b7744572..9145e3b0b 100644
--- a/doc/LectureNotes/_build/html/searchindex.js
+++ b/doc/LectureNotes/_build/html/searchindex.js
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Linear Regression","14. Building a Feed Forward Neural Network","15. Solving Differential Equations with Deep Learning","16. Convolutional Neural Networks","17. Recurrent neural networks: Overarching view","4. Ridge and Lasso Regression","5. Resampling Methods","6. Logistic Regression","8. Support Vector Machines, overarching aims","9. Decision trees, overarching aims","10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods","11. Basic ideas of the Principal Component Analysis (PCA)","13. Neural networks","7. Optimization, the central part of any Machine Learning algortithm","12. Clustering and Unsupervised Learning","Applied Data Analysis and Machine Learning","2. Linear Algebra, Handling of Arrays and more Python Features","Teaching schedule with links to material","1. Elements of Probability Theory and Statistical Data Analysis","Teachers and 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diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter1.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter1.ipynb
index 6596a4b79..f35523f45 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapter1.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/chapter1.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "d9b4c9c8",
+ "id": "27b96943",
"metadata": {
"editable": true
},
@@ -13,7 +13,7 @@
},
{
"cell_type": "markdown",
- "id": "65e44d92",
+ "id": "ee293e0b",
"metadata": {
"editable": true
},
@@ -23,7 +23,7 @@
},
{
"cell_type": "markdown",
- "id": "06b62649",
+ "id": "f6481760",
"metadata": {
"editable": true
},
@@ -65,7 +65,7 @@
},
{
"cell_type": "markdown",
- "id": "8de26fd1",
+ "id": "fd2c7eef",
"metadata": {
"editable": true
},
@@ -117,7 +117,7 @@
"Machine learning is an extremely rich field, in spite of its young\n",
"age. The increases we have seen during the last three decades in\n",
"computational capabilities have been followed by developments of\n",
- "methods and techniques for analyzing and handling large date sets,\n",
+ "methods and techniques for analyzing and handling large data sets,\n",
"relying heavily on statistics, computer science and mathematics. The\n",
"field is rather new and developing rapidly. Popular software packages\n",
"written in Python for machine learning like\n",
@@ -140,7 +140,7 @@
"problem, and let the computer deduce the logic behind it. On the other\n",
"hand, *unsupervised learning* is a method for finding patterns and\n",
"relationship in data sets without any prior knowledge of the system.\n",
- "Some authours also operate with a third category, namely\n",
+ "Some authors also operate with a third category, namely\n",
"*reinforcement learning*. This is a paradigm of learning inspired by\n",
"behavioral psychology, where learning is achieved by trial-and-error,\n",
"solely from rewards and punishment.\n",
@@ -167,7 +167,7 @@
},
{
"cell_type": "markdown",
- "id": "1ff6afb4",
+ "id": "ff3dccf1",
"metadata": {
"editable": true
},
@@ -202,7 +202,7 @@
},
{
"cell_type": "markdown",
- "id": "98d9014b",
+ "id": "89a1286b",
"metadata": {
"editable": true
},
@@ -212,14 +212,14 @@
"In science and engineering we often end up in situations where we want to infer (or learn) a\n",
"quantitative model $M$ for a given set of sample points $\\boldsymbol{X} \\in [x_1, x_2,\\dots x_N]$.\n",
"\n",
- "As we will see repeatedely in these lectures, we could try to fit these data points to a model given by a\n",
+ "As we will see repeatedly in these lectures, we could try to fit these data points to a model given by a\n",
"straight line, or if we wish to be more sophisticated to a more complex\n",
"function.\n",
"\n",
"The reason for inferring such a model is that it\n",
"serves many useful purposes. On the one hand, the model can reveal information\n",
"encoded in the data or underlying mechanisms from which the data were generated. For instance, we could discover important\n",
- "corelations that relate interesting physics interpretations.\n",
+ "correlations that relate interesting physics interpretations.\n",
"\n",
"In addition, it can simplify the representation of the given data set and help\n",
"us in making predictions about future data samples.\n",
@@ -253,7 +253,7 @@
},
{
"cell_type": "markdown",
- "id": "4214f050",
+ "id": "bf0c0745",
"metadata": {
"editable": true
},
@@ -286,7 +286,7 @@
},
{
"cell_type": "markdown",
- "id": "827d0b8e",
+ "id": "aff5ae6b",
"metadata": {
"editable": true
},
@@ -298,7 +298,7 @@
},
{
"cell_type": "markdown",
- "id": "860f3619",
+ "id": "9bf3106e",
"metadata": {
"editable": true
},
@@ -335,7 +335,7 @@
{
"cell_type": "code",
"execution_count": 1,
- "id": "b9b8fe1b",
+ "id": "8f9fe452",
"metadata": {
"collapsed": false,
"editable": true
@@ -343,7 +343,7 @@
"outputs": [
{
"data": {
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\n",
+ "image/png": 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\n",
"text/plain": [
""
]
@@ -383,7 +383,7 @@
},
{
"cell_type": "markdown",
- "id": "97a78fd5",
+ "id": "a7ce677a",
"metadata": {
"editable": true
},
@@ -400,7 +400,7 @@
},
{
"cell_type": "markdown",
- "id": "5036f5a0",
+ "id": "a9463a86",
"metadata": {
"editable": true
},
@@ -412,7 +412,7 @@
},
{
"cell_type": "markdown",
- "id": "0e276aea",
+ "id": "87b5de04",
"metadata": {
"editable": true
},
@@ -420,7 +420,7 @@
"where $x$ is defined as before. Does the fit look better? Indeed, by\n",
"reducing the role of the noise given by the normal distribution we see immediately that\n",
"our linear prediction seemingly reproduces better the training\n",
- "set. However, this testing 'by the eye' is obviouly not satisfactory in the\n",
+ "set. However, this testing 'by the eye' is obviously not satisfactory in the\n",
"long run. Here we have only defined the training data and our model, and \n",
"have not discussed a more rigorous approach to the **cost** function.\n",
"\n",
@@ -433,7 +433,7 @@
},
{
"cell_type": "markdown",
- "id": "66f6fd13",
+ "id": "e9e757d9",
"metadata": {
"editable": true
},
@@ -446,7 +446,7 @@
},
{
"cell_type": "markdown",
- "id": "f29b024f",
+ "id": "40298a87",
"metadata": {
"editable": true
},
@@ -477,7 +477,7 @@
},
{
"cell_type": "markdown",
- "id": "dcce4d43",
+ "id": "9c2c9d9d",
"metadata": {
"editable": true
},
@@ -489,7 +489,7 @@
},
{
"cell_type": "markdown",
- "id": "20cd881f",
+ "id": "9baeab03",
"metadata": {
"editable": true
},
@@ -507,7 +507,7 @@
{
"cell_type": "code",
"execution_count": 2,
- "id": "aca4204c",
+ "id": "bd76613f",
"metadata": {
"collapsed": false,
"editable": true
@@ -515,7 +515,7 @@
"outputs": [
{
"data": {
- "image/png": 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\n",
+ "image/png": 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UGRmpLVu2aMyYMfXms9vtstvtodkIAADQaoW1RSgqKkppaWkqKChwG19QUKCMjIx608fGxurjjz/W7t27XUNOTo769u2r3bt3a/jw4c1VOgAAaAPC2iIkSbNnz9a0adOUnp6uESNGaOXKlSopKVFOTo4k52mtw4cPa82aNWrXrp0GDRrkNv8555yj6OjoeuMBAAAaE/YglJ2drRMnTmjx4sUqLS3VoEGDlJ+fr+TkZElSaWlpo30KAQAABCLs/QiFA/0IAQDQ+rS5foQAAADCiSAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsiyAEAAAsq0UEoeXLlyslJUXR0dFKS0tTUVGR12m3bdumSy65RPHx8erQoYP69eunhx9+uBmrBQAAbUVkuAtYv369Zs2apeXLl+uSSy7R448/rvHjx2vPnj3q2bNnveljYmJ011136cILL1RMTIy2bdumGTNmKCYmRv/+7/8ehi0AAACtlc0YY8JZwPDhw5WamqoVK1a4xvXv31+TJk1SXl6eT8uYPHmyYmJi9Mwzz/g0fUVFheLi4lReXq7Y2NiA6gYAAM0rFMfvsJ4aq6qq0s6dO5WVleU2PisrS9u3b/dpGcXFxdq+fbtGjhzpdZrKykpVVFS4DQAAAGENQmVlZXI4HEpMTHQbn5iYqCNHjjQ4b/fu3WW325Wenq4777xTt912m9dp8/LyFBcX5xp69OgRlPoBAEDr1iIulrbZbG4/G2PqjaurqKhIO3bs0GOPPaalS5dq3bp1XqfNzc1VeXm5azh48GBQ6gYAAK1bWC+WTkhIUERERL3Wn2PHjtVrJaorJSVFkvTTn/5UR48e1cKFC3X99dd7nNZut8tutwenaAAA0GaEtUUoKipKaWlpKigocBtfUFCgjIwMn5djjFFlZWWwywMAAG1c2G+fnz17tqZNm6b09HSNGDFCK1euVElJiXJyciQ5T2sdPnxYa9askSQtW7ZMPXv2VL9+/SQ5+xV68MEH9etf/zps2wAAAFqnsAeh7OxsnThxQosXL1ZpaakGDRqk/Px8JScnS5JKS0tVUlLimv7MmTPKzc3V/v37FRkZqfPPP1+///3vNWPGjHBtAgAAaKXC3o9QONCPEAAArU+b60cIAAAgnAhCAADAsghCAADAsghCAADAsghCAADAsghCAADAsghCAADAsghCAADAsghCAADAspoUhN5//32tXbtWknTy5EkdOnQoKEUBAAA0h4CfNbZw4ULt2rVLn376qaZOnarvv/9eU6ZM0bZt24JZHwAAQMgE3CL08ssva/PmzYqJiZEkdevWTadPnw5aYQAAAKEWcBCy2+2SJJvNJkk6deqU6/8AAACtQcBB6Pbbb1d2drbKysq0ZMkSZWZmas6cOcGsDQAAIKRsxhgT6Mx79+7Vm2++KWOMxowZo4EDBwaztpCpqKhQXFycysvLFRsbG+5yAACAD0Jx/A74Yun8/HxlZWWpf//+QSkEAACguQV8amzDhg3q27evpk+frvz8fFVXVwezLgAAgJALOAg9/fTT+uyzzzRlyhRt3LhR/fr10y233BLM2gAAAEIq4FNjkhQZGamMjAwdP35cX331lQoLC4NUFgAAQOgF3CK0evVqTZgwQcOGDdPHH3+sRYsWaf/+/cGsDQAAIKQCbhHau3evFi1apPT09GDWAwAA0GyadPt8a8Xt8wAAtD4t4vb5adOm6ZlnntFFF13k1pO0MUY2m00ffPBBUAoDAAAINb+D0AMPPCBJuuaaa3TDDTe4xhtjXE+iBwAAaA0CPjWWmpqqXbt2uY0bPHiwPvroo6AUFkqcGgMAoPVpEafGnnjiCa1cuVKfffaZhg0b5hp/+vRpDR06NChFAQAANAe/W4TKy8v19ddf695779Xvfvc71/hOnTqpc+fOQS8wFGgRAgCg9QnF8bvJd40dPXpUlZWVrp979uzZ5KJCjSAEAEDrE4rjd8AdKr788svq37+/zj//fI0bN04pKSmaOHFiUIoCAABoDgEHofvuu0/vv/++LrjgAu3du1fvvfeehgwZEsTSAAAAQivgIGS3213NUlVVVRo2bFiruGMMAACgRsCP2EhKStKpU6d01VVX6YorrlB8fLy6dOkSzNoAAABCKiiP2CgsLFRFRYXGjRsnu90ejLpCioulAQBofVpEP0KejBo1KhiLAQAAaFZ+B6G6zxiri2eNAQCA1sLvILRhw4ZQ1AEAANDs/L5rLDk52TUcOXJE7777rpKTkxUbG6uIiIhQ1AgAABASAV8jtHDhQu3atUuffvqppk6dqu+++05TpkzRtm3bglkfAABAyDSpZ+nNmzcrJiZGktStWzdVVFQErTAAAIBQa1KHipJcF06fOnVK7doFvDgAAIBmF3Byuf3225Wdna2ysjItWbJEmZmZmjNnTjBrAwAACKmAO1T84Ycf9M9//lNvvvmmjDEaM2aMBg4cGOz6QoIOFQEAaH1aTIeKZ86c0UUXXaTdu3erf//+QSkEAACguQV0aqxdu3YaNmyYPvnkk2DXAwAA0GwCvn3+gw8+0NChQ9WnTx917NhRxhjZbDZ6lgYAAK1GwEFo8+bNwawDAACg2fkchMaOHav/+I//0Pjx4yU5e5iWJIfDQY/SAACgVfL5GqEdO3aoV69ekqT9+/e7xj/11FOaNm1a0AsDAAAINZ+DUFVVlTp16iRJGjx4sL744gtJUkZGht58883QVAcAABBCPp8au+CCC/T++++rU6dO+vbbb3Xq1ClJUqdOnXTy5MlQ1QcAABAyPrcI3XHHHbrttts0cuRIDR48WCtXrpQkFRUVKTExMWQFAgAAhIrPLUI5OTnq0qWLPv/8c/3qV7/SlClTdN5556m0tFR33XVXKGsEAAAIiYAfsVFdXa2XXnpJVVVVmjJlSqu6c4xHbAAA0Pq0mEdsSFJkZKR+8YtfBKUIAACAcAj46fMAAACtHUEIAABYFkEIAABYFkEIAABYFkEIAABYFkEIAABYFkEIAABYFkEIAABYFkEIAABYVosIQsuXL1dKSoqio6OVlpamoqIir9Nu2rRJl19+ubp06aLY2FiNGDFCr7/+ejNWCwAA2oqwB6H169dr1qxZmj9/voqLi5WZmanx48erpKTE4/TvvPOOLr/8cuXn52vnzp0aPXq0rrrqKhUXFzdz5QAAoLUL+KGrwTJ8+HClpqZqxYoVrnH9+/fXpEmTlJeX59MyBg4cqOzsbN13330+Tc9DVwEAaH1CcfwOa4tQVVWVdu7cqaysLLfxWVlZ2r59u0/LOHPmjE6fPq3OnTt7naayslIVFRVuAwAAQFiDUFlZmRwOhxITE93GJyYm6siRIz4t46GHHtK3336r6667zus0eXl5iouLcw09evRoUt0AAKBtCPs1QpJks9ncfjbG1Bvnybp167Rw4UKtX79e55xzjtfpcnNzVV5e7hoOHjzY5JoBAEDrFxnOlSckJCgiIqJe68+xY8fqtRLVtX79ev3yl7/Uiy++qLFjxzY4rd1ul91ub3K9AACgbQlri1BUVJTS0tJUUFDgNr6goEAZGRle51u3bp2mT5+utWvXasKECaEuEwAAtFFhbRGSpNmzZ2vatGlKT0/XiBEjtHLlSpWUlCgnJ0eS87TW4cOHtWbNGknOEHTTTTfpkUce0cUXX+xqTerQoYPi4uLCth0AAKD1CXsQys7O1okTJ7R48WKVlpZq0KBBys/PV3JysiSptLTUrU+hxx9/XNXV1brzzjt15513usbffPPNWr16dXOXDwAAWrGw9yMUDvQjBABA69Pm+hECAAAIJ4IQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwLIIQAACwrBYRhJYvX66UlBRFR0crLS1NRUVFXqctLS3V1KlT1bdvX7Vr106zZs1qvkIBAECbEvYgtH79es2aNUvz589XcXGxMjMzNX78eJWUlHicvrKyUl26dNH8+fM1ePDgZq4WAAC0JTZjjAlnAcOHD1dqaqpWrFjhGte/f39NmjRJeXl5Dc47atQoDRkyREuXLvVrnRUVFYqLi1N5ebliY2MDKRsAADSzUBy/w9oiVFVVpZ07dyorK8ttfFZWlrZv3x609VRWVqqiosJtAAAACGsQKisrk8PhUGJiotv4xMREHTlyJGjrycvLU1xcnGvo0aNH0JYNAABar7BfIyRJNpvN7WdjTL1xTZGbm6vy8nLXcPDgwaAtGwAAtF6R4Vx5QkKCIiIi6rX+HDt2rF4rUVPY7XbZ7fagLQ8AALQNYW0RioqKUlpamgoKCtzGFxQUKCMjI0xVAQAAqwhri5AkzZ49W9OmTVN6erpGjBihlStXqqSkRDk5OZKcp7UOHz6sNWvWuObZvXu3JOmbb77R8ePHtXv3bkVFRWnAgAHh2AQAANBKhT0IZWdn68SJE1q8eLFKS0s1aNAg5efnKzk5WZKzA8W6fQoNHTrU9f+dO3dq7dq1Sk5O1oEDB5qzdAAA0MqFvR+hcKAfIQAAWp82148QAABAOBGEAACAZRGEAACAZRGEAACAZRGEAACAZRGEAACAZRGEAACAZRGEAACAZRGEAACAZRGEAACAZRGEAACAZRGEAACAZRGEAACAZUWGu4BWz+GQioqk0lIpKUnKzJQiIsJdFQAA8AFBqCk2bZJmzpQOHfpxXPfu0iOPSJMnh68uAADgE06NBWrTJunaa91DkCQdPuwcv2lTeOoCAAA+IwgFwuFwtgQZU/93xjiHnBypqqr5awMAAD4jCAWiqKh+S1Bdx487T5PRMgQAQItFEApEaalv0x0/zmkyAABaMIJQIJKS/Jt+1izn6TQAANCiEIQCkZnpPO1lszU+rTHSwYPO02kAAKBFIQgFIiLCeYu8P3w9nQYAAJoNQShQkydLGzZICQm+Te/v6TQAABByBKGmmDzZ2W9Qly4NTxcf7zydFioOh1RYKK1b5/yX65EAAPAJQaipoqKkxx5reJoTJ6TNm0Oz/k2bpF69pNGjpalTnf/26sWdagAA+IAgFAwTJzpbfbyx2UJz5xi9WwMA0CQEoWAoKnK2+ngTijvHGuvdWuK2fQAAGkEQCgZf7wgL5p1jjfVuzW37AAA0iiAUDL7eERbMO8fCEb4AAGhjCELB0FgHizab1KNHcO8cC0f4AgCgjSEIBUPtDhbrhqGan5cudU4XLOEIXwAAtDEEoWCp6WCxWzf38d27O8dPnhzc9YUjfAEA0MbYjPF021HbVlFRobi4OJWXlys2Nja4C3c4nBcol5Y6T0tlZoY2jGza5Lx7rPaF0z16OENQsMMXAABhFIrjN0Eo2EEoHJo7fAEAEAahOH5HBmUpCK+ICGnUqHBXAQBAq0MQCidacgAACCuCULh4urane3fnBdBc2wMAQLPgrrFw4BlhAAC0CASh5uJwSIWF0nPPSTk5PCMMAIAWgFNjzcHTaTBvaj8jzNcLoLnWCACAgBCEQq3mNJi/vRT4+owwrjUCACBgnBoLJYfDGVIC6arJl2eEca0RAABNQhAKpaIi306H1RURIWVkNDxNQyHLGOfwq19Jb77J9UYAAHhBEAolX09v1eVwSNu3NzyNLyHr5Elp7FipVy9ahwAA8IAgFEq+nN7yprEQ5U/I4lQZAAAeEYQaUnPL+7p1zn/9PcWUmem8cLnu0+F9cfRow+v1J2RxWz4AAB4RhLyFnU2bnKeURo+Wpk51/uvvKaaICOfdW5J/YSgiQrr77obXWxOyfFX7tnwAACDJ6kHolVc8h525c4N3N9bkydKGDVK3br7PU7fVxtN6N2+Wvv/e92XWCPS6pWBramsbAABBYDMmkHu7W7eKigrFxcWpXFKsvzPbbM6WmP37/eu0sG6nh8ePS7Nnu4etiAjvgaD2ejdvDqxvIknaujX8T6qn7yMAQABcx+/ycsXG+n0E94ggFOhCghEoaoejo0edp8Ma8/rr0g03SGVl/q2rdpCSwtcTtbcOJmtOHW7YQBgCAHhEEAqSoAShe++VBgwIXpBYt855eq4xnTpJp0/7t+zaIUMKX2uMw+E89ejttv9AW9sAAJYQiiDEIzYCtWTJj/8PRpDw9S4wf0OQ5Kxv6VLn/z21xtRcgxTq1pjG+j6quaC7sNAZhHh2GgAgxGgRCsYCg3Fap6a15PDhwK79qevhh6XExB+DhBT+1hhfW706d3Z2BlmD64cAAApNi5C17xprjK+3vAejn55Ab7X3pEsX6Y47pOuvd17HFBHhe2tMKG+v97XVq3YIkugQEgAQMgShuqHDZnMO99zj3y3vwQgS3m6179zZv+UcPy6df757cPD1tvlQ3l4faAeTdAgJAAgRawehZ56pHzq6d3eGkQcekA4ccN4dtnat9POf+7bMpgaJyZPd17t1q/TCC/4vp24riq+tMU15LIgntfsLKiqS/vQn5/hAwhAdQgIAgsza1wiVlys2JqbxW8kdjh/7/mlM3WtzgnG9TaDXD9W9Zb6hZYTiGiFv/QVdf70zGNUeX/e6IG/WrnXOH4i6fTlxETZChfcaEBLcPh8kfr+QhYXOXqcb066ddObMjz8HcpGvty/Qmv53JP8vpq7p88jbMkLRh09j/QW98IKUkPDjdjoc0tixjS/Xl/6bPL2Gmzd77zZg4kTnPi4sdI4fNerHa6taCk/bJHGwbYnoMLR5hDJsEmRbrFAEIRkLKi8vN5JMeXm5bzOsXWuM85Du32CzOYeNG31bz8aNxnTv7r6M7t1/nN/T730Z1q5teB09evheoy+qqxuu02ZzrrO62n2ebt38m8fX1zA+3vsyJWN+8pP6v4uPD+5r4q/qamO2bnXuu0WL6r828fH1t6v2e6Up69u6tfHXuamae32hXmfNsmfNCvy7oGYZzz5rzMMPO/9trtcmlAJ93Ruar7HvyqYI5bJ9EY7PRivi9/HbBwQhX2zdGlgQ8vcAXnNgbugLtPaH5OGHfath0SL3dYX6g+br67V1q/v2NxRYfAmUL7wQ+H7yNjS2zmC9lnWDTyCB19/gXaO5v/jDcaAJxjq97Wtf/0Bp6LugoWU0x0G49ra98YZzCMb3Q6Cv+8aN9cN/t27O8b5+VwZab6iWXZs/76XmDGGhEsRjDkEoSPx+IWtaODx9QHwdah/0vS3f3y/QxuarGTp3Ds1fv97e1L62oNW0VG3c2PB0vrTOvPiiMRERwQ9C3bsbU1kZ2i+tQFv6/D3Yelt3c3zx+7q+RYuCcwCuGyybso3V1c5ldO5cf1/fc4//3wt1vwu8vSZ1a23OYBqMA3Gg7y1fvg+C8f6v+z1WWenb97C37wN/Xpe660lIMObKK72v19Pr5el7uCW2JgX5j5DyV181BKEgCChR1nyoAw1DtU9P1RVIC0qNRYt8m7duq1CgfHlT+7M91dUNf7HVLL+hD3RjX5xNHbp0qV+PtwNgIKdDmxKw/Xmv1OVvAPf2JVtd7WxBuPde5/DGG573l6/BPdAvy9qvqa/raWgb33jDmAULPJ86bcpQc8qrZh0NnRKuPdQ9CPvbcuNp//kawmw2Z4tr3eDg7aBbWVn/c9PQ6177fRSM1/vhh+svu3atL7zgOYz4suy603l7n3pqZfN26tTf96m3SwACPV0eSIDyZZ7G3l+zZjW+vjrbWi6ZNhmEli1bZnr16mXsdrtJTU0177zzToPTFxYWmtTUVGO3201KSopZsWKFX+sLuGnN05uvoQ977aGhA5O/LSiBzBsf3/S/Dvw5fddQC1rtD7WvQc7b6+dLkAr24MuBw5e/Sv0NBv4MDQXvGv4EVm8B+J57PL/+nlrx/D3F7M91NbUPcIEES2/bGIrB1+8MT0NDB+uGDnqetq1bN/8+O3Vf17otsDXr37jR91BR87kOxWtfu55Q7ldP79NQrbPmferre9yXz1AgLTa+zOPP95u39XnY1jYZhJ5//nnTvn1788QTT5g9e/aYmTNnmpiYGPPll196nP6LL74wHTt2NDNnzjR79uwxTzzxhGnfvr3ZsGGDz+ts0jlGb82pvhz0vWlKi5A/BxdfWgka2m5/Wg+8taDV/mBWV9c/3eBt8HZg9zVIhWNo7PVuyrVnwdjXvoboWbMCb7Wq/eUWyE0H/l5XE+jp0aZsY0sZvB30QtXq6Gn9/s6zdm3z1Rfqba95n4Zye5591v+A1dhnyN+WbV/n8ef7zdP6vBxz2mQQGjZsmMnJyXEb169fPzNv3jyP08+dO9f069fPbdyMGTPMxRdf7PM6g36xlS8H/Yb404Liad6mhglfBHoBdEN3qDU1xPmz7eEYGnu9A70bMdAvvUD3aVNaMGqf1mxK8Avkuhp/Bl9bMFr64OlUX3O0cgU6vPFGy66vpW2PrzfIeBrqfoYCvbvX13n8/X6ruz4v3xehCEJh7Vm6qqpKO3fuVFZWltv4rKwsbd++3eM87733Xr3px40bpx07duiHH34IWa0N8vZojJpeqhvrO6Sh54zV/Lx0qed+LCIinH2W+KIpvUYH8ogOT71k79//4+vh6zI7d/6x35zaiop864SxRnx8wz8HW2Ovd7B78W7svVJXY488sdmcz63zpSNRbw4d+rE38MxMZ99Rgaj9XnE4nO95YwKvq0bNNpaVNX1ZLYEx7j2wN/aMwXCx2aQePZz/D7S+pj6TMRQKC0P3enfu7HyvBqru920gz5/0Zx5/v9/qri+Uj3uqI7LZ1uRBWVmZHA6HEhMT3cYnJibqyJEjHuc5cuSIx+mrq6tVVlamJA8vfmVlpSorK10/l5eXS3J2zBQ0Y8dK/+//Sdu3S0eOSOeeK2VkOA9Ivqxn7FhpzRrpP/9T+uqrH8d37Sr9/vfO33tbzq9/7Tz4ff219+V36yYNHuxbLZ742nFVbGz9daSm/vj/b7/1f5kzZrjPV2PfPt/ml6TVq6Wrr66/f/72N+k3v6n/2nXqJJ0+7fvy6/Ll9R482Ll/a+9vX519tvPf2nX78l6pKy9PmjbN8++McXaKuWKF//XVtm/fj++BX/wisOXVfl8F8+AerG1saWpec38+I83JGOn++51/KPnr7LOd33e5uYF9dkKp1nEm6GbMkM46K/D56343+/reqP359WeeyZMD+36rWZ+X40PNFphg/CFUI2htSwE4fPiwkWS2b9/uNn7JkiWmb9++Hufp3bu3uf/++93Gbdu2zUgypaWlHudZsGCB0f81pzEwMDAwMDC07mHfvn3BCSLGmLC2CCUkJCgiIqJe68+xY8fqtfrUOPfccz1OHxkZqXgvpzpyc3M1e/Zs18+nTp1ScnKySkpKFBcX18StQFNUVFSoR48eOnjwYPC6S0dA2BctB/uiZWF/tBzl5eXq2bOnOnfuHLRlhjUIRUVFKS0tTQUFBbrmmmtc4wsKCjRx4kSP84wYMUJ//etf3cZt2bJF6enpat++vcd57Ha77HZ7vfFxcXG8qVuI2NhY9kULwb5oOdgXLQv7o+Vo1y54lziH9WJpSZo9e7aefPJJPf3009q7d6/uvvtulZSUKCcnR5KzNeemm25yTZ+Tk6Mvv/xSs2fP1t69e/X000/rqaee0pw5c8K1CQAAoJUKa4uQJGVnZ+vEiRNavHixSktLNWjQIOXn5ys5OVmSVFpaqpKSEtf0KSkpys/P1913361ly5apa9euevTRR/Xzn/88XJsAAABaqbAHIUm64447dMcdd3j83erVq+uNGzlypHbt2hXw+ux2uxYsWODxdBmaF/ui5WBftBzsi5aF/dFyhGJf2IwJ5j1oAAAArUfYrxECAAAIF4IQAACwLIIQAACwLIIQAACwrDYbhJYvX66UlBRFR0crLS1NRbUfHOfB22+/rbS0NEVHR+u8887TY4891kyVtn3+7ItNmzbp8ssvV5cuXRQbG6sRI0bo9ddfb8Zq2zZ/Pxc13n33XUVGRmrIkCGhLdBC/N0XlZWVmj9/vpKTk2W323X++efr6aefbqZq2zZ/98Vzzz2nwYMHq2PHjkpKStItt9yiEydONFO1bdc777yjq666Sl27dpXNZtPLL7/c6DxBOXYH7WEdLcjzzz9v2rdvb5544gmzZ88eM3PmTBMTE2O+/PJLj9N/8cUXpmPHjmbmzJlmz5495oknnjDt27c3GzZsaObK2x5/98XMmTPNH/7wB/PBBx+Yf/zjHyY3N9e0b9/e7Nq1q5krb3v83Rc1Tp06Zc477zyTlZVlBg8e3DzFtnGB7Iurr77aDB8+3BQUFJj9+/eb999/37z77rvNWHXb5O++KCoqMu3atTOPPPKI+eKLL0xRUZEZOHCgmTRpUjNX3vbk5+eb+fPnm40bNxpJ5qWXXmpw+mAdu9tkEBo2bJjJyclxG9evXz8zb948j9PPnTvX9OvXz23cjBkzzMUXXxyyGq3C333hyYABA8yiRYuCXZrlBLovsrOzzb333msWLFhAEAoSf/fF//7v/5q4uDhz4sSJ5ijPUvzdF3/84x/Neeed5zbu0UcfNd27dw9ZjVbkSxAK1rG7zZ0aq6qq0s6dO5WVleU2PisrS9u3b/c4z3vvvVdv+nHjxmnHjh364YcfQlZrWxfIvqjrzJkzOn36dFAfsGdFge6LVatWad++fVqwYEGoS7SMQPbFK6+8ovT0dD3wwAPq1q2b+vTpozlz5uj7779vjpLbrED2RUZGhg4dOqT8/HwZY3T06FFt2LBBEyZMaI6SUUuwjt0tomfpYCorK5PD4aj39PrExMR6T62vceTIEY/TV1dXq6ysTElJSSGrty0LZF/U9dBDD+nbb7/VddddF4oSLSOQffH5559r3rx5KioqUmRkm/uqCJtA9sUXX3yhbdu2KTo6Wi+99JLKysp0xx136OTJk1wn1ASB7IuMjAw999xzys7O1r/+9S9VV1fr6quv1p///OfmKBm1BOvY3eZahGrYbDa3n40x9cY1Nr2n8fCfv/uixrp167Rw4UKtX79e55xzTqjKsxRf94XD4dDUqVO1aNEi9enTp7nKsxR/PhdnzpyRzWbTc889p2HDhumKK67Qn/70J61evZpWoSDwZ1/s2bNHv/nNb3Tfffdp586deu2117R//37Xg8LRvIJx7G5zf+YlJCQoIiKiXpo/duxYveRY49xzz/U4fWRkpOLj40NWa1sXyL6osX79ev3yl7/Uiy++qLFjx4ayTEvwd1+cPn1aO3bsUHFxse666y5JzoOxMUaRkZHasmWLxowZ0yy1tzWBfC6SkpLUrVs3xcXFucb1799fxhgdOnRIvXv3DmnNbVUg+yIvL0+XXHKJ7rnnHknShRdeqJiYGGVmZmrJkiWcQWhGwTp2t7kWoaioKKWlpamgoMBtfEFBgTIyMjzOM2LEiHrTb9myRenp6Wrfvn3Iam3rAtkXkrMlaPr06Vq7di3n3YPE330RGxurjz/+WLt373YNOTk56tu3r3bv3q3hw4c3V+ltTiCfi0suuURfffWVvvnmG9e4f/zjH2rXrp26d+8e0nrbskD2xXfffad27dwPnREREZJ+bI1A8wjasduvS6tbiZrbIZ966imzZ88eM2vWLBMTE2MOHDhgjDFm3rx5Ztq0aa7pa27Bu/vuu82ePXvMU089xe3zQeLvvli7dq2JjIw0y5YtM6Wlpa7h1KlT4dqENsPffVEXd40Fj7/74vTp06Z79+7m2muvNZ988ol5++23Te/evc1tt90Wrk1oM/zdF6tWrTKRkZFm+fLlZt++fWbbtm0mPT3dDBs2LFyb0GacPn3aFBcXm+LiYiPJ/OlPfzLFxcWurgxCdexuk0HIGGOWLVtmkpOTTVRUlElNTTVvv/2263c333yzGTlypNv0hYWFZujQoSYqKsr06tXLrFixopkrbrv82RcjR440kuoNN998c/MX3gb5+7mojSAUXP7ui71795qxY8eaDh06mO7du5vZs2eb7777rpmrbpv83RePPvqoGTBggOnQoYNJSkoyN9xwgzl06FAzV932bN26tcHv/1Adu23G0JYHAACsqc1dIwQAAOArghAAALAsghAAALAsghAAALAsghAAALAsghAAALAsghAAALAsghAAALAsghAAALAsghAAALAsghCAVm/dunWKjo7W4cOHXeNuu+02XXjhhSovLw9jZQBaOp41BqDVM8ZoyJAhyszM1F/+8hctWrRITz75pP7+97+rW7du4S4PQAsWGe4CAKCpbDabfve73+naa69V165d9cgjj6ioqIgQBKBRtAgBaDNSU1P1ySefaMuWLRo5cmS4ywHQCnCNEIA24fXXX9enn34qh8OhxMTEcJcDoJWgRQhAq7dr1y6NGjVKy5Yt0/PPP6+OHTvqxRdfDHdZAFoBrhEC0KodOHBAEyZM0Lx58zRt2jQNGDBAF110kXbu3Km0tLRwlweghaNFCECrdfLkSV1yySW69NJL9fjjj7vGT5w4UZWVlXrttdfCWB2A1oAgBAAALIuLpQEAgGURhAAAgGURhAAAgGURhAAAgGURhAAAgGURhAAAgGURhAAAgGURhAAAgGURhAAAgGURhAAAgGURhAAAgGURhAAAgGX9fyAnsMmDVjFxAAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
@@ -550,7 +550,7 @@
},
{
"cell_type": "markdown",
- "id": "9925c6cb",
+ "id": "5c78adc9",
"metadata": {
"editable": true
},
@@ -572,7 +572,7 @@
{
"cell_type": "code",
"execution_count": 3,
- "id": "5f927fc2",
+ "id": "d38e9c7c",
"metadata": {
"collapsed": false,
"editable": true
@@ -583,18 +583,18 @@
"output_type": "stream",
"text": [
"The intercept alpha: \n",
- " [2.02408959]\n",
+ " [2.03523311]\n",
"Coefficient beta : \n",
- " [[4.92811987]]\n",
- "Mean squared error: 0.25\n",
- "Variance score: 0.89\n",
+ " [[4.99498108]]\n",
+ "Mean squared error: 0.27\n",
+ "Variance score: 0.87\n",
"Mean squared log error: 0.01\n",
- "Mean absolute error: 0.39\n"
+ "Mean absolute error: 0.41\n"
]
},
{
"data": {
- "image/png": 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\n",
+ "image/png": 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\n",
"text/plain": [
""
]
@@ -639,7 +639,7 @@
},
{
"cell_type": "markdown",
- "id": "3c238d46",
+ "id": "c76d7e9f",
"metadata": {
"editable": true
},
@@ -650,7 +650,7 @@
},
{
"cell_type": "markdown",
- "id": "428d6164",
+ "id": "6a528c0f",
"metadata": {
"editable": true
},
@@ -663,7 +663,7 @@
},
{
"cell_type": "markdown",
- "id": "a4046ea1",
+ "id": "74377872",
"metadata": {
"editable": true
},
@@ -684,7 +684,7 @@
},
{
"cell_type": "markdown",
- "id": "3c665298",
+ "id": "27ad828e",
"metadata": {
"editable": true
},
@@ -696,7 +696,7 @@
},
{
"cell_type": "markdown",
- "id": "dff6fbc4",
+ "id": "b7bf4db8",
"metadata": {
"editable": true
},
@@ -706,7 +706,7 @@
},
{
"cell_type": "markdown",
- "id": "81466e4e",
+ "id": "7530e179",
"metadata": {
"editable": true
},
@@ -718,7 +718,7 @@
},
{
"cell_type": "markdown",
- "id": "40f0760e",
+ "id": "4672d1e1",
"metadata": {
"editable": true
},
@@ -730,7 +730,7 @@
},
{
"cell_type": "markdown",
- "id": "2489c24a",
+ "id": "00840b14",
"metadata": {
"editable": true
},
@@ -742,7 +742,7 @@
},
{
"cell_type": "markdown",
- "id": "3f625a67",
+ "id": "0c5e43af",
"metadata": {
"editable": true
},
@@ -753,7 +753,7 @@
},
{
"cell_type": "markdown",
- "id": "6608f259",
+ "id": "a4a68023",
"metadata": {
"editable": true
},
@@ -765,7 +765,7 @@
},
{
"cell_type": "markdown",
- "id": "d63ae4a9",
+ "id": "adbc5f5f",
"metadata": {
"editable": true
},
@@ -787,7 +787,7 @@
},
{
"cell_type": "markdown",
- "id": "ba2ac7cd",
+ "id": "be191d7c",
"metadata": {
"editable": true
},
@@ -799,7 +799,7 @@
},
{
"cell_type": "markdown",
- "id": "31861c56",
+ "id": "f4549dc2",
"metadata": {
"editable": true
},
@@ -814,7 +814,7 @@
{
"cell_type": "code",
"execution_count": 4,
- "id": "e2e82632",
+ "id": "a6bd8c76",
"metadata": {
"collapsed": false,
"editable": true
@@ -822,7 +822,7 @@
"outputs": [
{
"data": {
- "image/png": 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\n",
+ "image/png": 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\n",
"text/plain": [
""
]
@@ -838,7 +838,7 @@
"name": "stdout",
"output_type": "stream",
"text": [
- "0.005\n"
+ "0.00499999999999999\n"
]
}
],
@@ -877,7 +877,7 @@
},
{
"cell_type": "markdown",
- "id": "9f77ad8a",
+ "id": "6c8b9965",
"metadata": {
"editable": true
},
@@ -892,7 +892,7 @@
},
{
"cell_type": "markdown",
- "id": "79ba67a3",
+ "id": "2852a934",
"metadata": {
"editable": true
},
@@ -904,7 +904,7 @@
},
{
"cell_type": "markdown",
- "id": "6ed1b749",
+ "id": "74fd99a0",
"metadata": {
"editable": true
},
@@ -914,7 +914,7 @@
},
{
"cell_type": "markdown",
- "id": "7f1a81f1",
+ "id": "386c640d",
"metadata": {
"editable": true
},
@@ -926,7 +926,7 @@
},
{
"cell_type": "markdown",
- "id": "3a92d75a",
+ "id": "9e7c7132",
"metadata": {
"editable": true
},
@@ -936,7 +936,7 @@
},
{
"cell_type": "markdown",
- "id": "2717347f",
+ "id": "3bfd0139",
"metadata": {
"editable": true
},
@@ -948,7 +948,7 @@
},
{
"cell_type": "markdown",
- "id": "96b2d4fb",
+ "id": "0ddf3bb3",
"metadata": {
"editable": true
},
@@ -958,7 +958,7 @@
},
{
"cell_type": "markdown",
- "id": "c7705b30",
+ "id": "e9c65dac",
"metadata": {
"editable": true
},
@@ -970,7 +970,7 @@
},
{
"cell_type": "markdown",
- "id": "4e679c00",
+ "id": "6addb221",
"metadata": {
"editable": true
},
@@ -986,7 +986,7 @@
},
{
"cell_type": "markdown",
- "id": "e5e89d2d",
+ "id": "75fd0e61",
"metadata": {
"editable": true
},
@@ -998,7 +998,7 @@
},
{
"cell_type": "markdown",
- "id": "d17826c1",
+ "id": "209a6361",
"metadata": {
"editable": true
},
@@ -1009,7 +1009,7 @@
},
{
"cell_type": "markdown",
- "id": "8cc3306a",
+ "id": "ecf9b9da",
"metadata": {
"editable": true
},
@@ -1021,7 +1021,7 @@
},
{
"cell_type": "markdown",
- "id": "b2ba5419",
+ "id": "a931cfa6",
"metadata": {
"editable": true
},
@@ -1035,7 +1035,7 @@
},
{
"cell_type": "markdown",
- "id": "a94d4658",
+ "id": "f2cbfc44",
"metadata": {
"editable": true
},
@@ -1047,7 +1047,7 @@
},
{
"cell_type": "markdown",
- "id": "0c7a9577",
+ "id": "719d770d",
"metadata": {
"editable": true
},
@@ -1072,7 +1072,7 @@
},
{
"cell_type": "markdown",
- "id": "acb382a9",
+ "id": "4983af73",
"metadata": {
"editable": true
},
@@ -1089,7 +1089,7 @@
{
"cell_type": "code",
"execution_count": 5,
- "id": "828ac44b",
+ "id": "b5c8db7d",
"metadata": {
"collapsed": false,
"editable": true
@@ -1133,7 +1133,7 @@
},
{
"cell_type": "markdown",
- "id": "12105e10",
+ "id": "b54a87d1",
"metadata": {
"editable": true
},
@@ -1144,7 +1144,7 @@
{
"cell_type": "code",
"execution_count": 6,
- "id": "f3512753",
+ "id": "180faa92",
"metadata": {
"collapsed": false,
"editable": true
@@ -1166,7 +1166,7 @@
},
{
"cell_type": "markdown",
- "id": "8d18c1cd",
+ "id": "6fe942e7",
"metadata": {
"editable": true
},
@@ -1183,7 +1183,7 @@
{
"cell_type": "code",
"execution_count": 7,
- "id": "9b164e78",
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@@ -4860,7 +4860,7 @@
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@@ -4909,7 +4909,7 @@
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{
"cell_type": "markdown",
- "id": "765be39e",
+ "id": "f5b4f42b",
"metadata": {
"editable": true
},
@@ -4919,7 +4919,7 @@
},
{
"cell_type": "markdown",
- "id": "371bb281",
+ "id": "abca9fed",
"metadata": {
"editable": true
},
@@ -4931,7 +4931,7 @@
},
{
"cell_type": "markdown",
- "id": "7531bc5c",
+ "id": "a3931447",
"metadata": {
"editable": true
},
@@ -4941,7 +4941,7 @@
},
{
"cell_type": "markdown",
- "id": "096367a8",
+ "id": "bff5fde9",
"metadata": {
"editable": true
},
@@ -4953,7 +4953,7 @@
},
{
"cell_type": "markdown",
- "id": "f2b48135",
+ "id": "cfcbbd41",
"metadata": {
"editable": true
},
@@ -4963,7 +4963,7 @@
},
{
"cell_type": "markdown",
- "id": "64e7a83f",
+ "id": "f21eecf5",
"metadata": {
"editable": true
},
@@ -4975,7 +4975,7 @@
},
{
"cell_type": "markdown",
- "id": "7cd415f6",
+ "id": "5d1bccf8",
"metadata": {
"editable": true
},
@@ -4985,7 +4985,7 @@
},
{
"cell_type": "markdown",
- "id": "b1d73cf8",
+ "id": "cd0ac1aa",
"metadata": {
"editable": true
},
@@ -4997,7 +4997,7 @@
},
{
"cell_type": "markdown",
- "id": "23c1b258",
+ "id": "e2689f44",
"metadata": {
"editable": true
},
@@ -5007,7 +5007,7 @@
},
{
"cell_type": "markdown",
- "id": "f26c3a7c",
+ "id": "3578ef22",
"metadata": {
"editable": true
},
@@ -5019,7 +5019,7 @@
},
{
"cell_type": "markdown",
- "id": "73594acc",
+ "id": "1b9ae1e2",
"metadata": {
"editable": true
},
@@ -5029,7 +5029,7 @@
},
{
"cell_type": "markdown",
- "id": "9e2c6bff",
+ "id": "3c67b152",
"metadata": {
"editable": true
},
@@ -5041,7 +5041,7 @@
},
{
"cell_type": "markdown",
- "id": "f0ecd236",
+ "id": "7e4a7fe2",
"metadata": {
"editable": true
},
@@ -5051,7 +5051,7 @@
},
{
"cell_type": "markdown",
- "id": "9a6ec43b",
+ "id": "0c255fd7",
"metadata": {
"editable": true
},
@@ -5063,7 +5063,7 @@
},
{
"cell_type": "markdown",
- "id": "eb98056f",
+ "id": "f0b00e3d",
"metadata": {
"editable": true
},
@@ -5073,7 +5073,7 @@
},
{
"cell_type": "markdown",
- "id": "5e5ac90a",
+ "id": "7c9a7b92",
"metadata": {
"editable": true
},
@@ -5085,7 +5085,7 @@
},
{
"cell_type": "markdown",
- "id": "c8bdfe01",
+ "id": "a8e3e7e8",
"metadata": {
"editable": true
},
@@ -5095,7 +5095,7 @@
},
{
"cell_type": "markdown",
- "id": "4dacfd83",
+ "id": "007406a0",
"metadata": {
"editable": true
},
@@ -5107,7 +5107,7 @@
},
{
"cell_type": "markdown",
- "id": "66ba7f8c",
+ "id": "20f80df6",
"metadata": {
"editable": true
},
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter1.py b/doc/LectureNotes/_build/jupyter_execute/chapter1.py
index 74dc30c53..0ce9fd445 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapter1.py
+++ b/doc/LectureNotes/_build/jupyter_execute/chapter1.py
@@ -87,7 +87,7 @@
# Machine learning is an extremely rich field, in spite of its young
# age. The increases we have seen during the last three decades in
# computational capabilities have been followed by developments of
-# methods and techniques for analyzing and handling large date sets,
+# methods and techniques for analyzing and handling large data sets,
# relying heavily on statistics, computer science and mathematics. The
# field is rather new and developing rapidly. Popular software packages
# written in Python for machine learning like
@@ -110,7 +110,7 @@
# problem, and let the computer deduce the logic behind it. On the other
# hand, *unsupervised learning* is a method for finding patterns and
# relationship in data sets without any prior knowledge of the system.
-# Some authours also operate with a third category, namely
+# Some authors also operate with a third category, namely
# *reinforcement learning*. This is a paradigm of learning inspired by
# behavioral psychology, where learning is achieved by trial-and-error,
# solely from rewards and punishment.
@@ -166,14 +166,14 @@
# In science and engineering we often end up in situations where we want to infer (or learn) a
# quantitative model $M$ for a given set of sample points $\boldsymbol{X} \in [x_1, x_2,\dots x_N]$.
#
-# As we will see repeatedely in these lectures, we could try to fit these data points to a model given by a
+# As we will see repeatedly in these lectures, we could try to fit these data points to a model given by a
# straight line, or if we wish to be more sophisticated to a more complex
# function.
#
# The reason for inferring such a model is that it
# serves many useful purposes. On the one hand, the model can reveal information
# encoded in the data or underlying mechanisms from which the data were generated. For instance, we could discover important
-# corelations that relate interesting physics interpretations.
+# correlations that relate interesting physics interpretations.
#
# In addition, it can simplify the representation of the given data set and help
# us in making predictions about future data samples.
@@ -304,7 +304,7 @@ plt.show()
# where $x$ is defined as before. Does the fit look better? Indeed, by
# reducing the role of the noise given by the normal distribution we see immediately that
# our linear prediction seemingly reproduces better the training
-# set. However, this testing 'by the eye' is obviouly not satisfactory in the
+# set. However, this testing 'by the eye' is obviously not satisfactory in the
# long run. Here we have only defined the training data and our model, and
# have not discussed a more rigorous approach to the **cost** function.
#
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter1_17_0.png b/doc/LectureNotes/_build/jupyter_execute/chapter1_17_0.png
index 3ef6ce168..4b6e6f4df 100644
Binary files a/doc/LectureNotes/_build/jupyter_execute/chapter1_17_0.png and b/doc/LectureNotes/_build/jupyter_execute/chapter1_17_0.png differ
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter1_19_1.png b/doc/LectureNotes/_build/jupyter_execute/chapter1_19_1.png
index 294e0807a..9bf420175 100644
Binary files a/doc/LectureNotes/_build/jupyter_execute/chapter1_19_1.png and b/doc/LectureNotes/_build/jupyter_execute/chapter1_19_1.png differ
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter1_33_0.png b/doc/LectureNotes/_build/jupyter_execute/chapter1_33_0.png
index 58c2544fe..ad3769945 100644
Binary files a/doc/LectureNotes/_build/jupyter_execute/chapter1_33_0.png and b/doc/LectureNotes/_build/jupyter_execute/chapter1_33_0.png differ
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter1_9_0.png b/doc/LectureNotes/_build/jupyter_execute/chapter1_9_0.png
index 47c1974b9..2ed039749 100644
Binary files a/doc/LectureNotes/_build/jupyter_execute/chapter1_9_0.png and b/doc/LectureNotes/_build/jupyter_execute/chapter1_9_0.png differ
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter2.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter2.ipynb
index 09a18df1c..ae45ecc7a 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapter2.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/chapter2.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "7d4ecb5d",
+ "id": "74d0d498",
"metadata": {
"editable": true
},
@@ -13,7 +13,7 @@
},
{
"cell_type": "markdown",
- "id": "1b85d5f1",
+ "id": "acd544cd",
"metadata": {
"editable": true
},
@@ -23,7 +23,7 @@
},
{
"cell_type": "markdown",
- "id": "a252fe86",
+ "id": "0acaa875",
"metadata": {
"editable": true
},
@@ -37,7 +37,7 @@
},
{
"cell_type": "markdown",
- "id": "bc95be71",
+ "id": "0924b488",
"metadata": {
"editable": true
},
@@ -49,7 +49,7 @@
},
{
"cell_type": "markdown",
- "id": "c77a2611",
+ "id": "b7307eb7",
"metadata": {
"editable": true
},
@@ -61,7 +61,7 @@
},
{
"cell_type": "markdown",
- "id": "d427f76c",
+ "id": "8096b1f0",
"metadata": {
"editable": true
},
@@ -73,7 +73,7 @@
},
{
"cell_type": "markdown",
- "id": "f0fe9791",
+ "id": "d64adaf2",
"metadata": {
"editable": true
},
@@ -83,7 +83,7 @@
},
{
"cell_type": "markdown",
- "id": "76d07f64",
+ "id": "78b35483",
"metadata": {
"editable": true
},
@@ -95,7 +95,7 @@
},
{
"cell_type": "markdown",
- "id": "12f77a55",
+ "id": "f4a3ff68",
"metadata": {
"editable": true
},
@@ -105,7 +105,7 @@
},
{
"cell_type": "markdown",
- "id": "5ce0346b",
+ "id": "5704d260",
"metadata": {
"editable": true
},
@@ -117,7 +117,7 @@
},
{
"cell_type": "markdown",
- "id": "2aeccd66",
+ "id": "12fa775a",
"metadata": {
"editable": true
},
@@ -130,7 +130,7 @@
},
{
"cell_type": "markdown",
- "id": "e36d0875",
+ "id": "a694774d",
"metadata": {
"editable": true
},
@@ -142,7 +142,7 @@
},
{
"cell_type": "markdown",
- "id": "48cdf012",
+ "id": "e0775433",
"metadata": {
"editable": true
},
@@ -154,7 +154,7 @@
},
{
"cell_type": "markdown",
- "id": "89fb4555",
+ "id": "ec16ae7d",
"metadata": {
"editable": true
},
@@ -166,7 +166,7 @@
},
{
"cell_type": "markdown",
- "id": "3cce2fbf",
+ "id": "258fbf6a",
"metadata": {
"editable": true
},
@@ -176,7 +176,7 @@
},
{
"cell_type": "markdown",
- "id": "623e11d4",
+ "id": "05ea3605",
"metadata": {
"editable": true
},
@@ -188,7 +188,7 @@
},
{
"cell_type": "markdown",
- "id": "3677f8ed",
+ "id": "db5ed2d4",
"metadata": {
"editable": true
},
@@ -198,7 +198,7 @@
},
{
"cell_type": "markdown",
- "id": "65a16065",
+ "id": "e99ad8e8",
"metadata": {
"editable": true
},
@@ -210,7 +210,7 @@
},
{
"cell_type": "markdown",
- "id": "e4dc61d4",
+ "id": "1cc7938a",
"metadata": {
"editable": true
},
@@ -220,7 +220,7 @@
},
{
"cell_type": "markdown",
- "id": "6d333c04",
+ "id": "0e3fc9d5",
"metadata": {
"editable": true
},
@@ -246,7 +246,7 @@
"This is given by the **Singular Value Decomposition** (SVD) algorithm,\n",
"perhaps the most powerful linear algebra algorithm. The SVD provides\n",
"a numerically stable matrix decomposition that is used in a large\n",
- "swath oc applications and the decomposition is always stable\n",
+ "swath of applications and the decomposition is always stable\n",
"numerically.\n",
"\n",
"In machine learning it plays a central role in dealing with for\n",
@@ -262,12 +262,12 @@
"are problems with near singular or singular matrices. The column vectors of $\\boldsymbol{X}$ \n",
"may be linearly dependent, normally referred to as super-collinearity. \n",
"This means that the matrix may be rank deficient and it is basically impossible to \n",
- "to model the data using linear regression. As an example, consider the matrix"
+ "model the data using linear regression. As an example, consider the matrix"
]
},
{
"cell_type": "markdown",
- "id": "baba6f65",
+ "id": "6d2bc570",
"metadata": {
"editable": true
},
@@ -290,7 +290,7 @@
},
{
"cell_type": "markdown",
- "id": "97aaa550",
+ "id": "fdda638f",
"metadata": {
"editable": true
},
@@ -299,7 +299,7 @@
"the first column is the row-wise sum of the other two columns. The rank (more correct,\n",
"the column rank) of a matrix is the dimension of the space spanned by the\n",
"column vectors. Hence, the rank of $\\mathbf{X}$ is equal to the number\n",
- "of linearly independent columns. In this particular case the matrix has rank 2.\n",
+ "of linearly independent columns. In this particular case the matrix has rank 1.\n",
"\n",
"Super-collinearity of an $(n \\times p)$-dimensional design matrix $\\mathbf{X}$ implies\n",
"that the inverse of the matrix $\\boldsymbol{X}^T\\boldsymbol{X}$ (the matrix we need to invert to solve the linear regression equations) is non-invertible. If we have a square matrix that does not have an inverse, we say this matrix singular. The example here demonstrates this"
@@ -307,7 +307,7 @@
},
{
"cell_type": "markdown",
- "id": "d196128e",
+ "id": "29a3a620",
"metadata": {
"editable": true
},
@@ -326,7 +326,7 @@
},
{
"cell_type": "markdown",
- "id": "d9d92d89",
+ "id": "3278b038",
"metadata": {
"editable": true
},
@@ -339,7 +339,7 @@
},
{
"cell_type": "markdown",
- "id": "b3d65641",
+ "id": "7b66f623",
"metadata": {
"editable": true
},
@@ -357,14 +357,14 @@
},
{
"cell_type": "markdown",
- "id": "ef75ca28",
+ "id": "c97ae6c5",
"metadata": {
"editable": true
},
"source": [
"has linearly dependent column vectors, we will not be able to compute the inverse\n",
"of $\\boldsymbol{X}^T\\boldsymbol{X}$ and we cannot find the parameters (estimators) $\\beta_i$. \n",
- "The estimators are only well-defined if $(\\boldsymbol{X}^{T}\\boldsymbol{X})^{-1}$ exits. \n",
+ "The estimators are only well-defined if $(\\boldsymbol{X}^{T}\\boldsymbol{X})$ can be inverted. \n",
"This is more likely to happen when the matrix $\\boldsymbol{X}$ is high-dimensional. In this case it is likely to encounter a situation where \n",
"the regression parameters $\\beta_i$ cannot be estimated.\n",
"\n",
@@ -373,7 +373,7 @@
},
{
"cell_type": "markdown",
- "id": "bcba41b4",
+ "id": "af0bfc59",
"metadata": {
"editable": true
},
@@ -385,7 +385,7 @@
},
{
"cell_type": "markdown",
- "id": "dda8ceea",
+ "id": "6469bfe8",
"metadata": {
"editable": true
},
@@ -395,14 +395,14 @@
},
{
"cell_type": "markdown",
- "id": "454a5885",
+ "id": "75d45f30",
"metadata": {
"editable": true
},
"source": [
"## Basic math of the SVD\n",
"\n",
- "From standard linear algebra we know that a square matrix $\\boldsymbol{X}$ can be diagonalized if and only it is \n",
+ "From standard linear algebra we know that a square matrix $\\boldsymbol{X}$ can be diagonalized if and only if it is \n",
"a so-called [normal matrix](https://en.wikipedia.org/wiki/Normal_matrix), that is if $\\boldsymbol{X}\\in {\\mathbb{R}}^{n\\times n}$\n",
"we have $\\boldsymbol{X}\\boldsymbol{X}^T=\\boldsymbol{X}^T\\boldsymbol{X}$ or if $\\boldsymbol{X}\\in {\\mathbb{C}}^{n\\times n}$ we have $\\boldsymbol{X}\\boldsymbol{X}^{\\dagger}=\\boldsymbol{X}^{\\dagger}\\boldsymbol{X}$.\n",
"The matrix has then a set of eigenpairs"
@@ -410,7 +410,7 @@
},
{
"cell_type": "markdown",
- "id": "be408a56",
+ "id": "28b4fac2",
"metadata": {
"editable": true
},
@@ -422,7 +422,7 @@
},
{
"cell_type": "markdown",
- "id": "5f9d9612",
+ "id": "085b2de7",
"metadata": {
"editable": true
},
@@ -432,7 +432,7 @@
},
{
"cell_type": "markdown",
- "id": "208d2b7b",
+ "id": "1fb42fdc",
"metadata": {
"editable": true
},
@@ -444,7 +444,7 @@
},
{
"cell_type": "markdown",
- "id": "abe59381",
+ "id": "0f7b8c0d",
"metadata": {
"editable": true
},
@@ -454,7 +454,7 @@
},
{
"cell_type": "markdown",
- "id": "1105a012",
+ "id": "057f3ed2",
"metadata": {
"editable": true
},
@@ -466,7 +466,7 @@
},
{
"cell_type": "markdown",
- "id": "be0d3499",
+ "id": "628031b9",
"metadata": {
"editable": true
},
@@ -478,7 +478,7 @@
},
{
"cell_type": "markdown",
- "id": "d2a7f70e",
+ "id": "3177dcfe",
"metadata": {
"editable": true
},
@@ -493,7 +493,7 @@
},
{
"cell_type": "markdown",
- "id": "2927bf84",
+ "id": "a392a54d",
"metadata": {
"editable": true
},
@@ -514,7 +514,7 @@
},
{
"cell_type": "markdown",
- "id": "f0881611",
+ "id": "3496079e",
"metadata": {
"editable": true
},
@@ -526,7 +526,7 @@
},
{
"cell_type": "markdown",
- "id": "2b00326b",
+ "id": "77b61c68",
"metadata": {
"editable": true
},
@@ -536,7 +536,7 @@
},
{
"cell_type": "markdown",
- "id": "0b928939",
+ "id": "dbb84089",
"metadata": {
"editable": true
},
@@ -548,7 +548,7 @@
},
{
"cell_type": "markdown",
- "id": "dd9b5714",
+ "id": "04fc9eec",
"metadata": {
"editable": true
},
@@ -594,7 +594,7 @@
},
{
"cell_type": "markdown",
- "id": "1524a26d",
+ "id": "4f1e3bb4",
"metadata": {
"editable": true
},
@@ -605,7 +605,7 @@
{
"cell_type": "code",
"execution_count": 1,
- "id": "0c5ee0f0",
+ "id": "a39cbeb0",
"metadata": {
"collapsed": false,
"editable": true
@@ -667,7 +667,7 @@
},
{
"cell_type": "markdown",
- "id": "541be9f2",
+ "id": "dca36481",
"metadata": {
"editable": true
},
@@ -697,7 +697,7 @@
},
{
"cell_type": "markdown",
- "id": "8088b20a",
+ "id": "b9b3c7db",
"metadata": {
"editable": true
},
@@ -711,7 +711,7 @@
{
"cell_type": "code",
"execution_count": 2,
- "id": "0a1aeb6a",
+ "id": "6aa5981e",
"metadata": {
"collapsed": false,
"editable": true
@@ -723,7 +723,7 @@
},
{
"cell_type": "markdown",
- "id": "c94ae586",
+ "id": "ae58132b",
"metadata": {
"editable": true
},
@@ -734,7 +734,7 @@
{
"cell_type": "code",
"execution_count": 3,
- "id": "1604fc1a",
+ "id": "761d48f5",
"metadata": {
"collapsed": false,
"editable": true
@@ -782,7 +782,6 @@
" return np.matmul(V,np.matmul(invD,UT))\n",
"\n",
"\n",
- "#X = np.array([ [1.0, -1.0, 2.0], [1.0, 0.0, 1.0], [1.0, 2.0, -1.0], [1.0, 1.0, 0.0] ])\n",
"# Non-singular square matrix\n",
"X = np.array( [ [1,2,3],[2,4,5],[3,5,6]])\n",
"print(X)\n",
@@ -795,7 +794,7 @@
},
{
"cell_type": "markdown",
- "id": "ec171bab",
+ "id": "6297c4ec",
"metadata": {
"editable": true
},
@@ -808,12 +807,12 @@
"It is also called the the Moore-Penrose Inverse after two independent discoverers of the method or the Generalized Inverse.\n",
"It is used for the calculation of the inverse for singular or near singular matrices and for rectangular matrices.\n",
"\n",
- "Using the SVD we can obtain the pseudoinverse of a matrix $\\boldsymbol{A}$ (labeled here as $\\boldsymbol{A}_{\\mathrm{PI}}$"
+ "Using the SVD we can obtain the pseudoinverse (PI) of a matrix $\\boldsymbol{A}$ (labeled here as $\\boldsymbol{A}_{\\mathrm{PI}}$"
]
},
{
"cell_type": "markdown",
- "id": "28d8e04d",
+ "id": "2bb1f4b8",
"metadata": {
"editable": true
},
@@ -825,7 +824,7 @@
},
{
"cell_type": "markdown",
- "id": "d61db81e",
+ "id": "832a6404",
"metadata": {
"editable": true
},
@@ -836,7 +835,7 @@
{
"cell_type": "code",
"execution_count": 4,
- "id": "42ee64fb",
+ "id": "d393c8c7",
"metadata": {
"collapsed": false,
"editable": true
@@ -885,7 +884,7 @@
},
{
"cell_type": "markdown",
- "id": "de54283f",
+ "id": "3d0570c2",
"metadata": {
"editable": true
},
@@ -895,7 +894,7 @@
},
{
"cell_type": "markdown",
- "id": "12dcb1c3",
+ "id": "071ff3b6",
"metadata": {
"editable": true
},
@@ -909,7 +908,7 @@
},
{
"cell_type": "markdown",
- "id": "7e9df537",
+ "id": "113247f9",
"metadata": {
"editable": true
},
@@ -928,7 +927,7 @@
},
{
"cell_type": "markdown",
- "id": "4ca18cc5",
+ "id": "05603c38",
"metadata": {
"editable": true
},
@@ -938,7 +937,7 @@
},
{
"cell_type": "markdown",
- "id": "fb195f64",
+ "id": "8848e319",
"metadata": {
"editable": true
},
@@ -950,21 +949,21 @@
},
{
"cell_type": "markdown",
- "id": "76f68d8d",
+ "id": "5b4146e5",
"metadata": {
"editable": true
},
"source": [
"where $\\boldsymbol{U}$ is an orthogonal matrix of dimension $n\\times n$, meaning that $\\boldsymbol{U}\\boldsymbol{U}^T=\\boldsymbol{U}^T\\boldsymbol{U}=\\boldsymbol{I}_n$. Here $\\boldsymbol{I}_n$ is the unit matrix of dimension $n \\times n$.\n",
"\n",
- "Similarly, $\\boldsymbol{V}$ is an orthogonal matrix of dimension $p\\times p$, meaning that $\\boldsymbol{V}\\boldsymbol{V}^T=\\boldsymbol{V}^T\\boldsymbol{V}=\\boldsymbol{I}_p$. Here $\\boldsymbol{I}_n$ is the unit matrix of dimension $p \\times p$.\n",
+ "Similarly, $\\boldsymbol{V}$ is an orthogonal matrix of dimension $p\\times p$, meaning that $\\boldsymbol{V}\\boldsymbol{V}^T=\\boldsymbol{V}^T\\boldsymbol{V}=\\boldsymbol{I}_p$. Here $\\boldsymbol{I}_p$ is the unit matrix of dimension $p \\times p$.\n",
"\n",
"Finally $\\boldsymbol{\\Sigma}$ contains the singular values $\\sigma_i$. This matrix has dimension $n\\times p$ and the singular values $\\sigma_i$ are all positive. The non-zero values are ordered in descending order, that is"
]
},
{
"cell_type": "markdown",
- "id": "258a1c95",
+ "id": "43701d21",
"metadata": {
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@@ -976,7 +975,7 @@
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{
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- "id": "1e5d87a5",
+ "id": "7cdca00d",
"metadata": {
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@@ -988,7 +987,7 @@
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{
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- "id": "640e515f",
+ "id": "add83821",
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@@ -1005,7 +1004,7 @@
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{
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+ "id": "3746dd8d",
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@@ -1015,7 +1014,7 @@
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{
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- "id": "c9ffceed",
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@@ -1031,7 +1030,7 @@
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{
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- "id": "a99d261a",
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@@ -1041,7 +1040,7 @@
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{
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+ "id": "c674e8da",
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@@ -1057,7 +1056,7 @@
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{
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- "id": "c1429159",
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@@ -1067,7 +1066,7 @@
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{
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- "id": "2b0a9b45",
+ "id": "27e17584",
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@@ -1083,7 +1082,7 @@
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{
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@@ -1093,7 +1092,7 @@
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{
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+ "id": "195d30c4",
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@@ -1110,7 +1109,7 @@
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@@ -1124,7 +1123,7 @@
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@@ -1136,7 +1135,7 @@
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@@ -1146,7 +1145,7 @@
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@@ -1158,7 +1157,7 @@
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@@ -1170,7 +1169,7 @@
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@@ -1182,7 +1181,7 @@
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@@ -1192,7 +1191,7 @@
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@@ -1204,7 +1203,7 @@
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@@ -1214,7 +1213,7 @@
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@@ -1226,7 +1225,7 @@
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@@ -1236,7 +1235,7 @@
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@@ -1248,7 +1247,7 @@
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@@ -1260,7 +1259,7 @@
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@@ -1270,7 +1269,7 @@
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@@ -1282,7 +1281,7 @@
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@@ -1293,7 +1292,7 @@
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@@ -1305,7 +1304,7 @@
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@@ -1315,7 +1314,7 @@
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{
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@@ -1327,7 +1326,7 @@
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@@ -1337,7 +1336,7 @@
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@@ -1349,7 +1348,7 @@
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{
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@@ -1360,7 +1359,7 @@
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{
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@@ -1372,7 +1371,7 @@
},
{
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- "id": "db2c339c",
+ "id": "80e47710",
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@@ -1390,7 +1389,7 @@
},
{
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- "id": "8ab3d49f",
+ "id": "1dc0f98b",
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@@ -1406,7 +1405,7 @@
},
{
"cell_type": "markdown",
- "id": "e57f948b",
+ "id": "c5f9ce8b",
"metadata": {
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@@ -1418,19 +1417,19 @@
},
{
"cell_type": "markdown",
- "id": "6312fe8c",
+ "id": "c803fdb7",
"metadata": {
"editable": true
},
"source": [
- "This quantity defines was what is called the Hessian matrix (the second derivative of a function we want to optimize).\n",
+ "This quantity defines what is called the Hessian matrix (the second derivative of the cost function we want to optimize).\n",
"\n",
"The Hessian matrix plays an important role and is defined in this course as"
]
},
{
"cell_type": "markdown",
- "id": "2cfe093b",
+ "id": "eef3c89e",
"metadata": {
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@@ -1442,7 +1441,7 @@
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- "id": "3d95fdcc",
+ "id": "e886f303",
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@@ -1461,7 +1460,7 @@
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@@ -1475,7 +1474,7 @@
},
{
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@@ -1485,7 +1484,7 @@
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+ "id": "9d676665",
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@@ -1497,7 +1496,7 @@
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@@ -1507,7 +1506,7 @@
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@@ -1519,7 +1518,7 @@
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@@ -1529,7 +1528,7 @@
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{
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@@ -1543,7 +1542,7 @@
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@@ -1566,7 +1565,7 @@
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@@ -1578,7 +1577,7 @@
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{
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@@ -1591,7 +1590,7 @@
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@@ -1605,7 +1604,7 @@
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@@ -1618,7 +1617,7 @@
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@@ -1637,7 +1636,7 @@
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@@ -1649,7 +1648,7 @@
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@@ -1661,7 +1660,7 @@
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{
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- "id": "d675f83c",
+ "id": "94e8929f",
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@@ -1671,7 +1670,7 @@
},
{
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- "id": "0724af92",
+ "id": "3f10861a",
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@@ -1683,20 +1682,20 @@
},
{
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- "id": "e85a73eb",
+ "id": "173fbc84",
"metadata": {
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},
"source": [
"With these definitions, we can now rewrite our $2\\times 2$\n",
- "correlation/covariance matrix in terms of a moe general design/feature\n",
+ "correlation/covariance matrix in terms of a more general design/feature\n",
"matrix $\\boldsymbol{X}\\in {\\mathbb{R}}^{n\\times p}$. This leads to a $p\\times p$\n",
"covariance matrix for the vectors $\\boldsymbol{x}_i$ with $i=0,1,\\dots,p-1$"
]
},
{
"cell_type": "markdown",
- "id": "21d58ff5",
+ "id": "0913dc51",
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@@ -1715,7 +1714,7 @@
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@@ -1725,7 +1724,7 @@
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@@ -1744,7 +1743,7 @@
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@@ -1760,7 +1759,7 @@
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@@ -1774,7 +1773,7 @@
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+ "id": "1fa1423f",
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@@ -1789,7 +1788,7 @@
{
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"execution_count": 5,
- "id": "e422a526",
+ "id": "f277b044",
"metadata": {
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"editable": true
@@ -1799,10 +1798,10 @@
"name": "stdout",
"output_type": "stream",
"text": [
- "0.04413933503955871\n",
- "4.12330280229368\n",
- "[[0.80162359 2.38222896]\n",
- " [2.38222896 8.12167821]]\n"
+ "-0.08873443359350565\n",
+ "3.7851533175757255\n",
+ "[[ 0.98248312 3.05483267]\n",
+ " [ 3.05483267 10.24784064]]\n"
]
}
],
@@ -1821,7 +1820,7 @@
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{
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- "id": "456786dc",
+ "id": "02205795",
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@@ -1836,7 +1835,7 @@
{
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"execution_count": 6,
- "id": "aee5e3f0",
+ "id": "6c182a7d",
"metadata": {
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"editable": true
@@ -1846,10 +1845,10 @@
"name": "stdout",
"output_type": "stream",
"text": [
- "0.06786925114666595\n",
- "1.9635449873404844\n",
- "[[1. 0.65522261]\n",
- " [0.65522261 1. ]]\n"
+ "0.07858099596662704\n",
+ "2.071920625289855\n",
+ "[[1. 0.71822416]\n",
+ " [0.71822416 1. ]]\n"
]
}
],
@@ -1879,7 +1878,7 @@
},
{
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- "id": "333e1d75",
+ "id": "16ff9454",
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@@ -1890,13 +1889,13 @@
"\n",
"The above procedure with **numpy** can be made more compact if we use **pandas**.\n",
"\n",
- "We whow here how we can set up the correlation matrix using **pandas**, as done in this simple code"
+ "We know here how we can set up the correlation matrix using **pandas**, as done in this simple code"
]
},
{
"cell_type": "code",
"execution_count": 7,
- "id": "cbb245b4",
+ "id": "903635fb",
"metadata": {
"collapsed": false,
"editable": true
@@ -1906,30 +1905,30 @@
"name": "stdout",
"output_type": "stream",
"text": [
- "[[-0.27091656 -1.29083183]\n",
- " [ 0.31980301 0.87495119]\n",
- " [-0.10835935 1.61413333]\n",
- " [ 0.5188328 2.80380438]\n",
- " [-0.04996008 -1.95742107]\n",
- " [ 1.19432526 2.68719389]\n",
- " [ 0.19710439 1.35590603]\n",
- " [-0.23857423 -2.50104946]\n",
- " [-0.94054854 -2.09034902]\n",
- " [-0.62170669 -1.49633743]]\n",
+ "[[ -2.84861838 -10.07337358]\n",
+ " [ 0.53938383 2.59445979]\n",
+ " [ -0.40980089 -0.48871288]\n",
+ " [ 0.05834332 -0.39384255]\n",
+ " [ 2.25385387 7.58112299]\n",
+ " [ 0.68246434 2.46650488]\n",
+ " [ -0.25366775 -1.97047717]\n",
+ " [ 0.79081838 2.03807267]\n",
+ " [ -0.06150169 -0.57109235]\n",
+ " [ -0.75127504 -1.18266178]]\n",
+ " 0 1\n",
+ "0 -2.848618 -10.073374\n",
+ "1 0.539384 2.594460\n",
+ "2 -0.409801 -0.488713\n",
+ "3 0.058343 -0.393843\n",
+ "4 2.253854 7.581123\n",
+ "5 0.682464 2.466505\n",
+ "6 -0.253668 -1.970477\n",
+ "7 0.790818 2.038073\n",
+ "8 -0.061502 -0.571092\n",
+ "9 -0.751275 -1.182662\n",
" 0 1\n",
- "0 -0.270917 -1.290832\n",
- "1 0.319803 0.874951\n",
- "2 -0.108359 1.614133\n",
- "3 0.518833 2.803804\n",
- "4 -0.049960 -1.957421\n",
- "5 1.194325 2.687194\n",
- "6 0.197104 1.355906\n",
- "7 -0.238574 -2.501049\n",
- "8 -0.940549 -2.090349\n",
- "9 -0.621707 -1.496337\n",
- " 0 1\n",
- "0 1.000000 0.800615\n",
- "1 0.800615 1.000000\n"
+ "0 1.000000 0.984525\n",
+ "1 0.984525 1.000000\n"
]
}
],
@@ -1952,7 +1951,7 @@
},
{
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- "id": "598beae1",
+ "id": "034c38ef",
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@@ -1963,7 +1962,7 @@
{
"cell_type": "code",
"execution_count": 8,
- "id": "5bb6727b",
+ "id": "91afb8cb",
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@@ -1975,37 +1974,37 @@
"text": [
" 0 1 2 3 4 5 6 7 \\\n",
"0 0.0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 \n",
- "1 0.0 0.084006 0.079882 0.084682 0.084092 0.083417 0.076315 0.076097 \n",
- "2 0.0 0.079882 0.077644 0.078542 0.078962 0.079424 0.069534 0.069977 \n",
- "3 0.0 0.084682 0.078542 0.090649 0.088758 0.086665 0.085105 0.084008 \n",
- "4 0.0 0.084092 0.078962 0.088758 0.087573 0.086250 0.082424 0.081832 \n",
- "5 0.0 0.083417 0.079424 0.086665 0.086250 0.085776 0.079486 0.079438 \n",
- "6 0.0 0.076315 0.069534 0.085105 0.082424 0.079486 0.082288 0.080588 \n",
- "7 0.0 0.076097 0.069977 0.084008 0.081832 0.079438 0.080588 0.079264 \n",
- "8 0.0 0.076022 0.070618 0.082990 0.081357 0.079553 0.078908 0.077986 \n",
- "9 0.0 0.076079 0.071460 0.082027 0.080984 0.079823 0.077219 0.076729 \n",
- "10 0.0 0.068075 0.061188 0.078143 0.075043 0.071666 0.077200 0.075149 \n",
- "11 0.0 0.067712 0.061308 0.077144 0.074420 0.071445 0.075770 0.074006 \n",
- "12 0.0 0.067499 0.061604 0.076264 0.073938 0.071388 0.074418 0.072955 \n",
- "13 0.0 0.067443 0.062089 0.075498 0.073597 0.071505 0.073134 0.071991 \n",
- "14 0.0 0.067547 0.062777 0.074845 0.073400 0.071804 0.071908 0.071106 \n",
+ "1 0.0 0.090241 0.082140 0.090564 0.084086 0.078082 0.082282 0.076619 \n",
+ "2 0.0 0.082140 0.075227 0.083102 0.077428 0.072150 0.075982 0.070945 \n",
+ "3 0.0 0.090564 0.083102 0.096893 0.090268 0.084107 0.091647 0.085571 \n",
+ "4 0.0 0.084086 0.077428 0.090268 0.084286 0.078707 0.085655 0.080120 \n",
+ "5 0.0 0.078082 0.072150 0.084107 0.078707 0.073657 0.080061 0.075020 \n",
+ "6 0.0 0.082282 0.075982 0.091647 0.085655 0.080061 0.089082 0.083380 \n",
+ "7 0.0 0.076619 0.070945 0.085571 0.080120 0.075020 0.083380 0.078158 \n",
+ "8 0.0 0.071394 0.066284 0.079944 0.074984 0.070333 0.078082 0.073299 \n",
+ "9 0.0 0.066569 0.061966 0.074729 0.070216 0.065973 0.073159 0.068776 \n",
+ "10 0.0 0.073831 0.068541 0.084523 0.079224 0.074258 0.083779 0.078587 \n",
+ "11 0.0 0.068867 0.064081 0.079021 0.074183 0.069640 0.078484 0.073716 \n",
+ "12 0.0 0.064284 0.059952 0.073925 0.069506 0.065349 0.073567 0.069187 \n",
+ "13 0.0 0.060048 0.056127 0.069202 0.065165 0.061359 0.068999 0.064974 \n",
+ "14 0.0 0.056131 0.052581 0.064823 0.061133 0.057648 0.064753 0.061054 \n",
"\n",
" 8 9 10 11 12 13 14 \n",
"0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 \n",
- "1 0.076022 0.076079 0.068075 0.067712 0.067499 0.067443 0.067547 \n",
- "2 0.070618 0.071460 0.061188 0.061308 0.061604 0.062089 0.062777 \n",
- "3 0.082990 0.082027 0.078143 0.077144 0.076264 0.075498 0.074845 \n",
- "4 0.081357 0.080984 0.075043 0.074420 0.073938 0.073597 0.073400 \n",
- "5 0.079553 0.079823 0.071666 0.071445 0.071388 0.071505 0.071804 \n",
- "6 0.078908 0.077219 0.077200 0.075770 0.074418 0.073134 0.071908 \n",
- "7 0.077986 0.076729 0.075149 0.074006 0.072955 0.071991 0.071106 \n",
- "8 0.077140 0.076349 0.073080 0.072240 0.071510 0.070887 0.070370 \n",
- "9 0.076349 0.076066 0.070961 0.070443 0.070056 0.069801 0.069681 \n",
- "10 0.073080 0.070961 0.073601 0.071922 0.070288 0.068689 0.067110 \n",
- "11 0.072240 0.070443 0.071922 0.070466 0.069065 0.067709 0.066388 \n",
- "12 0.071510 0.070056 0.070288 0.069065 0.067907 0.066808 0.065761 \n",
- "13 0.070887 0.069801 0.068689 0.067709 0.066808 0.065983 0.065228 \n",
- "14 0.070370 0.069681 0.067110 0.066388 0.065761 0.065228 0.064787 \n"
+ "1 0.071394 0.066569 0.073831 0.068867 0.064284 0.060048 0.056131 \n",
+ "2 0.066284 0.061966 0.068541 0.064081 0.059952 0.056127 0.052581 \n",
+ "3 0.079944 0.074729 0.084523 0.079021 0.073925 0.069202 0.064823 \n",
+ "4 0.074984 0.070216 0.079224 0.074183 0.069506 0.065165 0.061133 \n",
+ "5 0.070333 0.065973 0.074258 0.069640 0.065349 0.061359 0.057648 \n",
+ "6 0.078082 0.073159 0.083779 0.078484 0.073567 0.068999 0.064753 \n",
+ "7 0.073299 0.068776 0.078587 0.073716 0.069187 0.064974 0.061054 \n",
+ "8 0.068841 0.064684 0.073750 0.069268 0.065095 0.061209 0.057588 \n",
+ "9 0.064684 0.060863 0.069242 0.065118 0.061272 0.057686 0.054340 \n",
+ "10 0.073750 0.069242 0.079948 0.075028 0.070450 0.066189 0.062220 \n",
+ "11 0.069268 0.065118 0.075028 0.070494 0.066270 0.062333 0.058663 \n",
+ "12 0.065095 0.061272 0.070450 0.066270 0.062370 0.058732 0.055337 \n",
+ "13 0.061209 0.057686 0.066189 0.062333 0.058732 0.055369 0.052227 \n",
+ "14 0.057588 0.054340 0.062220 0.058663 0.055337 0.052227 0.049318 \n"
]
}
],
@@ -2057,7 +2056,7 @@
},
{
"cell_type": "markdown",
- "id": "6841e847",
+ "id": "9d8768f8",
"metadata": {
"editable": true
},
@@ -2076,7 +2075,7 @@
},
{
"cell_type": "markdown",
- "id": "494c9f8f",
+ "id": "a7de38a0",
"metadata": {
"editable": true
},
@@ -2088,7 +2087,7 @@
},
{
"cell_type": "markdown",
- "id": "28031e99",
+ "id": "4855248a",
"metadata": {
"editable": true
},
@@ -2098,7 +2097,7 @@
},
{
"cell_type": "markdown",
- "id": "f9e03888",
+ "id": "3a150f73",
"metadata": {
"editable": true
},
@@ -2115,7 +2114,7 @@
},
{
"cell_type": "markdown",
- "id": "f50a073c",
+ "id": "6ab3f1f7",
"metadata": {
"editable": true
},
@@ -2125,7 +2124,7 @@
},
{
"cell_type": "markdown",
- "id": "e8332df1",
+ "id": "ae35f475",
"metadata": {
"editable": true
},
@@ -2140,7 +2139,7 @@
},
{
"cell_type": "markdown",
- "id": "40e85f2e",
+ "id": "9f6b4b6b",
"metadata": {
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@@ -2150,7 +2149,7 @@
},
{
"cell_type": "markdown",
- "id": "b38921ca",
+ "id": "af0c59a3",
"metadata": {
"editable": true
},
@@ -2164,7 +2163,7 @@
},
{
"cell_type": "markdown",
- "id": "6cb1f379",
+ "id": "824ae63b",
"metadata": {
"editable": true
},
@@ -2178,7 +2177,7 @@
},
{
"cell_type": "markdown",
- "id": "6f71019b",
+ "id": "5b480160",
"metadata": {
"editable": true
},
@@ -2190,7 +2189,7 @@
},
{
"cell_type": "markdown",
- "id": "ae0b0c45",
+ "id": "506a98da",
"metadata": {
"editable": true
},
@@ -2202,7 +2201,7 @@
},
{
"cell_type": "markdown",
- "id": "89acbca7",
+ "id": "72b1e665",
"metadata": {
"editable": true
},
@@ -2212,7 +2211,7 @@
},
{
"cell_type": "markdown",
- "id": "9e52517d",
+ "id": "6ea9123f",
"metadata": {
"editable": true
},
@@ -2224,7 +2223,7 @@
},
{
"cell_type": "markdown",
- "id": "5dd4bae9",
+ "id": "ab471475",
"metadata": {
"editable": true
},
@@ -2234,7 +2233,7 @@
},
{
"cell_type": "markdown",
- "id": "d0c48d0a",
+ "id": "ff364443",
"metadata": {
"editable": true
},
@@ -2251,7 +2250,7 @@
},
{
"cell_type": "markdown",
- "id": "238fd7dc",
+ "id": "4619ec8f",
"metadata": {
"editable": true
},
@@ -2261,7 +2260,7 @@
},
{
"cell_type": "markdown",
- "id": "5b30b7ea",
+ "id": "529d5ed0",
"metadata": {
"editable": true
},
@@ -2273,7 +2272,7 @@
},
{
"cell_type": "markdown",
- "id": "38a1ee92",
+ "id": "762e07ea",
"metadata": {
"editable": true
},
@@ -2283,7 +2282,7 @@
},
{
"cell_type": "markdown",
- "id": "fb441672",
+ "id": "f45c2ce1",
"metadata": {
"editable": true
},
@@ -2295,7 +2294,7 @@
},
{
"cell_type": "markdown",
- "id": "20d9a077",
+ "id": "35835939",
"metadata": {
"editable": true
},
@@ -2307,7 +2306,7 @@
},
{
"cell_type": "markdown",
- "id": "7b4732c4",
+ "id": "901c3505",
"metadata": {
"editable": true
},
@@ -2319,7 +2318,7 @@
},
{
"cell_type": "markdown",
- "id": "d6de6e76",
+ "id": "63486657",
"metadata": {
"editable": true
},
@@ -2341,7 +2340,7 @@
},
{
"cell_type": "markdown",
- "id": "b85d60d8",
+ "id": "b8cb7b04",
"metadata": {
"editable": true
},
@@ -2353,7 +2352,7 @@
},
{
"cell_type": "markdown",
- "id": "681abce5",
+ "id": "8962eeb3",
"metadata": {
"editable": true
},
@@ -2370,7 +2369,7 @@
},
{
"cell_type": "markdown",
- "id": "a0061112",
+ "id": "ff83bf5a",
"metadata": {
"editable": true
},
@@ -2382,7 +2381,7 @@
},
{
"cell_type": "markdown",
- "id": "67af75b4",
+ "id": "67c405ee",
"metadata": {
"editable": true
},
@@ -2392,7 +2391,7 @@
},
{
"cell_type": "markdown",
- "id": "14e03bab",
+ "id": "d2279b06",
"metadata": {
"editable": true
},
@@ -2404,7 +2403,7 @@
},
{
"cell_type": "markdown",
- "id": "ef2fc352",
+ "id": "c08bd913",
"metadata": {
"editable": true
},
@@ -2414,7 +2413,7 @@
},
{
"cell_type": "markdown",
- "id": "cb03894b",
+ "id": "585fcec4",
"metadata": {
"editable": true
},
@@ -2426,7 +2425,7 @@
},
{
"cell_type": "markdown",
- "id": "322818b0",
+ "id": "c5ee7c18",
"metadata": {
"editable": true
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@@ -2436,7 +2435,7 @@
},
{
"cell_type": "markdown",
- "id": "10f1ad94",
+ "id": "250d6a7b",
"metadata": {
"editable": true
},
@@ -2448,7 +2447,7 @@
},
{
"cell_type": "markdown",
- "id": "17865864",
+ "id": "26dca3eb",
"metadata": {
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@@ -2465,7 +2464,7 @@
},
{
"cell_type": "markdown",
- "id": "30dddf0b",
+ "id": "43ae52cf",
"metadata": {
"editable": true
},
@@ -2478,7 +2477,7 @@
},
{
"cell_type": "markdown",
- "id": "8633ef50",
+ "id": "fa5c2da2",
"metadata": {
"editable": true
},
@@ -2490,7 +2489,7 @@
},
{
"cell_type": "markdown",
- "id": "a7ec868f",
+ "id": "ef125654",
"metadata": {
"editable": true
},
@@ -2500,7 +2499,7 @@
},
{
"cell_type": "markdown",
- "id": "772f70dc",
+ "id": "3e398c3d",
"metadata": {
"editable": true
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@@ -2513,7 +2512,7 @@
},
{
"cell_type": "markdown",
- "id": "eda842c9",
+ "id": "6e4285d1",
"metadata": {
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@@ -2523,7 +2522,7 @@
},
{
"cell_type": "markdown",
- "id": "4f4cbc79",
+ "id": "c1d8fde6",
"metadata": {
"editable": true
},
@@ -2535,7 +2534,7 @@
},
{
"cell_type": "markdown",
- "id": "c960bc44",
+ "id": "5b082cd2",
"metadata": {
"editable": true
},
@@ -2548,7 +2547,7 @@
},
{
"cell_type": "markdown",
- "id": "1d5e2196",
+ "id": "306b6062",
"metadata": {
"editable": true
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@@ -2561,7 +2560,7 @@
},
{
"cell_type": "markdown",
- "id": "000880d6",
+ "id": "f9c22f99",
"metadata": {
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@@ -2573,7 +2572,7 @@
},
{
"cell_type": "markdown",
- "id": "a9d1e159",
+ "id": "8fa998f9",
"metadata": {
"editable": true
},
@@ -2585,7 +2584,7 @@
},
{
"cell_type": "markdown",
- "id": "6882c9cf",
+ "id": "954b3b63",
"metadata": {
"editable": true
},
@@ -2595,7 +2594,7 @@
},
{
"cell_type": "markdown",
- "id": "a21757d3",
+ "id": "40d226a6",
"metadata": {
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@@ -2608,7 +2607,7 @@
},
{
"cell_type": "markdown",
- "id": "f072b07c",
+ "id": "571654e9",
"metadata": {
"editable": true
},
@@ -2620,7 +2619,7 @@
},
{
"cell_type": "markdown",
- "id": "733a6413",
+ "id": "4b96f90f",
"metadata": {
"editable": true
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@@ -2632,7 +2631,7 @@
},
{
"cell_type": "markdown",
- "id": "c1fe1a2c",
+ "id": "6af80b33",
"metadata": {
"editable": true
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@@ -2642,7 +2641,7 @@
},
{
"cell_type": "markdown",
- "id": "d39258b1",
+ "id": "ed4e7687",
"metadata": {
"editable": true
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@@ -2654,7 +2653,7 @@
},
{
"cell_type": "markdown",
- "id": "59c47ad9",
+ "id": "2eb319cc",
"metadata": {
"editable": true
},
@@ -2668,7 +2667,7 @@
},
{
"cell_type": "markdown",
- "id": "eb60430f",
+ "id": "8528934c",
"metadata": {
"editable": true
},
@@ -2680,7 +2679,7 @@
},
{
"cell_type": "markdown",
- "id": "265d31a8",
+ "id": "22a7e810",
"metadata": {
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@@ -2690,7 +2689,7 @@
},
{
"cell_type": "markdown",
- "id": "8ab4a19c",
+ "id": "01d9c1c9",
"metadata": {
"editable": true
},
@@ -2702,7 +2701,7 @@
},
{
"cell_type": "markdown",
- "id": "e1cf6baf",
+ "id": "5d910fd1",
"metadata": {
"editable": true
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@@ -2714,7 +2713,7 @@
},
{
"cell_type": "markdown",
- "id": "0769ccf1",
+ "id": "b8bbfa39",
"metadata": {
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@@ -2726,7 +2725,7 @@
},
{
"cell_type": "markdown",
- "id": "b2efb7e5",
+ "id": "51ac6ef1",
"metadata": {
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@@ -2745,7 +2744,7 @@
},
{
"cell_type": "markdown",
- "id": "2fac59a0",
+ "id": "12ee6646",
"metadata": {
"editable": true
},
@@ -2757,7 +2756,7 @@
},
{
"cell_type": "markdown",
- "id": "6783041f",
+ "id": "22852ccf",
"metadata": {
"editable": true
},
@@ -2767,7 +2766,7 @@
},
{
"cell_type": "markdown",
- "id": "cb5777d1",
+ "id": "68d87eac",
"metadata": {
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@@ -2779,7 +2778,7 @@
},
{
"cell_type": "markdown",
- "id": "4b124b41",
+ "id": "0219a1a8",
"metadata": {
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@@ -2791,7 +2790,7 @@
},
{
"cell_type": "markdown",
- "id": "379a857f",
+ "id": "be1f339c",
"metadata": {
"editable": true
},
@@ -2803,7 +2802,7 @@
},
{
"cell_type": "markdown",
- "id": "2125cb49",
+ "id": "7e1d5221",
"metadata": {
"editable": true
},
@@ -2821,7 +2820,7 @@
},
{
"cell_type": "markdown",
- "id": "f40d87ac",
+ "id": "0b4bc87c",
"metadata": {
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@@ -2833,7 +2832,7 @@
},
{
"cell_type": "markdown",
- "id": "04c2c26c",
+ "id": "de7e0986",
"metadata": {
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@@ -2843,7 +2842,7 @@
},
{
"cell_type": "markdown",
- "id": "8d6fe816",
+ "id": "0ae7dd26",
"metadata": {
"editable": true
},
@@ -2855,7 +2854,7 @@
},
{
"cell_type": "markdown",
- "id": "77db7bc0",
+ "id": "5caa1086",
"metadata": {
"editable": true
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@@ -2865,7 +2864,7 @@
},
{
"cell_type": "markdown",
- "id": "77ebce0a",
+ "id": "c737b14f",
"metadata": {
"editable": true
},
@@ -2877,7 +2876,7 @@
},
{
"cell_type": "markdown",
- "id": "30e3d7f9",
+ "id": "60570cf0",
"metadata": {
"editable": true
},
@@ -2893,7 +2892,7 @@
},
{
"cell_type": "markdown",
- "id": "b76bf6d6",
+ "id": "f0c2e386",
"metadata": {
"editable": true
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@@ -2905,7 +2904,7 @@
},
{
"cell_type": "markdown",
- "id": "ec68ccb3",
+ "id": "5f3e91d2",
"metadata": {
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@@ -2915,7 +2914,7 @@
},
{
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- "id": "7849b038",
+ "id": "66b637e8",
"metadata": {
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@@ -2927,7 +2926,7 @@
},
{
"cell_type": "markdown",
- "id": "e2596a14",
+ "id": "4082c969",
"metadata": {
"editable": true
},
@@ -2937,7 +2936,7 @@
},
{
"cell_type": "markdown",
- "id": "5912b05e",
+ "id": "2c0b085b",
"metadata": {
"editable": true
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@@ -2949,7 +2948,7 @@
},
{
"cell_type": "markdown",
- "id": "5a85cd53",
+ "id": "bf355533",
"metadata": {
"editable": true
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@@ -2959,7 +2958,7 @@
},
{
"cell_type": "markdown",
- "id": "048012bd",
+ "id": "928d6cb3",
"metadata": {
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@@ -2971,7 +2970,7 @@
},
{
"cell_type": "markdown",
- "id": "efef81d5",
+ "id": "39a40fd9",
"metadata": {
"editable": true
},
@@ -2981,12 +2980,12 @@
"Let us assume that our design matrix is given by unit (identity) matrix, that is a square diagonal matrix with ones only along the\n",
"diagonal. In this case we have an equal number of rows and columns $n=p$.\n",
"\n",
- "Our model approximation is just $\\tilde{\\boldsymbol{y}}=\\boldsymbol{\\beta}$ and the mean squared error and thereby the cost function for ordinary least sqquares (OLS) is then (we drop the term $1/n$)"
+ "Our model approximation is just $\\tilde{\\boldsymbol{y}}=\\boldsymbol{\\beta}$ and the mean squared error and thereby the cost function for ordinary least squares (OLS) is then (we drop the term $1/n$)"
]
},
{
"cell_type": "markdown",
- "id": "54ca6b87",
+ "id": "5d891e5c",
"metadata": {
"editable": true
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@@ -2998,7 +2997,7 @@
},
{
"cell_type": "markdown",
- "id": "1e2ef9fc",
+ "id": "f9ea4d16",
"metadata": {
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@@ -3008,7 +3007,7 @@
},
{
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- "id": "87f035f4",
+ "id": "59b56446",
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@@ -3020,7 +3019,7 @@
},
{
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- "id": "f9ebafc4",
+ "id": "b178aedb",
"metadata": {
"editable": true
},
@@ -3030,7 +3029,7 @@
},
{
"cell_type": "markdown",
- "id": "ff097451",
+ "id": "3c7c60e4",
"metadata": {
"editable": true
},
@@ -3042,7 +3041,7 @@
},
{
"cell_type": "markdown",
- "id": "6e5a4735",
+ "id": "2f5d3c17",
"metadata": {
"editable": true
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@@ -3052,7 +3051,7 @@
},
{
"cell_type": "markdown",
- "id": "2b787e5e",
+ "id": "2a612078",
"metadata": {
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@@ -3064,7 +3063,7 @@
},
{
"cell_type": "markdown",
- "id": "3349660d",
+ "id": "dfb11d07",
"metadata": {
"editable": true
},
@@ -3074,7 +3073,7 @@
},
{
"cell_type": "markdown",
- "id": "da17bea5",
+ "id": "9331f4a6",
"metadata": {
"editable": true
},
@@ -3086,7 +3085,7 @@
},
{
"cell_type": "markdown",
- "id": "ba3eb166",
+ "id": "b4661ad6",
"metadata": {
"editable": true
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@@ -3096,7 +3095,7 @@
},
{
"cell_type": "markdown",
- "id": "5003889b",
+ "id": "60adb333",
"metadata": {
"editable": true
},
@@ -3108,7 +3107,7 @@
},
{
"cell_type": "markdown",
- "id": "8c9da994",
+ "id": "d5fa48d0",
"metadata": {
"editable": true
},
@@ -3118,7 +3117,7 @@
},
{
"cell_type": "markdown",
- "id": "171cb28c",
+ "id": "bee441a6",
"metadata": {
"editable": true
},
@@ -3132,20 +3131,20 @@
},
{
"cell_type": "markdown",
- "id": "5d749681",
+ "id": "dc6929bb",
"metadata": {
"editable": true
},
"source": [
"Plotting these results ([figure in handwritten notes for week 36](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2021/NotesSeptember9.pdf)) shows clearly that Lasso regression suppresses (sets to zero) values of $\\beta_i$ for specific values of $\\lambda$. Ridge regression reduces on the other hand the values of $\\beta_i$ as function of $\\lambda$.\n",
"\n",
- "As another examples, \n",
+ "As another example, \n",
"let us assume we have a data set with outputs/targets given by the vector"
]
},
{
"cell_type": "markdown",
- "id": "ec36a482",
+ "id": "954061f9",
"metadata": {
"editable": true
},
@@ -3157,7 +3156,7 @@
},
{
"cell_type": "markdown",
- "id": "153e6fdb",
+ "id": "97efa82b",
"metadata": {
"editable": true
},
@@ -3167,7 +3166,7 @@
},
{
"cell_type": "markdown",
- "id": "2dbc8ef3",
+ "id": "f2ed5f9b",
"metadata": {
"editable": true
},
@@ -3179,7 +3178,7 @@
},
{
"cell_type": "markdown",
- "id": "c5077dc7",
+ "id": "1c424fc1",
"metadata": {
"editable": true
},
@@ -3191,7 +3190,7 @@
},
{
"cell_type": "markdown",
- "id": "cb8e4e64",
+ "id": "95467447",
"metadata": {
"editable": true
},
@@ -3203,7 +3202,7 @@
},
{
"cell_type": "markdown",
- "id": "b7761fa1",
+ "id": "5da0739a",
"metadata": {
"editable": true
},
@@ -3213,7 +3212,7 @@
},
{
"cell_type": "markdown",
- "id": "12478361",
+ "id": "47e7e72f",
"metadata": {
"editable": true
},
@@ -3225,7 +3224,7 @@
},
{
"cell_type": "markdown",
- "id": "49d1c0e3",
+ "id": "974570c8",
"metadata": {
"editable": true
},
@@ -3237,7 +3236,7 @@
},
{
"cell_type": "markdown",
- "id": "bbf2a7e1",
+ "id": "dd9e2341",
"metadata": {
"editable": true
},
@@ -3249,7 +3248,7 @@
},
{
"cell_type": "markdown",
- "id": "5465e48e",
+ "id": "70f08735",
"metadata": {
"editable": true
},
@@ -3259,7 +3258,7 @@
},
{
"cell_type": "markdown",
- "id": "6ae8cea7",
+ "id": "c0a08b76",
"metadata": {
"editable": true
},
@@ -3271,7 +3270,7 @@
},
{
"cell_type": "markdown",
- "id": "073f7084",
+ "id": "1d8ed72a",
"metadata": {
"editable": true
},
@@ -3286,7 +3285,7 @@
},
{
"cell_type": "markdown",
- "id": "9f700c62",
+ "id": "9d4ef6fd",
"metadata": {
"editable": true
},
@@ -3298,7 +3297,7 @@
},
{
"cell_type": "markdown",
- "id": "dc606935",
+ "id": "3ba1fd07",
"metadata": {
"editable": true
},
@@ -3310,7 +3309,7 @@
},
{
"cell_type": "markdown",
- "id": "9f027657",
+ "id": "2c6a0484",
"metadata": {
"editable": true
},
@@ -3320,7 +3319,7 @@
},
{
"cell_type": "markdown",
- "id": "73ab89da",
+ "id": "7f86e745",
"metadata": {
"editable": true
},
@@ -3332,7 +3331,7 @@
},
{
"cell_type": "markdown",
- "id": "d90641d4",
+ "id": "46c8a1af",
"metadata": {
"editable": true
},
@@ -3342,7 +3341,7 @@
},
{
"cell_type": "markdown",
- "id": "783e4acf",
+ "id": "33d6b311",
"metadata": {
"editable": true
},
@@ -3354,7 +3353,7 @@
},
{
"cell_type": "markdown",
- "id": "54e34208",
+ "id": "1e4eae3a",
"metadata": {
"editable": true
},
@@ -3364,7 +3363,7 @@
},
{
"cell_type": "markdown",
- "id": "e1d51c0f",
+ "id": "7a68a399",
"metadata": {
"editable": true
},
@@ -3376,7 +3375,7 @@
},
{
"cell_type": "markdown",
- "id": "df26eb7d",
+ "id": "89874fbd",
"metadata": {
"editable": true
},
@@ -3389,7 +3388,7 @@
},
{
"cell_type": "markdown",
- "id": "52773a3b",
+ "id": "a849fabc",
"metadata": {
"editable": true
},
@@ -3401,7 +3400,7 @@
},
{
"cell_type": "markdown",
- "id": "7147420f",
+ "id": "445f0b08",
"metadata": {
"editable": true
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@@ -3413,7 +3412,7 @@
},
{
"cell_type": "markdown",
- "id": "0148b8ed",
+ "id": "669385c5",
"metadata": {
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@@ -3423,7 +3422,7 @@
},
{
"cell_type": "markdown",
- "id": "a289ee68",
+ "id": "d5d14c30",
"metadata": {
"editable": true
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@@ -3435,7 +3434,7 @@
},
{
"cell_type": "markdown",
- "id": "a134de53",
+ "id": "1db05ce9",
"metadata": {
"editable": true
},
@@ -3454,7 +3453,7 @@
},
{
"cell_type": "markdown",
- "id": "42525db3",
+ "id": "48598bde",
"metadata": {
"editable": true
},
@@ -3466,7 +3465,7 @@
},
{
"cell_type": "markdown",
- "id": "8cb8693f",
+ "id": "458cc863",
"metadata": {
"editable": true
},
@@ -3476,7 +3475,7 @@
},
{
"cell_type": "markdown",
- "id": "941c059c",
+ "id": "ff948eca",
"metadata": {
"editable": true
},
@@ -3488,7 +3487,7 @@
},
{
"cell_type": "markdown",
- "id": "c9505d7b",
+ "id": "38dfba54",
"metadata": {
"editable": true
},
@@ -3498,7 +3497,7 @@
},
{
"cell_type": "markdown",
- "id": "706d9352",
+ "id": "bc715180",
"metadata": {
"editable": true
},
@@ -3510,7 +3509,7 @@
},
{
"cell_type": "markdown",
- "id": "a36f3223",
+ "id": "62e9a17c",
"metadata": {
"editable": true
},
@@ -3520,7 +3519,7 @@
},
{
"cell_type": "markdown",
- "id": "a16a4703",
+ "id": "e564b775",
"metadata": {
"editable": true
},
@@ -3532,7 +3531,7 @@
},
{
"cell_type": "markdown",
- "id": "62e13728",
+ "id": "2bdbcac1",
"metadata": {
"editable": true
},
@@ -3548,7 +3547,7 @@
{
"cell_type": "code",
"execution_count": 9,
- "id": "4b9e0425",
+ "id": "a1e3dee1",
"metadata": {
"collapsed": false,
"editable": true
@@ -3634,24 +3633,24 @@
},
{
"cell_type": "markdown",
- "id": "7ad7e409",
+ "id": "5973148f",
"metadata": {
"editable": true
},
"source": [
- "We see here that we reach a plateau for the Ridge results. Writing out the coefficients $\\boldsymbol{\\beta}$, we that they are getting smaller and smaller and our error stabilizes since the predicted values of $\\tilde{\\boldsymbol{y}}$ approach zero.\n",
+ "We see here that we reach a plateau for the Ridge results. Writing out the coefficients $\\boldsymbol{\\beta}$, we observe that they are getting smaller and smaller and our error stabilizes since the predicted values of $\\tilde{\\boldsymbol{y}}$ approach zero.\n",
"\n",
"This happens also for Lasso regression, as seen from the next code\n",
"output. The difference is that Lasso shrinks the values of $\\beta$ to\n",
"zero at a much earlier stage and the results flatten out. We see that\n",
"Lasso gives also an excellent fit for small values of $\\lambda$ and\n",
- "shows rthe best performance of the three regression methods."
+ "shows the best performance of the three regression methods."
]
},
{
"cell_type": "code",
"execution_count": 10,
- "id": "5618fe91",
+ "id": "a961f69c",
"metadata": {
"collapsed": false,
"editable": true
@@ -3942,7 +3941,7 @@
},
{
"cell_type": "markdown",
- "id": "d11661fb",
+ "id": "60cfd641",
"metadata": {
"editable": true
},
@@ -3961,7 +3960,7 @@
{
"cell_type": "code",
"execution_count": 11,
- "id": "22f6ce96",
+ "id": "171876b3",
"metadata": {
"collapsed": false,
"editable": true
@@ -4076,7 +4075,7 @@
},
{
"cell_type": "markdown",
- "id": "2ab56f06",
+ "id": "947928e7",
"metadata": {
"editable": true
},
@@ -4091,7 +4090,7 @@
},
{
"cell_type": "markdown",
- "id": "86c7b9aa",
+ "id": "9559d0a8",
"metadata": {
"editable": true
},
@@ -4120,7 +4119,7 @@
},
{
"cell_type": "markdown",
- "id": "1a8cf62c",
+ "id": "6810eb7d",
"metadata": {
"editable": true
},
@@ -4136,7 +4135,7 @@
},
{
"cell_type": "markdown",
- "id": "03c65270",
+ "id": "bd997167",
"metadata": {
"editable": true
},
@@ -4159,7 +4158,7 @@
},
{
"cell_type": "markdown",
- "id": "423800c4",
+ "id": "4ff740b9",
"metadata": {
"editable": true
},
@@ -4171,7 +4170,7 @@
},
{
"cell_type": "markdown",
- "id": "54abfaf4",
+ "id": "fe0b2250",
"metadata": {
"editable": true
},
@@ -4182,7 +4181,7 @@
},
{
"cell_type": "markdown",
- "id": "630d72b6",
+ "id": "87e6b9b3",
"metadata": {
"editable": true
},
@@ -4194,7 +4193,7 @@
},
{
"cell_type": "markdown",
- "id": "5de630a0",
+ "id": "68d0de57",
"metadata": {
"editable": true
},
@@ -4204,7 +4203,7 @@
},
{
"cell_type": "markdown",
- "id": "aa85b4cd",
+ "id": "2f239890",
"metadata": {
"editable": true
},
@@ -4220,7 +4219,7 @@
},
{
"cell_type": "markdown",
- "id": "2f903151",
+ "id": "2a724679",
"metadata": {
"editable": true
},
@@ -4231,7 +4230,7 @@
},
{
"cell_type": "markdown",
- "id": "a9378db4",
+ "id": "2d710e45",
"metadata": {
"editable": true
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@@ -4254,7 +4253,7 @@
},
{
"cell_type": "markdown",
- "id": "5eeef81e",
+ "id": "488a73d8",
"metadata": {
"editable": true
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@@ -4267,7 +4266,7 @@
},
{
"cell_type": "markdown",
- "id": "e3aa6792",
+ "id": "9b1dca9a",
"metadata": {
"editable": true
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@@ -4279,7 +4278,7 @@
},
{
"cell_type": "markdown",
- "id": "d9f4d5aa",
+ "id": "07089a59",
"metadata": {
"editable": true
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@@ -4293,7 +4292,7 @@
},
{
"cell_type": "markdown",
- "id": "52725327",
+ "id": "690bd104",
"metadata": {
"editable": true
},
@@ -4324,7 +4323,7 @@
},
{
"cell_type": "markdown",
- "id": "ae6de7ff",
+ "id": "6a9132ce",
"metadata": {
"editable": true
},
@@ -4346,7 +4345,7 @@
},
{
"cell_type": "markdown",
- "id": "3b7642a3",
+ "id": "68cce775",
"metadata": {
"editable": true
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@@ -4358,7 +4357,7 @@
},
{
"cell_type": "markdown",
- "id": "6519d923",
+ "id": "a9c3f89a",
"metadata": {
"editable": true
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@@ -4371,7 +4370,7 @@
},
{
"cell_type": "markdown",
- "id": "d5c90c4b",
+ "id": "f9e2f9d7",
"metadata": {
"editable": true
},
@@ -4383,7 +4382,7 @@
},
{
"cell_type": "markdown",
- "id": "32d45fbe",
+ "id": "58443fe8",
"metadata": {
"editable": true
},
@@ -4395,7 +4394,7 @@
},
{
"cell_type": "markdown",
- "id": "7e7e08c2",
+ "id": "cc34c059",
"metadata": {
"editable": true
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@@ -4407,7 +4406,7 @@
},
{
"cell_type": "markdown",
- "id": "1f3b3e08",
+ "id": "6ad9c8e3",
"metadata": {
"editable": true
},
@@ -4419,7 +4418,7 @@
},
{
"cell_type": "markdown",
- "id": "8c4539a9",
+ "id": "7c09657d",
"metadata": {
"editable": true
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@@ -4442,7 +4441,7 @@
},
{
"cell_type": "markdown",
- "id": "6e53e7aa",
+ "id": "abe9915b",
"metadata": {
"editable": true
},
@@ -4454,7 +4453,7 @@
},
{
"cell_type": "markdown",
- "id": "0a8f5e0e",
+ "id": "326e0c75",
"metadata": {
"editable": true
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@@ -4465,7 +4464,7 @@
},
{
"cell_type": "markdown",
- "id": "de7e332e",
+ "id": "567fb1b1",
"metadata": {
"editable": true
},
@@ -4477,19 +4476,19 @@
},
{
"cell_type": "markdown",
- "id": "e4873c9c",
+ "id": "107abe1c",
"metadata": {
"editable": true
},
"source": [
"which reads as finding the likelihood of an event $y_i$ with the input variables $\\boldsymbol{X}$ given the parameters (to be determined) $\\boldsymbol{\\beta}$.\n",
"\n",
- "Since these events are assumed to be independent and identicall distributed we can build the probability distribution function (PDF) for all possible event $\\boldsymbol{y}$ as the product of the single events, that is we have"
+ "Since these events are assumed to be independent and identically distributed we can build the probability distribution function (PDF) for all possible event $\\boldsymbol{y}$ as the product of the single events, that is we have"
]
},
{
"cell_type": "markdown",
- "id": "7bd0f3cb",
+ "id": "f11ddf78",
"metadata": {
"editable": true
},
@@ -4501,7 +4500,7 @@
},
{
"cell_type": "markdown",
- "id": "181adb8d",
+ "id": "2abd6e3b",
"metadata": {
"editable": true
},
@@ -4512,7 +4511,7 @@
},
{
"cell_type": "markdown",
- "id": "90fc5963",
+ "id": "caddb652",
"metadata": {
"editable": true
},
@@ -4524,7 +4523,7 @@
},
{
"cell_type": "markdown",
- "id": "ee0229b0",
+ "id": "291e1dd6",
"metadata": {
"editable": true
},
@@ -4535,7 +4534,7 @@
},
{
"cell_type": "markdown",
- "id": "543c8ca5",
+ "id": "73ac95c1",
"metadata": {
"editable": true
},
@@ -4547,7 +4546,7 @@
},
{
"cell_type": "markdown",
- "id": "38881820",
+ "id": "ce49493b",
"metadata": {
"editable": true
},
@@ -4582,7 +4581,7 @@
},
{
"cell_type": "markdown",
- "id": "0f1fea5a",
+ "id": "1ff54861",
"metadata": {
"editable": true
},
@@ -4594,7 +4593,7 @@
},
{
"cell_type": "markdown",
- "id": "4c07b706",
+ "id": "e8cdd425",
"metadata": {
"editable": true
},
@@ -4604,7 +4603,7 @@
},
{
"cell_type": "markdown",
- "id": "20a2d9f1",
+ "id": "95d54be7",
"metadata": {
"editable": true
},
@@ -4616,7 +4615,7 @@
},
{
"cell_type": "markdown",
- "id": "d65c8233",
+ "id": "731e3e2a",
"metadata": {
"editable": true
},
@@ -4626,7 +4625,7 @@
},
{
"cell_type": "markdown",
- "id": "251536f6",
+ "id": "8c40a24c",
"metadata": {
"editable": true
},
@@ -4638,7 +4637,7 @@
},
{
"cell_type": "markdown",
- "id": "c24acd35",
+ "id": "1e298a02",
"metadata": {
"editable": true
},
@@ -4648,7 +4647,7 @@
},
{
"cell_type": "markdown",
- "id": "2594074f",
+ "id": "fd5c3e4f",
"metadata": {
"editable": true
},
@@ -4660,7 +4659,7 @@
},
{
"cell_type": "markdown",
- "id": "bb7f7b33",
+ "id": "d3aab131",
"metadata": {
"editable": true
},
@@ -4680,7 +4679,7 @@
},
{
"cell_type": "markdown",
- "id": "84b10307",
+ "id": "64646b7c",
"metadata": {
"editable": true
},
@@ -4692,7 +4691,7 @@
},
{
"cell_type": "markdown",
- "id": "2ed6eff3",
+ "id": "0ad4cc29",
"metadata": {
"editable": true
},
@@ -4702,19 +4701,19 @@
},
{
"cell_type": "markdown",
- "id": "bee02bb6",
+ "id": "8dfd2150",
"metadata": {
"editable": true
},
"source": [
"$$\n",
- "p(X \\cup Y)= p(X,Y)= p(X\\vert Y)p(Y)=p(Y\\vert X)p(X),\n",
+ "p(X \\cap Y)= p(X,Y)= p(X\\vert Y)p(Y)=p(Y\\vert X)p(X),\n",
"$$"
]
},
{
"cell_type": "markdown",
- "id": "f9cb00d6",
+ "id": "9c0313b7",
"metadata": {
"editable": true
},
@@ -4728,7 +4727,7 @@
},
{
"cell_type": "markdown",
- "id": "bf8b6016",
+ "id": "af94800f",
"metadata": {
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},
@@ -4740,7 +4739,7 @@
},
{
"cell_type": "markdown",
- "id": "192d323f",
+ "id": "3ed2ccef",
"metadata": {
"editable": true
},
@@ -4750,7 +4749,7 @@
},
{
"cell_type": "markdown",
- "id": "f593b004",
+ "id": "7a74ee19",
"metadata": {
"editable": true
},
@@ -4762,7 +4761,7 @@
},
{
"cell_type": "markdown",
- "id": "515aeb1a",
+ "id": "5191a71e",
"metadata": {
"editable": true
},
@@ -4772,7 +4771,7 @@
},
{
"cell_type": "markdown",
- "id": "4f069d49",
+ "id": "5d5de8f7",
"metadata": {
"editable": true
},
@@ -4784,7 +4783,7 @@
},
{
"cell_type": "markdown",
- "id": "bfeebc26",
+ "id": "cca75f59",
"metadata": {
"editable": true
},
@@ -4794,7 +4793,7 @@
},
{
"cell_type": "markdown",
- "id": "8a0fadd6",
+ "id": "9113e675",
"metadata": {
"editable": true
},
@@ -4806,7 +4805,7 @@
},
{
"cell_type": "markdown",
- "id": "24bd831c",
+ "id": "a21d13da",
"metadata": {
"editable": true
},
@@ -4842,7 +4841,7 @@
},
{
"cell_type": "markdown",
- "id": "ed5051fd",
+ "id": "0c7abec6",
"metadata": {
"editable": true
},
@@ -4854,7 +4853,7 @@
},
{
"cell_type": "markdown",
- "id": "3ee252d1",
+ "id": "2eccb1af",
"metadata": {
"editable": true
},
@@ -4867,7 +4866,7 @@
},
{
"cell_type": "markdown",
- "id": "5f96bad5",
+ "id": "3c6635e5",
"metadata": {
"editable": true
},
@@ -4879,7 +4878,7 @@
},
{
"cell_type": "markdown",
- "id": "c58a4b8e",
+ "id": "ecf0a0b6",
"metadata": {
"editable": true
},
@@ -4893,7 +4892,7 @@
},
{
"cell_type": "markdown",
- "id": "5415897f",
+ "id": "166345a1",
"metadata": {
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},
@@ -4905,7 +4904,7 @@
},
{
"cell_type": "markdown",
- "id": "8a2bffd1",
+ "id": "8a73e80e",
"metadata": {
"editable": true
},
@@ -4916,7 +4915,7 @@
},
{
"cell_type": "markdown",
- "id": "2dd3ffc5",
+ "id": "01441388",
"metadata": {
"editable": true
},
@@ -4928,7 +4927,7 @@
},
{
"cell_type": "markdown",
- "id": "d7f4ee89",
+ "id": "93fe1e0a",
"metadata": {
"editable": true
},
@@ -4940,7 +4939,7 @@
},
{
"cell_type": "markdown",
- "id": "45729327",
+ "id": "d6860415",
"metadata": {
"editable": true
},
@@ -4958,7 +4957,7 @@
},
{
"cell_type": "markdown",
- "id": "c2f81821",
+ "id": "9710dd92",
"metadata": {
"editable": true
},
@@ -4976,7 +4975,7 @@
},
{
"cell_type": "markdown",
- "id": "7e97b2f6",
+ "id": "23e3912e",
"metadata": {
"editable": true
},
@@ -4986,7 +4985,7 @@
},
{
"cell_type": "markdown",
- "id": "43e854ca",
+ "id": "cf500f71",
"metadata": {
"editable": true
},
@@ -5015,7 +5014,7 @@
{
"cell_type": "code",
"execution_count": 12,
- "id": "62e17aee",
+ "id": "134d0a22",
"metadata": {
"collapsed": false,
"editable": true
@@ -5113,7 +5112,7 @@
},
{
"cell_type": "markdown",
- "id": "c03f356d",
+ "id": "7dcfe550",
"metadata": {
"editable": true
},
@@ -5143,7 +5142,7 @@
{
"cell_type": "code",
"execution_count": 13,
- "id": "1ecda570",
+ "id": "5ff5d7c2",
"metadata": {
"collapsed": false,
"editable": true
@@ -5498,7 +5497,7 @@
},
{
"cell_type": "markdown",
- "id": "bd3186fd",
+ "id": "f1680928",
"metadata": {
"editable": true
},
@@ -5509,12 +5508,12 @@
"noise. Here we recommend to use $\\sigma^2=1$ as variance for the\n",
"added noise (which follows a normal distribution with mean value zero).\n",
"Comment your results. If you have a large noise term, do the parameters $\\beta_j$ vary more as function\n",
- "model complexity? And what about their variance?"
+ "of model complexity? And what about their variance?"
]
},
{
"cell_type": "markdown",
- "id": "10f8e3d1",
+ "id": "5b458403",
"metadata": {
"editable": true
},
@@ -5532,7 +5531,7 @@
},
{
"cell_type": "markdown",
- "id": "6a0b1e1c",
+ "id": "6e2d6bf6",
"metadata": {
"editable": true
},
@@ -5544,7 +5543,7 @@
},
{
"cell_type": "markdown",
- "id": "642cfda6",
+ "id": "098b6cbd",
"metadata": {
"editable": true
},
@@ -5554,7 +5553,7 @@
},
{
"cell_type": "markdown",
- "id": "dc785785",
+ "id": "8a02d0aa",
"metadata": {
"editable": true
},
@@ -5566,7 +5565,7 @@
},
{
"cell_type": "markdown",
- "id": "a2591c04",
+ "id": "97f22408",
"metadata": {
"editable": true
},
@@ -5576,7 +5575,7 @@
},
{
"cell_type": "markdown",
- "id": "37438bbe",
+ "id": "27038459",
"metadata": {
"editable": true
},
@@ -5588,7 +5587,7 @@
},
{
"cell_type": "markdown",
- "id": "9ad42344",
+ "id": "f682a8c3",
"metadata": {
"editable": true
},
@@ -5598,7 +5597,7 @@
},
{
"cell_type": "markdown",
- "id": "a95978e7",
+ "id": "7fdaa748",
"metadata": {
"editable": true
},
@@ -5610,12 +5609,12 @@
},
{
"cell_type": "markdown",
- "id": "434a17cd",
+ "id": "1e7fa52c",
"metadata": {
"editable": true
},
"source": [
- "We have a model for $p(\\boldsymbol{D}\\vert\\boldsymbol{\\beta})$ but need one for the **prior** $p(\\boldsymbol{\\beta}$! \n",
+ "We have a model for $p(\\boldsymbol{D}\\vert\\boldsymbol{\\beta})$ but need one for the **prior** $p(\\boldsymbol{\\beta})$! \n",
"\n",
"With the posterior probability defined by a likelihood which we have\n",
"already modeled and an unknown prior, we are now ready to make\n",
@@ -5628,7 +5627,7 @@
},
{
"cell_type": "markdown",
- "id": "c3581bd6",
+ "id": "501d66f4",
"metadata": {
"editable": true
},
@@ -5640,7 +5639,7 @@
},
{
"cell_type": "markdown",
- "id": "19277aa0",
+ "id": "f029c143",
"metadata": {
"editable": true
},
@@ -5650,7 +5649,7 @@
},
{
"cell_type": "markdown",
- "id": "3aa17c65",
+ "id": "7f7c3e11",
"metadata": {
"editable": true
},
@@ -5662,7 +5661,7 @@
},
{
"cell_type": "markdown",
- "id": "169fd184",
+ "id": "1f39114c",
"metadata": {
"editable": true
},
@@ -5675,7 +5674,7 @@
},
{
"cell_type": "markdown",
- "id": "8340686e",
+ "id": "81cc7b03",
"metadata": {
"editable": true
},
@@ -5687,7 +5686,7 @@
},
{
"cell_type": "markdown",
- "id": "46d497c8",
+ "id": "1e614b9b",
"metadata": {
"editable": true
},
@@ -5697,7 +5696,7 @@
},
{
"cell_type": "markdown",
- "id": "db839f5a",
+ "id": "77252afc",
"metadata": {
"editable": true
},
@@ -5709,7 +5708,7 @@
},
{
"cell_type": "markdown",
- "id": "7b412be2",
+ "id": "14953579",
"metadata": {
"editable": true
},
@@ -5721,7 +5720,7 @@
},
{
"cell_type": "markdown",
- "id": "98250878",
+ "id": "36f1f63d",
"metadata": {
"editable": true
},
@@ -5733,7 +5732,7 @@
},
{
"cell_type": "markdown",
- "id": "e0374cc2",
+ "id": "50dd90a5",
"metadata": {
"editable": true
},
@@ -5743,7 +5742,7 @@
},
{
"cell_type": "markdown",
- "id": "f251157b",
+ "id": "de39cb12",
"metadata": {
"editable": true
},
@@ -5755,7 +5754,7 @@
},
{
"cell_type": "markdown",
- "id": "5beb906a",
+ "id": "ad1fc46e",
"metadata": {
"editable": true
},
@@ -5767,19 +5766,19 @@
},
{
"cell_type": "markdown",
- "id": "18264240",
+ "id": "ff8695d4",
"metadata": {
"editable": true
},
"source": [
"$$\n",
- "C(\\boldsymbol{\\beta}=\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta})\\vert\\vert_2^2}{2\\sigma^2}+\\frac{1}{\\tau}\\vert\\vert\\boldsymbol{\\beta}\\vert\\vert_1,\n",
+ "C(\\boldsymbol{\\beta})=\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta})\\vert\\vert_2^2}{2\\sigma^2}+\\frac{1}{\\tau}\\vert\\vert\\boldsymbol{\\beta}\\vert\\vert_1,\n",
"$$"
]
},
{
"cell_type": "markdown",
- "id": "b977c7cd",
+ "id": "0de8080e",
"metadata": {
"editable": true
},
@@ -5789,19 +5788,19 @@
},
{
"cell_type": "markdown",
- "id": "80b2f3e2",
+ "id": "3965e5ef",
"metadata": {
"editable": true
},
"source": [
"$$\n",
- "C(\\boldsymbol{\\beta}=\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta})\\vert\\vert_2^2}{2\\sigma^2}+\\lambda\\vert\\vert\\boldsymbol{\\beta}\\vert\\vert_1,\n",
+ "C(\\boldsymbol{\\beta})=\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta})\\vert\\vert_2^2}{2\\sigma^2}+\\lambda\\vert\\vert\\boldsymbol{\\beta}\\vert\\vert_1,\n",
"$$"
]
},
{
"cell_type": "markdown",
- "id": "dd62775a",
+ "id": "5c978cdf",
"metadata": {
"editable": true
},
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter2.py b/doc/LectureNotes/_build/jupyter_execute/chapter2.py
index 940d29deb..c5d2b1900 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapter2.py
+++ b/doc/LectureNotes/_build/jupyter_execute/chapter2.py
@@ -88,7 +88,7 @@
# This is given by the **Singular Value Decomposition** (SVD) algorithm,
# perhaps the most powerful linear algebra algorithm. The SVD provides
# a numerically stable matrix decomposition that is used in a large
-# swath oc applications and the decomposition is always stable
+# swath of applications and the decomposition is always stable
# numerically.
#
# In machine learning it plays a central role in dealing with for
@@ -104,7 +104,7 @@
# are problems with near singular or singular matrices. The column vectors of $\boldsymbol{X}$
# may be linearly dependent, normally referred to as super-collinearity.
# This means that the matrix may be rank deficient and it is basically impossible to
-# to model the data using linear regression. As an example, consider the matrix
+# model the data using linear regression. As an example, consider the matrix
# $$
# \begin{align*}
@@ -125,7 +125,7 @@
# the first column is the row-wise sum of the other two columns. The rank (more correct,
# the column rank) of a matrix is the dimension of the space spanned by the
# column vectors. Hence, the rank of $\mathbf{X}$ is equal to the number
-# of linearly independent columns. In this particular case the matrix has rank 2.
+# of linearly independent columns. In this particular case the matrix has rank 1.
#
# Super-collinearity of an $(n \times p)$-dimensional design matrix $\mathbf{X}$ implies
# that the inverse of the matrix $\boldsymbol{X}^T\boldsymbol{X}$ (the matrix we need to invert to solve the linear regression equations) is non-invertible. If we have a square matrix that does not have an inverse, we say this matrix singular. The example here demonstrates this
@@ -158,7 +158,7 @@
# has linearly dependent column vectors, we will not be able to compute the inverse
# of $\boldsymbol{X}^T\boldsymbol{X}$ and we cannot find the parameters (estimators) $\beta_i$.
-# The estimators are only well-defined if $(\boldsymbol{X}^{T}\boldsymbol{X})^{-1}$ exits.
+# The estimators are only well-defined if $(\boldsymbol{X}^{T}\boldsymbol{X})$ can be inverted.
# This is more likely to happen when the matrix $\boldsymbol{X}$ is high-dimensional. In this case it is likely to encounter a situation where
# the regression parameters $\beta_i$ cannot be estimated.
#
@@ -172,7 +172,7 @@
# ## Basic math of the SVD
#
-# From standard linear algebra we know that a square matrix $\boldsymbol{X}$ can be diagonalized if and only it is
+# From standard linear algebra we know that a square matrix $\boldsymbol{X}$ can be diagonalized if and only if it is
# a so-called [normal matrix](https://en.wikipedia.org/wiki/Normal_matrix), that is if $\boldsymbol{X}\in {\mathbb{R}}^{n\times n}$
# we have $\boldsymbol{X}\boldsymbol{X}^T=\boldsymbol{X}^T\boldsymbol{X}$ or if $\boldsymbol{X}\in {\mathbb{C}}^{n\times n}$ we have $\boldsymbol{X}\boldsymbol{X}^{\dagger}=\boldsymbol{X}^{\dagger}\boldsymbol{X}$.
# The matrix has then a set of eigenpairs
@@ -359,7 +359,6 @@ def SVDinv(A):
return np.matmul(V,np.matmul(invD,UT))
-#X = np.array([ [1.0, -1.0, 2.0], [1.0, 0.0, 1.0], [1.0, 2.0, -1.0], [1.0, 1.0, 0.0] ])
# Non-singular square matrix
X = np.array( [ [1,2,3],[2,4,5],[3,5,6]])
print(X)
@@ -378,7 +377,7 @@ print(np.abs(B-C))
# It is also called the the Moore-Penrose Inverse after two independent discoverers of the method or the Generalized Inverse.
# It is used for the calculation of the inverse for singular or near singular matrices and for rectangular matrices.
#
-# Using the SVD we can obtain the pseudoinverse of a matrix $\boldsymbol{A}$ (labeled here as $\boldsymbol{A}_{\mathrm{PI}}$
+# Using the SVD we can obtain the pseudoinverse (PI) of a matrix $\boldsymbol{A}$ (labeled here as $\boldsymbol{A}_{\mathrm{PI}}$
# $$
# \boldsymbol{A}_{\mathrm{PI}}= \boldsymbol{V}\boldsymbol{D}_{\mathrm{PI}}\boldsymbol{U}^T,
@@ -441,7 +440,7 @@ print(np.abs(C-B))
# where $\boldsymbol{U}$ is an orthogonal matrix of dimension $n\times n$, meaning that $\boldsymbol{U}\boldsymbol{U}^T=\boldsymbol{U}^T\boldsymbol{U}=\boldsymbol{I}_n$. Here $\boldsymbol{I}_n$ is the unit matrix of dimension $n \times n$.
#
-# Similarly, $\boldsymbol{V}$ is an orthogonal matrix of dimension $p\times p$, meaning that $\boldsymbol{V}\boldsymbol{V}^T=\boldsymbol{V}^T\boldsymbol{V}=\boldsymbol{I}_p$. Here $\boldsymbol{I}_n$ is the unit matrix of dimension $p \times p$.
+# Similarly, $\boldsymbol{V}$ is an orthogonal matrix of dimension $p\times p$, meaning that $\boldsymbol{V}\boldsymbol{V}^T=\boldsymbol{V}^T\boldsymbol{V}=\boldsymbol{I}_p$. Here $\boldsymbol{I}_p$ is the unit matrix of dimension $p \times p$.
#
# Finally $\boldsymbol{\Sigma}$ contains the singular values $\sigma_i$. This matrix has dimension $n\times p$ and the singular values $\sigma_i$ are all positive. The non-zero values are ordered in descending order, that is
@@ -603,7 +602,7 @@ print(np.abs(C-B))
# \frac{\partial^2 C(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}^T\partial \boldsymbol{\beta}} =\frac{2}{n}\boldsymbol{X}^T\boldsymbol{X}.
# $$
-# This quantity defines was what is called the Hessian matrix (the second derivative of a function we want to optimize).
+# This quantity defines what is called the Hessian matrix (the second derivative of the cost function we want to optimize).
#
# The Hessian matrix plays an important role and is defined in this course as
@@ -709,7 +708,7 @@ print(np.abs(C-B))
# $$
# With these definitions, we can now rewrite our $2\times 2$
-# correlation/covariance matrix in terms of a moe general design/feature
+# correlation/covariance matrix in terms of a more general design/feature
# matrix $\boldsymbol{X}\in {\mathbb{R}}^{n\times p}$. This leads to a $p\times p$
# covariance matrix for the vectors $\boldsymbol{x}_i$ with $i=0,1,\dots,p-1$
@@ -810,7 +809,7 @@ print(C)
#
# The above procedure with **numpy** can be made more compact if we use **pandas**.
#
-# We whow here how we can set up the correlation matrix using **pandas**, as done in this simple code
+# We know here how we can set up the correlation matrix using **pandas**, as done in this simple code
# In[7]:
@@ -1208,7 +1207,7 @@ print(covariance_matrix)
# Let us assume that our design matrix is given by unit (identity) matrix, that is a square diagonal matrix with ones only along the
# diagonal. In this case we have an equal number of rows and columns $n=p$.
#
-# Our model approximation is just $\tilde{\boldsymbol{y}}=\boldsymbol{\beta}$ and the mean squared error and thereby the cost function for ordinary least sqquares (OLS) is then (we drop the term $1/n$)
+# Our model approximation is just $\tilde{\boldsymbol{y}}=\boldsymbol{\beta}$ and the mean squared error and thereby the cost function for ordinary least squares (OLS) is then (we drop the term $1/n$)
# $$
# C(\boldsymbol{\beta})=\sum_{i=0}^{p-1}(y_i-\beta_i)^2,
@@ -1254,7 +1253,7 @@ print(covariance_matrix)
# Plotting these results ([figure in handwritten notes for week 36](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2021/NotesSeptember9.pdf)) shows clearly that Lasso regression suppresses (sets to zero) values of $\beta_i$ for specific values of $\lambda$. Ridge regression reduces on the other hand the values of $\beta_i$ as function of $\lambda$.
#
-# As another examples,
+# As another example,
# let us assume we have a data set with outputs/targets given by the vector
# $$
@@ -1443,13 +1442,13 @@ plt.legend()
plt.show()
-# We see here that we reach a plateau for the Ridge results. Writing out the coefficients $\boldsymbol{\beta}$, we that they are getting smaller and smaller and our error stabilizes since the predicted values of $\tilde{\boldsymbol{y}}$ approach zero.
+# We see here that we reach a plateau for the Ridge results. Writing out the coefficients $\boldsymbol{\beta}$, we observe that they are getting smaller and smaller and our error stabilizes since the predicted values of $\tilde{\boldsymbol{y}}$ approach zero.
#
# This happens also for Lasso regression, as seen from the next code
# output. The difference is that Lasso shrinks the values of $\beta$ to
# zero at a much earlier stage and the results flatten out. We see that
# Lasso gives also an excellent fit for small values of $\lambda$ and
-# shows rthe best performance of the three regression methods.
+# shows the best performance of the three regression methods.
# In[10]:
@@ -1800,7 +1799,7 @@ plt.show()
# which reads as finding the likelihood of an event $y_i$ with the input variables $\boldsymbol{X}$ given the parameters (to be determined) $\boldsymbol{\beta}$.
#
-# Since these events are assumed to be independent and identicall distributed we can build the probability distribution function (PDF) for all possible event $\boldsymbol{y}$ as the product of the single events, that is we have
+# Since these events are assumed to be independent and identically distributed we can build the probability distribution function (PDF) for all possible event $\boldsymbol{y}$ as the product of the single events, that is we have
# $$
# p(\boldsymbol{y},\boldsymbol{X}\vert\boldsymbol{\beta})=\prod_{i=0}^{n-1}\frac{1}{\sqrt{2\pi\sigma^2}}\exp{\left[-\frac{(y_i-\boldsymbol{X}_{i,*}\boldsymbol{\beta})^2}{2\sigma^2}\right]}=\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta}).
@@ -1888,7 +1887,7 @@ plt.show()
# The product rule (aka joint probability) is given by
# $$
-# p(X \cup Y)= p(X,Y)= p(X\vert Y)p(Y)=p(Y\vert X)p(X),
+# p(X \cap Y)= p(X,Y)= p(X\vert Y)p(Y)=p(Y\vert X)p(X),
# $$
# where we read $p(X\vert Y)$ as the likelihood of obtaining $X$ given $Y$.
@@ -2161,7 +2160,7 @@ for i in range(nlambdas):
# noise. Here we recommend to use $\sigma^2=1$ as variance for the
# added noise (which follows a normal distribution with mean value zero).
# Comment your results. If you have a large noise term, do the parameters $\beta_j$ vary more as function
-# model complexity? And what about their variance?
+# of model complexity? And what about their variance?
# ## Linking Bayes' Theorem with Ridge and Lasso Regression
#
@@ -2195,7 +2194,7 @@ for i in range(nlambdas):
# p(\boldsymbol{\beta}\vert\boldsymbol{D})\propto p(\boldsymbol{D}\vert\boldsymbol{\beta})p(\boldsymbol{\beta}).
# $$
-# We have a model for $p(\boldsymbol{D}\vert\boldsymbol{\beta})$ but need one for the **prior** $p(\boldsymbol{\beta}$!
+# We have a model for $p(\boldsymbol{D}\vert\boldsymbol{\beta})$ but need one for the **prior** $p(\boldsymbol{\beta})$!
#
# With the posterior probability defined by a likelihood which we have
# already modeled and an unknown prior, we are now ready to make
@@ -2249,13 +2248,13 @@ for i in range(nlambdas):
# constants terms that do not depend on $\beta$, we have
# $$
-# C(\boldsymbol{\beta}=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}+\frac{1}{\tau}\vert\vert\boldsymbol{\beta}\vert\vert_1,
+# C(\boldsymbol{\beta})=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}+\frac{1}{\tau}\vert\vert\boldsymbol{\beta}\vert\vert_1,
# $$
# and replacing $1/\tau$ with $\lambda$ we have
# $$
-# C(\boldsymbol{\beta}=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}+\lambda\vert\vert\boldsymbol{\beta}\vert\vert_1,
+# C(\boldsymbol{\beta})=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}+\lambda\vert\vert\boldsymbol{\beta}\vert\vert_1,
# $$
# which is our Lasso cost function!
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapteroptimization.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapteroptimization.ipynb
index f5d9a4c5a..2c0534d8a 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapteroptimization.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/chapteroptimization.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "4d72e1df",
+ "id": "f84a9d0d",
"metadata": {
"editable": true
},
@@ -13,7 +13,7 @@
},
{
"cell_type": "markdown",
- "id": "fb6e8fcd",
+ "id": "d40fde79",
"metadata": {
"editable": true
},
@@ -39,7 +39,7 @@
},
{
"cell_type": "markdown",
- "id": "a507b82a",
+ "id": "5e16ce97",
"metadata": {
"editable": true
},
@@ -54,7 +54,7 @@
},
{
"cell_type": "markdown",
- "id": "4071429e",
+ "id": "48b8210e",
"metadata": {
"editable": true
},
@@ -70,7 +70,7 @@
},
{
"cell_type": "markdown",
- "id": "a3cca0b2",
+ "id": "160bfec6",
"metadata": {
"editable": true
},
@@ -82,7 +82,7 @@
},
{
"cell_type": "markdown",
- "id": "12a4ad28",
+ "id": "cf829958",
"metadata": {
"editable": true
},
@@ -93,7 +93,7 @@
},
{
"cell_type": "markdown",
- "id": "5d6e7796",
+ "id": "a0ee64a1",
"metadata": {
"editable": true
},
@@ -105,7 +105,7 @@
},
{
"cell_type": "markdown",
- "id": "b324ae78",
+ "id": "9d6e5d8f",
"metadata": {
"editable": true
},
@@ -119,7 +119,7 @@
},
{
"cell_type": "markdown",
- "id": "7c39cc3f",
+ "id": "4af11aa5",
"metadata": {
"editable": true
},
@@ -131,7 +131,7 @@
},
{
"cell_type": "markdown",
- "id": "10749f5d",
+ "id": "8801711a",
"metadata": {
"editable": true
},
@@ -141,7 +141,7 @@
},
{
"cell_type": "markdown",
- "id": "3ec50136",
+ "id": "34c3d5a7",
"metadata": {
"editable": true
},
@@ -153,7 +153,7 @@
},
{
"cell_type": "markdown",
- "id": "0145d9eb",
+ "id": "452bbf0a",
"metadata": {
"editable": true
},
@@ -181,7 +181,7 @@
},
{
"cell_type": "markdown",
- "id": "43c17534",
+ "id": "e7d6fca4",
"metadata": {
"editable": true
},
@@ -197,7 +197,7 @@
},
{
"cell_type": "markdown",
- "id": "32ef04f0",
+ "id": "afcf6c29",
"metadata": {
"editable": true
},
@@ -208,7 +208,7 @@
},
{
"cell_type": "markdown",
- "id": "6700017c",
+ "id": "e0e9aca3",
"metadata": {
"editable": true
},
@@ -220,7 +220,7 @@
},
{
"cell_type": "markdown",
- "id": "8791dec4",
+ "id": "5d70696d",
"metadata": {
"editable": true
},
@@ -230,7 +230,7 @@
},
{
"cell_type": "markdown",
- "id": "69008872",
+ "id": "df759be1",
"metadata": {
"editable": true
},
@@ -242,7 +242,7 @@
},
{
"cell_type": "markdown",
- "id": "fce4ef1f",
+ "id": "d9f2bf15",
"metadata": {
"editable": true
},
@@ -252,7 +252,7 @@
},
{
"cell_type": "markdown",
- "id": "e64aef7e",
+ "id": "70cf6701",
"metadata": {
"editable": true
},
@@ -264,7 +264,7 @@
},
{
"cell_type": "markdown",
- "id": "9acecc44",
+ "id": "e2a70850",
"metadata": {
"editable": true
},
@@ -287,7 +287,7 @@
},
{
"cell_type": "markdown",
- "id": "18bc9fd6",
+ "id": "883881e4",
"metadata": {
"editable": true
},
@@ -300,7 +300,7 @@
},
{
"cell_type": "markdown",
- "id": "7dcad370",
+ "id": "8704ba9a",
"metadata": {
"editable": true
},
@@ -310,7 +310,7 @@
},
{
"cell_type": "markdown",
- "id": "f1724121",
+ "id": "f5ae25a5",
"metadata": {
"editable": true
},
@@ -328,7 +328,7 @@
},
{
"cell_type": "markdown",
- "id": "d04bfa9f",
+ "id": "884ca09b",
"metadata": {
"editable": true
},
@@ -338,7 +338,7 @@
},
{
"cell_type": "markdown",
- "id": "a4d3a9e3",
+ "id": "9852d9e6",
"metadata": {
"editable": true
},
@@ -353,7 +353,7 @@
},
{
"cell_type": "markdown",
- "id": "d9d6ff69",
+ "id": "475ecae5",
"metadata": {
"editable": true
},
@@ -363,7 +363,7 @@
},
{
"cell_type": "markdown",
- "id": "362a86a3",
+ "id": "d20911ef",
"metadata": {
"editable": true
},
@@ -377,7 +377,7 @@
},
{
"cell_type": "markdown",
- "id": "4b8c2937",
+ "id": "8c9e3f44",
"metadata": {
"editable": true
},
@@ -387,7 +387,7 @@
},
{
"cell_type": "markdown",
- "id": "7580aa9a",
+ "id": "eec377bf",
"metadata": {
"editable": true
},
@@ -401,7 +401,7 @@
},
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"$\\mathbb{R}$. Examples of convex sets of $\\mathbb{R}^2$ are the\n",
"regular polygons (triangles, rectangles, pentagons, etc...).\n",
"\n",
- "**Convex function**: Let $X \\subset \\mathbb{R}^n$ be a convex set. Assume that the function $f: X \\rightarrow \\mathbb{R}$ is continuous, then $f$ is said to be convex if $$f(tx_1 + (1-t)x_2) \\leq tf(x_1) + (1-t)f(x_2) $$ for all $x_1, x_2 \\in X$ and for all $t \\in [0,1]$. If $\\leq$ is replaced with a strict inequaltiy in the definition, we demand $x_1 \\neq x_2$ and $t\\in(0,1)$ then $f$ is said to be strictly convex. For a single variable function, convexity means that if you draw a straight line connecting $f(x_1)$ and $f(x_2)$, the value of the function on the interval $[x_1,x_2]$ is always below the line as illustrated below.\n",
+ "**Convex function**: Let $X \\subset \\mathbb{R}^n$ be a convex\n",
+ "set. Assume that the function $f: X \\rightarrow \\mathbb{R}$ is\n",
+ "continuous, then $f$ is said to be convex if\n",
+ "$f(tx_1 + (1-t)x_2) \\leq tf(x_1) + (1-t)f(x_2)$\n",
+ "for all\n",
+ "$x_1, x_2 \\in X$ and for all $t \\in [0,1]$.\n",
+ "\n",
+ "If $\\leq$ is replaced with a strict inequality in the\n",
+ "definition, we demand $x_1 \\neq x_2$ and $t\\in(0,1)$ then $f$ is said\n",
+ "to be strictly convex. For a single variable function, convexity means\n",
+ "that if you draw a straight line connecting $f(x_1)$ and $f(x_2)$, the\n",
+ "value of the function on the interval $[x_1,x_2]$ is always below the\n",
+ "line as discussed below.\n",
"\n",
"In the following we state first and second-order conditions which\n",
"ensures convexity of a function $f$. We write $D_f$ to denote the\n",
@@ -550,7 +562,7 @@
"is a convex set and $$f(y) \\geq f(x) + \\nabla f(x)^T (y-x) $$ holds\n",
"for all $x,y \\in D_f$. This condition means that for a convex function\n",
"the first order Taylor expansion (right hand side above) at any point\n",
- "a global under estimator of the function. To convince yourself you can\n",
+ "is a global under estimator of the function. To convince yourself you can\n",
"make a drawing of $f(x) = x^2+1$ and draw the tangent line to $f(x)$ and\n",
"note that it is always below the graph.\n",
"\n",
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+ "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_96694/483257001.py:18: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().\n",
" ax = fig.gca(projection=\"3d\")\n"
]
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"text": [
- "[0.34158665 3.94915262]\n",
- "[[3.97117751]\n",
- " [3.11850274]]\n",
- "[[3.97117751]\n",
- " [3.11850274]]\n"
+ "[0.2831603 4.55553537]\n",
+ "[[3.91511388]\n",
+ " [3.13030182]]\n",
+ "[[3.91511388]\n",
+ " [3.13030182]]\n"
]
},
{
"data": {
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V9Y9//AOrVq3CAw88gJdffhlxcXG4desWjh8/juXLl2PevHmIiorCqlWrMH36dLz55pumoRmmT5+OiRMnokePHnjkkUcAGIKrBQsWID4+Hq1bt8b27dsxY8YMq4FJTYWHh6Nnz5548803ERQUhLlz5+LQoUNVdq+fP38++vXrh759+2LkyJFo1KgRLl26hIMHD2LHjh1YuHChQ8pLVC0uTuAmkqVdu3aJUaNGiZiYGKFWq4W/v79o3ry5ePrpp8Xq1avNth0xYoQICgqyuJ8DBw6I3r17i+DgYFG3bl3x2GOPiZMnTwoA4q233jLbdsmSJaJ169bCz89PNG7cWLz33nvirbfeqrI3mRBCXLt2TbzxxhsiLi5O+Pn5iZCQENGqVSsxfvx4s55AAMTYsWMrlNPSPqdMmSIiIyOFl5dXhZ5Clnz22WeiRYsWws/PT9xzzz3iiy++ECNGjDDrTSaEoUv8Bx98INq0aSP8/f1FrVq1RHx8vBg9erQ4cuSIEMLQC+yRRx4RTZo0EWq1WoSFhYnu3buLJUuWmO3r5s2b4v/+7/9Mxw0LCxM9e/YUmzZtMtvuiy++EJ06dRJBQUEiICBAxMbGiqefflps27bNtE337t1Fy5YtK5yXpXPIyMgQ8fHxwtfX1+J7Wd758+fFyy+/LGJiYoSvr68IDQ0V7du3F6+//rq4du2aOHPmjKhfv77o2bOnWS8rvV4vBg0aJOrUqWPq2Xf58mXxzDPPiPr164vAwEDRtWtXsX79etG9e3fRvXt302uNPbzKdoEX4u4wCOV7Hxo/a+fPnzctM35e5s6dK2JjY4Wvr6+Ij48X3333ndlrLfUmE0KI3bt3i8cff1zUr19f+Pr6igYNGoiePXuKefPmVXq9iJxNJYQQrgrEiIhIvlQqFcaOHYs5c+a4uihEDsXeZERERKRoDIaIiIhI0ZhATUREFjGLgpSCNUNERESkaAyGiIiISNEYDBEREZGiKSJnSK/X48yZMwgODrY4bQIRERHJjxACV69erXIewppSRDB05swZREdHu7oYREREVA35+fkOG2UdUEgwZJxCID8/36ZpFIiIiMj1iouLER0dbXEqICkpIhgyNo3Vrl2bwRAREZGbcXSKCxOoiYiISNEYDBEREZGiMRgiIiIiRWMwRERERIrGYIiIiIgUjcEQERERKRqDISIiIlI0BkNERESkaAyGiIiISNEYDBEREZGiMRgiIiIiRWMwRERERIrGYIiIiIgUjcEQERERKRqDISIiIlI0BkNERESkaAyGiIiISNFcHgytW7cOgwYNQmRkJFQqFbKzs61uO3r0aKhUKsyaNctp5SMiIiLP5vJg6Pr162jTpg3mzJlT6XbZ2dnYsmULIiMjnVQyIiIiUgIfVxegX79+6NevX6XbnD59Gi+++CJ++eUXDBgwwEklIyIiIiVwec1QVfR6PYYPH45JkyahZcuWri4OEREReRiX1wxV5f3334ePjw9efvllm19TUlKCkpIS0/Pi4mJHFI2IiIg8gKxrhrZv347Zs2djwYIFUKlUNr9u+vTpCAkJMT2io6MdWEoiIiJyZ7IOhtavX49z586hcePG8PHxgY+PD06cOIFXXnkFTZs2tfq6KVOmoKioyPTIz893XqGJiIjIrci6mWz48OF48MEHzZb17dsXw4cPx6hRo6y+Tq1WQ61WO7p4RERE5AFcHgxdu3YNR48eNT3Py8vDrl27EBoaisaNGyMsLMxse19fXzRo0ABxcXHOLioRERF5IJcHQ9u2bUNKSorp+YQJEwAAI0aMwIIFC1xUKiIiIlIKlwdDPXr0gBDC5u2PHz/uuMIQERGR4sg6gZqIiIjI0RgMERERkaIxGCIiIiJFYzBEREREisZgiIiIiBSNwRAREREpGoMhIiIiUjQGQ0RERKRoDIaIiIhI0RgMERERkaIxGCIiIiJFYzBEREREisZgiIiIiBSNwRAREREpGoMhIiIiUjQGQ0RERKRoDIaIiIhI0RgMERERkaIxGCIiIiJFYzBEREREisZgiIiIiBSNwRAREREpGoMhIiIiUjQGQ0RERKRoDIaIiIhI0RgMERERkaIxGCIiIiJFYzBEREREisZgiIiIiBSNwRAREREpGoMhIiIiUjQGQ0RERKRoDIaIiIhI0RgMERERkaIxGCIiIiJFYzBEREREisZgiIiIiBSNwRAREREpGoMhIiIiUjSXB0Pr1q3DoEGDEBkZCZVKhezsbNO6O3fu4LXXXkOrVq0QFBSEyMhIPP300zhz5ozrCkxERER36XRAbi6QkWH4q9O5ukR2c3kwdP36dbRp0wZz5sypsO7GjRvYsWMH3nzzTezYsQNZWVn4448/8PDDD7ugpERERGQmKwto2hRISQGGDTP8bdrUsNyNqIQQwtWFMFKpVFi8eDFSU1OtbrN161Z07NgRJ06cQOPGjW3ab3FxMUJCQlBUVITatWtLVFoiIiIFy8oChgwByocRKpXh76JFwODBNTqEs+7fLq8ZsldRURFUKhXq1KljdZuSkhIUFxebPYiIiEgiOh0wblzFQAi4uywtzW2azNwqGLp16xYmT56MYcOGVRohTp8+HSEhIaZHdHS0E0tJRETk4davB06dsr5eCCA/37CdG3CbYOjOnTsYOnQo9Ho95s6dW+m2U6ZMQVFRkemRn5/vpFISEREpQEGBtNu5mI+rC2CLO3fu4PHHH0deXh7WrFlTZbuhWq2GWq12UumIiIgUpmFDabdzMdnXDBkDoSNHjuDXX39FWFiYq4tERESkbMnJQFTU3WTp8lQqIDrasJ0bcHnN0LVr13D06FHT87y8POzatQuhoaGIjIzEkCFDsGPHDixbtgw6nQ6FhYUAgNDQUPj5+bmq2ERERMrl7Q3Mnm3oTaZSmSdSGwOkWbMM27kBl3etz83NRUpKSoXlI0aMwNSpUxETE2PxdTk5OejRo4dNx2DXeiIiIgfIyjL0KiubTB0dbQiEatitHnDe/dvlwZAzMBgiIiJyEJ3O0GusoMCQI5ScLFmNkLPu3y5vJiMiIiI35u0N2NhSI1eyT6AmIiIiciQGQ0RERKRoDIaIiIhI0RgMERERkaIxGCIiIiJFYzBEREREisZgiIiIiBSNwRAREREpGgddJCIiKs+BoyqT/DAYIiIiKsvSfFtRUYaJSSWYb4sqUT4IbdPGKYdlMERERGSUlWWYib38tJ2nTxuWL1rEgMhRLAWhkZFOOTQnaiUiIgIMtRJNm5rfjMtSqQw1RHl5bDKTmpUgtBhACODw+zcTqImIiABD84y1QAgw3Kjz8w3bkXR0OkONkAvrZthMRkREBBjyVKTczh3IIVG8qiDUCRgMERERAYZgQMrt5E4uieIyCC7ZTEZERAQYakWiogy5QZaoVEB0tGE7d2fM0SlfI2NMFM/KMtQa5eYCGRmGvzqdY8oig+CSCdRERERGxiABMM9hMQZIntCbzJZE8dBQICDAObVGxvKcPs0EaiIiIpcbPNgQ8DRqZL48KsozAiHAtkTxixcrrzWSkre3IcgCrNfKORiDISIiorIGDwaOHwdycoD0dMPfvDzPCISA6ufoGGtt0tKkbzKzFoSWf+4gbCYjIiJSktxcICWlZvvIyQF69JCiNObK9W4rbtMGIaGhDr9/szcZERGRkhgTxS3k6NjMUT3AvL3Ng6ziYsccpxw2kxERESmJFDk6MugBJiUGQ0REREpTWaJ4WJgyhhcog8EQERGREllKFD9+HPj0U8P68gGR8fmsWR43NxtzhoiIiJSqfI4OcLfWyNLo1LNmeU6vujIYDBEREZG5wYMBjcb585aVnyutTRvHHu9PDIaIiIioIku1Ro5kaa60yEinHJrBEBEREbmWcRqU8l39z5xxyuGZQE1ERESuo9MZaoRcOAY0gyEiIiJynarmSnMCBkNERETkOo4azdoODIaIiIjIdWQwmjUTqImIyFz57s3O6FJNyiXFXGk1xJohIiK6KysLaNrUMKv5sGGGv02bGpYTOYIUc6XVEIMhIiIyMHZvLp/Mevq0YTkDInIUa3OllX/uICohXNiXzUmKi4sREhKCoqIi1K5d29XFISKSH53OUANkrVePSmVoysjLY5MZOc6fTbTnc/dh3ZpSzNnTBrlFPR1+/2bOEBERVd29WQggP9+wnTNHJSZFEHqBXT8chnZ+IbS/N8Cumz3+XFPslOO7vJls3bp1GDRoECIjI6FSqZCdnW22XgiBqVOnIjIyEgEBAejRowf279/vmsISEXkqW7s3y6AbNHmGOzfuYPWMHXi5zVo09TuNdsPiMW1tD+y6GQ8v6JBcezfe7rveKWVxeTB0/fp1tGnTBnPmzLG4/l//+hc+/PBDzJkzB1u3bkWDBg3Qu3dvXL161cklJSLyYLZ2b5ZBN2hyX1fPXMXCCZvxVMxG1K91HQ++2g7/2dMdJ3VRCMANaBpswZfPbEDhgctYV9QGL/2Y7JRyySpnSKVSYfHixUhNTQVgqBWKjIxEWloaXnvtNQBASUkJIiIi8P7772P06NE27Zc5Q0REVTDmDFnr3sycIaqmgl1nsWTGYWhXBWD1+da4DbVpXbjqAgY1P4jUx/zw4PhWCAwPNHuts+7fss4ZysvLQ2FhIfr06WNaplar0b17d2zatMlqMFRSUoKSkhLT8+Ji57Q5EhG5LWP35iFDDIFP2YDI2N151iwGQlQloRc4uOwYtB+fgnZjOLZcTwIQYVrf3Pc4NK2PI/Wvoej8bEt4+zmn9qcysg6GCgsLAQARERFmyyMiInDixAmrr5s+fTqmTZvm0LIREXkcY/fmcePMk6mjogyB0ODBLisayZvutg6bP9sP7ZeXoN3dBEfuNAfQ3LS+Y9A+aB64gNQXo5AwMBYqr6YuK6slsg6GjFTlBmESQlRYVtaUKVMwYcIE0/Pi4mJER0c7rHxERB5j8GBAo+EI1OVxVO4Kbl66iVUz90C78DaWHo3HedHatM4PJegZvgepfW5i0Cv3ILJdkgtLWjVZB0MNGjQAYKghalgmae/cuXMVaovKUqvVUKvVVtcTEVElvL3Zfb6srCzLtWWzZyuutuzC4YtYNuMgtMt9sLKgFW6gk2ldCIowoMk+pA72Qt8JLVE7qoMLS2ofWQdDMTExaNCgAVatWoV7770XAHD79m2sXbsW77//votLR0REHs84Knf5pHLjqNyLFnl8QHRszQloZ+dBu7YONhS1gh5dTeuivU9Dk3gUqcOD0W1sK/gGdnFhSavP5cHQtWvXcPToUdPzvLw87Nq1C6GhoWjcuDHS0tLw7rvvokWLFmjRogXeffddBAYGYtiwYS4sNREReTydzlAjZKl3nRCGxPK0NEOzogc1mQm9wLZvDkL733PQbmuEfSUtADQxrW/jfxiajgVIfb4B2v4lDiov50yZ4UguD4a2bduGlJQU03Njrs+IESOwYMECvPrqq7h58ybGjBmDy5cvo1OnTli5ciWCg4NdVWQiIlICBY3KffvabeTM3gNtxg0sOdgCp/WJABIBAN4oRbc6e5HasxgPj49F065xAOJcWl6pyWqcIUfhOENERGS3jAzAllaI9HTgiSccXx5A0kTuopNFWD5jP7Ra4Of8lihGiGldEK7hoUZ7kTpIj/4TExEaW1eqM7ALxxkiIiLlkGNvLVtH2z571lB+R5dXgkTuU1sLoJ3xB7SrayH3UivcwQOmdRFe5/DwPYeg+UsAeqW1gn+dzlKfgWyxZoiIiFxLrr21qhqVuyxHl9daIrdxmBkridxCL7Bv8RFkzz0D7W/1sf1Gotn6eL9j0NybD81fw9Dpry3h5ePyWbrMOOv+zWCIiIhcp5o3eacxlg+oPCByZHmNQZm1/KVyU6WU3irFxvn7kP1VEbR7Y5BX2vjuptCjc/A+aLpegualxojr10zaskqMwZCEGAwREUlMimYtO2/yLmOp5soSR5U3Nxco09HImvVDP8Znv7fGsrxEXBKhpuVq3ELv+nugeagEgybFIyKpnnRlczBn3b/lVR9GRETyl5VlCGJSUgwJxikphudZWfbtx57eWq40eDBw/Djw0UeVb+eo8hYU2LTZ3O/r4uv/dcUlEYpQ1SU83WwDMif9hgsFpVh6tiOe/SrZrQIhZ2ICNRER2U7KQQhtvMnbvJ0jeXsDlcx8YEbq8tqayO3lhbQ2a6F5OgRdn0+Cj3/Xql9DABgMERGRraQehNDWm7yt2zmaC8qrL9Xj9z/qIt6vHmrfvgAvVLz2AsCdsAZIL3gUKl/e1quDzWRERGQbqZu1kpMNOTbWJt5WqYDoaMN2cuCk8t66cgvLp23Fcwnr0Eh9Hp1Ht8Ffb88DAOhR7tgqFVQqFfw+/ZiBUA0wGCIiIttI3azl7W3ojg5UDDCMz2fNcv14Q0YOLO/lvCv49oWNGBK1GeF1SzFgagf891A3FOojEIxi+EU3wMZ+b1esdYqKcn2POw/AMJKIiGzjiGaiwYMNN3NL4wzNmiW/m7yE5T2x8RS0Hx5D9praWHelFXS4O8lppFcBNAlHoHkiED1eagV17QcAPADoXpPf4JQegF3riYjINlUNQliTruVyHIG6MtUor9AL7PrhMLLnFUL7e0PsvmU+v1eS+gg0952G5m/10f7JeNkNgOgKnI6DiIjkxdhMNGSIIfApGxDVtFnL29u9Jju1sbx3btzBuo/3QvvtVWj3x+KkLh5APADACzp0DdkLTfcr0IyLQWzPFgBaOLTYsiKjAJjBEBER2c7dmrVc4OqZq1jxwT5oF+vx04mWuCLamdYF4Ab6NtwDTf9SDJyUgPC4tq4rqCvJbAoWNpMREZH9ZPSrXg4Kdp3FkhmHkb0yAGsutMZtqE3rwlUX8HDzg9A85ocHx7dCYHigC0sqA3ZMwcLpOCTEYIiIyAPIKAATeoGDy45B+/EpZG8Mx+/Xk8zWN/c9jtQ2x6EZFYrOz7aEt59yA0Uzdk7BwpwhIiJSHmsBjwyaVXS3ddj82X5ov7yE7N1NcfROcwDNTes7Be2DpssFaMZGIWFgLFReTe3YuXwCPYeyZ6wqJ+aQMRgiIiJ5sBbwPPEE8MEH0kwBYqebl25i1cw90C68jaVH43FetDat80MJetXbA03vmxj0yj2IbJdUyZ4qIYNAz2lkOgULm8mIiMj1rOWRVMUBM8VfOHwRy2YchHa5D34paI2buJvjE4IiDGy6D5pHvPDQxCQERwZb3omtNT125M94hNxcw8S+VcnJAXr0YM6QlBgMERHJWFV5JLb48+Zp2p+dTU7H1pyAdnYesnPrYmNxEvS4u32092mktjwKzVPB6Da2FXwDfSsvi601PXbmz3iEqsaqAoCwMODsWeYMERGRglSVR2ILY7OKjYGIvlSP7d8dgva/55C9rRH2l7QA0MS0vm3AIWg6FkIzugHa/iUOKq9GtpXDWk2PpSY9mebPOJRxrKpHH7W+zcWLgFbr1BoxBkNERIByEljlSIr8kIYNqwxE7nzzPdYcbwZtxg1oD7bAGX0igEQAgDdK0a3OXqT2LMbD42PRtOvdwRFtptMZAjFLNR5CGGp60tIAjcbw2ZJp/ozDaTSG2p+LFy2vL3udnITBEBGRkhJY5cieuczKMzYlPfAAEBtrNRDRAzj71AT0xwlTE1gQruGhRnuROkiP/hMTERp7b/XLAdhf0+OIud7cwfr11gMhwPw6tWtnfTsJMRgiImWzp1mDHCM52RDQVJZHAlQ+BcimTZUGIl4AonAaGtUS1IsLg2ZoAHqOawX/Op0lOQUA9tf0VHXexkAvOVm6MsqBDGvEOAscESlXVc0agKG6XqdzarEUx5hHAtwNcIxUKsNj0iSgUbm8nagoYNEiiNRHcDJ7h02HWvT1Dcw/2A393+oA/zr+EhS+DHtreqo6b6D6c73JmQxrxBgMEZFy2dOsQdLT6QxdrTMygNBQ4IcfrAY8+Ne/gOPHDb3G0tOh++VX5KYtxvi3wxCrzsfTs21rTvGKsjERujqMNT3lAxsjlQqIjjav6THO9WbtvD2xVrI618nB2ExGRMrl6up6JSdtW8vT+ugjIDzc4jW5fvEWflnuD21mNJblJeKSCDW9tBBhOO9VH+H6c7B4i3VGk5OxpmfIkMqb9Mq/x4MHG5KFlfJZqO51ciShAEVFRQKAKCoqcnVRiEhOcnKEMPxXXPkjJ0f6Y2dmChEVZX6cqCjDckcpLTWcS3q64W9pqeOOVZnMTCFUqorXWaUyPMpcg8K958R/n14nBtbfIvxxw2zzUNVF8XSz9SLr1c3i2tlrd/dbft8W9uvw8yv/3kZHO+/47sKG6+Ss+zcHXSQi5apqADhHDXrnilGH5dJjzoaBBu+ENcCs+75B9sZ62Hw1CaJMRkeMz0loWuUhdUQIuoxOgo9/uQYOS+cZHW2oaXD2eSqlpqcmqrhOHIFaQgyGiMgqY2ACWK6uNwYmUt3cXDHqsJymfLBxOoYeyMFa9AAAtA88gNTO56B5IRJJj7SAystKrokRAxGPwRGoiYicwZjAaqnWxFibIGWtirNHHbZ3IEBHszH/qk/QRjw+UIWHX7kHUR3uDo5oE29vzxmxmZyCwRARUWUJrFKPQ+TspG0ZTflw6dhlbMu4gD42bPv3ZV2AHt0dWh4iIwZDRESA5doER9SqOHuMFRf3mDu+4RS0Hx6DNqc21l1pBYExOI5/oRFOwwsKGmiQZI3BEBGRNY6oVXH2qMOOCL4qyckReoFdPxxG9rxCaH9viN234gBEmV6apD6C9TF/wxOHpkKoVFDJoVs1KR6DISIiaxxRq+LsMVakDr4s5E+JRo2wt2ca/rurA5YciMVJ3d1JTr2gQ9eQvdB0vwLNuBjE9mwB4P+ArKTK87SInIjBEBGRNY5q0rIlaVsqUgZfVvKnxOkzSPrmVZzGIpxEdwTgBvo23ANN/1IMnJSA8Li2FfeltIEGSdbYtZ6IyBpHj0PkzC7gNR1/R6eDLjIaXucKLI7wrIcKl33qYePExXjwlbYIDA+UquSkYOxaT0SexR3HfnF0k5Yzu4BXoyZG6AUOLjuG7DmnkL8+D5/cst4c6AWBsNJzeLjvbYCBELkZBkNE5HhyGf24OpzZpGWP6gSXNgRfuts6bP5sP7K/uATtnqY4eqc5gOYYChfP4yYn7hjYU6VkHwyVlpZi6tSp+O6771BYWIiGDRti5MiReOONN+Dl5VX1DojItaQep8cV5JbfInFweePCDaz6cC+0i25j2dF4nBetTev8UIJe9fbgidbngNU27EyqIQHkyp0De7JK9jlD77zzDj766CN89dVXaNmyJbZt24ZRo0bh7bffxrhx42zaB3OGiFzEFVNPeDqJptY4f/ACfnp/H44uOYD8y4E4gaZYj2To4Y06qisY0GQ/NI944aGJSQiODHbdPG5yIqdpTRSCc5P9aeDAgYiIiMDnn39uWvboo48iMDAQ33zzjU37YDBE5CI2zkOFnBxOn2CLGgaXR1efgHZWHrTr6qJ+8RF8hPGIxt19Xfath1PDXkX83HHwDfStuH9b53Gz53zkUttWFQb2LuGs+7fs25m6du2K1atX448//gAA7N69Gxs2bED//v1dXDIiqpKLRz92OJ3OEPBlZBj+6nSOPZ49g0AC0JfqsfWrA3i9Sy6S/I+gxYNNMHFZD4QXH8OPeByNYL6vuqUX0OrrV+G7Yqnl/Rvzpxo1Ml8eFWV/IJSVZQguUlKAYcMMf5s2NSyXIzuvPbkX2ecMvfbaaygqKkJ8fDy8vb2h0+nwzjvv4IknnrD6mpKSEpSUlJieFxcXO6Oo5Cru9OtSaZw99YQzuSJ3xMagcffcjZg31gtLDrXAGf3dSU69UYqUOjvxVcnzUN0UFbvI2zLFiBT5U+6YR+bpgb3SCZnLyMgQUVFRIiMjQ+zZs0d8/fXXIjQ0VCxYsMDqa9566y0BoMKjqKjIiSUnp8jMFCIqSgjDf6uGR1SUYTm5Xmmp4f1QqczfI+NDpRIiOtqwnTvJzLR8TiqV4eGoz19OjuXrWO7RHTmmp7VQLIY02iS+eX6DuHj0ks37EDk5jjkH42fC2nHl+plw9XVTqKKiIqfcv2WfMxQdHY3Jkydj7NixpmVvv/02vv32Wxw6dMjiayzVDEVHRzNnyNMwmdE9SJ1n4mquzB2pIolZDxVOIQqdVb9hYNxRaIYGoOeLifDfu/VuLc7p08BTT1V9rPR0oJIa+Gpz1zwyJpC7BHOG/nTjxo0KXei9vb2h1+utvkatVqN27dpmD/IwVc0mDhiq+h2dw0FVkzLPRA5clDsi9AJ7Fh/Dwjp/g14YAp+y9FBBBYGbL0xA/u0GmH+wG/q3yod/23jzvJy0NNsOaG/Tpa35U+7a3GQcgBO4G8gbcYJZtyf7nKFBgwbhnXfeQePGjdGyZUvs3LkTH374If7617+6umjkSo6YTdxTySGnSm7j9NSEE2/mpbdKsWHePmi/LkL23mY4XnoPgP/DI0jCbIwz6wnmFW0YBDLOGFxaqzm9cKHqA4eGGj43Op3tc5bZmj/lznlkch2Ak2rOoY1wEiguLhbjxo0TjRs3Fv7+/qJZs2bi9ddfFyUlJTbvw1ltjuRE6em2td+np7u6pK6l5Jyq0lJD/kZ6uuGvVDkoDs4duVpwVWRO2iyGN1svQlUXzXbpjxtiUMRv4rMR60ThrgLr51dVXk7Z/JzK1tvyWbE3f8oT8sgc9dmiCpx1/5Z9MCQFBkMeiMmMVXNVkq8cODIIdMDNvHDvOfHfp9eJAfW3CDVumu0uTHVBjIhdL7Je3Syunb1m2w5t/X7Uq1d1sFTZZ6W6ydDGz2b5a6iEzybZhcGQhBgMeSBP+HXpSO7aY0cKzggCJbiZH1p+TLzfL0d0rrVHqKAz200zn+NifLsckTtrp7hz84795bO15vTbb4X49VchQkOr91mpyY8SSwFrdDQDITLjrPu37HOGiCxy9Gzi7k6pOVW2JtZbG0PHVtXIHdGX6rHli/3QfnER2Tsb4/DtZgCamdbfF3gAms7noHkhEkmPtIDKq0n1y2drvo0xqf3SJevbVPZZqUn+lCflkZHbsysYys/PR3R0tKPKQmQfJjNa5649dmqqqiAQkC4ItOFmfuvKLayetRfaH25iyR/xOKtvZVrngzvoGbYbmgev4+FX7kFUh7uDI9ZYcrLhe1BVN/DkZODHH23bp6XPiq1BV/36lpd7e3tWME5uy65gKD4+HhMmTMDkyZMRFBTkqDIR2Y6/Li1z5x47NXH6tG3babXS3IQt3MwvHbuMn2bsR/ZSH/xyJgnX0cG0rjaK0L/xfmg0QL+JLRHS+L6al8FauWytOa3JZ6WqoMto5EjO6k7yZk+b2saNG0XHjh1Fw4YNxRdffOGopjvJMWeIFEeJOVWZmUKEh9ueOCzhueetzxezHskVPersEN64Y3aoRl5nxJikXPHLu9tEyVXbe8FKwpa8HFt6nlX2WbGWP8XEaJKArBOov/rqKxEVFSXatm0rctygtw6DIVIkJfXYsZY0bW9Sr430Or3Y/u0B8X/dckQb/0MVdp2k/kO80TVHbP1qv9Dr9JKdZrXY0g180qTKr9WkSZUfIzNTiEaNKt+HJwbg5HCyn47j5s2bmD59OmbOnIk+ffpgxowZaN68uZSVVpJx1nDeRLJjaTC86GjPyqmqanoMa+ycbuLOjTtYO2cvtN9ehfZAc+Tr7o6o7QUduobsRWqPK9CkNUOzHo3tK4sr2XL9oqOrnmZi9WrgwQerPp7cptlwV3IYTNUJnHX/rnZvMiEE+vTpg6tXr+Lf//43fv75Z4wdOxZTp05FcHCwlGUkoupSQk6VLUnTltiQK1N8qhgrZu6DdrHATyeSUIR2pnWBuI6+DfdCM6AUAyYmIDyurf1lkAOpks7PnbPteJ6WtO8K9oz4TTaxKxiaN28etm7diq1bt+LgwYPw9vZG69atMXbsWLRt2xbfffcdEhMTsXjxYtx3n4MSA4nIPp7eY8fem2vZnlQWnNlRiCUf/AHtqgCsudAat/GAaV091Xk83OIQNI+r8eD4VggIvb8mJZcHqXoeKjVp39msTbNy+rRhuTvO9ycDdjWTRUdH4/777zc97rvvPqjVarNt3n33XaSnp2Pfvn2SF7a62ExGHsNdq8YdWW5bZ0EH7vakKnPDEHqBA0uPQfvxKWg3heP360lmL2nhm4fUtiegGRWK+59pCW8/N7je9pBqFnnO6u54VTVpeuA1dtr9W+okpMLCQuHl5SX1bmuECdTkEdx1njFHl7uqnnMWelKVlpSKdf/ZJV5pnyOa++ZV2KxT0F4xvW+OOLD0qOsToB1Nyp6HSkradwUFTkPktiNQ169fH2vWrJF6t0TK5q5V484od2Vj6hilpeFWj774ZXNtaCfrsHTIZVwQbUyr/VCCXvX2ILXPTQyaGIeGbZMq7sNTSTmaOwdCdSylDqbqBNXuTeZO2ExGbs1dq8adXW4LSaW6Bo2wNuF5/Ptgb6wsbIWbCDStq6O6goFN90HziDf6vpKE4EgbO364a1NlVaTseeip18jVpGrSdCPOun8zGCKSO3f9D9AV5dbpcHrWQuz6bj9+OdwEn9x4GqXwM61u7H0KqUnHoBleG8kvJME30Ne+/Xt6Lx4GMfKmwLws2XetJzfF/+zcT02qxl35fjupSl9fqse2bw5C+9l5aLc3wv6SoWbr2wYcgqZjIVJfaIg2j90DlVdU9Q7krk2V9vD0nofujhNUOwyDISXx9F+1nqq6XZZd/X47sKt1SXEJcv69F9qMG1hyqAXO6Fua1nmjFN3r7kFqz6t4eHwsmnSJBxBv9zHM6HSGa2np17gQhhtRWpphTCfeiMiRmJflEGwmUwprv2otdDUmmalO1bgc3m+Jq/SvnCjC8n/tg3apCj/nJ+Eq7n6Xa+EqHmq0D6kP69F/UkvUjakj3XkA7ttUSZ5LIbX8bCYj6fBXrXuzt2pcDu+38T/qIUMMZSvPxir9/C1noP3gCLRraiH3UmuUootpXQOvs3j4nsNIfSIAKS+3gn+dztKeQ1nsxUNywyZNSTEYUoKqhtsXwrbh9sl17Kkad/X7bal5ztvbECAZWanSF3qBvVlHkD33DLS/RWDHzQQAkab1CX7HoGmXj9Rnw9FhRCK8fCKkL78lch9dWSG1BESOwmBICZTwq1YJNwNb5xlz5fttrXlOrzf8HTIEiI83BGF/BmKlt0qxfu5eaL8phnZfMxwvvQfAPQAAFfR4IHgfNMmXoHm5Ce7pGwsgVvpyVyU52RDAVdXkZ2WKD4dydW4YkQdgMKQEcv9VW1NKuhnYUjXuqve7quY5wFC7BQBvv40bterjs6CXMe3cC7gk7jVt6o+b6B2xB5qHbmPgxHhEJLWWtpzVIddePJ7ew00JP3JIFphArQSePDaFHBKF5cZV77c9c4QB0MPwHg3BIqxTdcfAZgeR+pgveo9PQlD9IOnKJSUpByasKXcdjNNWSvqRQ1Zx0EUJKT4YAu4GDYDlX7XuGDR4+s2gJlzxfmdkAMOG2fUSAaCkTgR8Tp2AT5C6yu1lQS61FZ7cw40/cuhPzrp/ezlszyQvxgTcRo3Ml0dFue9/LPYkCiuNK97vajS7qQD4XzkLn62bpS+PoxibKp94wvDXVYG2p+YC2tLcmpZmnpBPVEPMGVISWxNw3YWn3gyk4qT3+9aVW/j1wz1Y8oPAVDREAxTCC3ZWOCv1PaoJT80FdHVvSFIkBkOOIpeq9PI8aWwKT70ZSMlB7/elY5fx04z9yF7qg1/OJOE6OgIALmAOFmEI9LCz2lnJ71F1ybmHW03wRw65AIMhR2Din3N46s1Apo5vOAXth8eQnVMb66+0gg5dTesaeRVAk/gHNMOaQNf4e/hOfqXyX/dGfI+qT6493GqKP3LIBZhALTUm/jmXuyaGy7XmsAyhF9iZcQjZ889Cu7Uh9tyKM1vfyv8PaO47A83f6qP9UwlQeanurix7fkeOAG+9Zf2GLdf3yF3IqYebFDy59yvZjb3JJOS0YIi9m1zD3W4GMq45vHPjDtbO2Yvsb69iyYHmyNfdTcD2gg7JIXuh6XEFmrRmaNajse07drf3yN24QXBtF3f9kUOSYzAkIacFQ57c1VXuHHkzkHLfMqw5LD5VjBUz9yF7scDyE0koQohpXSCuo2/DvdAMKMWAiQkIjwu7+0J7r4un3bDJsRhAExgMScppwZCt46ykpxu65ZL8SVmLI6OawzM7CrHkgz+QvTIQay62xh34mdbVV53HoBaHoHlcjQfHt0JAaEDFHci4dos8CANoxeOs9e6IiX+eReqpDlzYZVjoBQ4sPYbsOaeg3VwPW6+3BNDAtL6Fbx5S256AZlQo7n+mJbz9Kklo9vQpIEg+PKn3K8kagyEpsXeT56hq4DeVyjDwm0Zj+y9VJ3cZ1t3WYdOn+5C94DK0u2NwrLQ5gOam9ffX2gtNl4vQvBiN+P7NoPKKsWGnDrguREQuxmBISu7U1ZXVz5VzRC2OE2oOb1y4gVUf7kX2wttYdiwBF0Qb0zo/lODBenug6XMTgybGoWHbVvYfgAPiEZEHYjAkFWNwUVICTJ0KfPqpoYbIKCpKPol/zPeomiNqcRxUc3j+4AUsm3EQ2T/7YVVhK9xEJ9O6OqorGNh0HzSPeKPvK0kIjuxg174r4IB4ROSBGAxJwVpwMW0a0KKFvGpeXJnv4U61UY6oxZGw5vDo6hPQzspD9rq62FScBD3uBlCNvU8hNekYNMNrI/mFJPgGdq1kT3ZiXhwReSD2JqspGXaVtsqVvZncrTbKkQO/VaPLsL5Uj23fHIT2s/PI3h6FAyXNzdbfG3AQmk5noXm+Ido8do/5AIhScsaAeDUNmt0p6CaiSjmtN7hQgKKiIgFAFBUVSbfT0lIhfv1ViNBQIQy3hYoPlUqI6GjDtnKQk2O9rGUfOTnSHjcz03AtLF0flcqwXo6M5S5fdinKXVpquM7p6Ya/Fj4jt4puiZ//uVU8n7hWNPQqMCuCN+6IXnW3i38/miuOb8ivfjmqw5HXJTNTiKgo8/1GRdm+z5q+nohkxSH3bwsYDFWHpf9wnRlcVFd6um3lTU+/+xobbtqVKi2t/FrJLWAsz9J7HR3tsJvr5eNXxHdjNojHozeKYBSZHbYWisVjUZvEty9sEJf+d9khx7eZI65LTYNmdw26icgqBkNlnDp1Sjz55JMiNDRUBAQEiDZt2oht27bZ/HpJL6a1/3BtDS5cado0+4I3KX5lu6o2Sko1DQircPK30+I/Q3LFg6HbhA9um12WBl6FYnTCWrF82u/iVtEt6Q4qxTlJeV1qGjS7e9BNRBY5KxiSfQL15cuX0aVLF6SkpODnn39G/fr1cezYMdSpU8f5halsjJXKyCGZNCvLMFlmZcr2ZpIq0dre3kdyzPeQeOA3oRfYs+gPaOcVQPtbBHbcTAAQaVqf4HcMqe3zoXkmHB1GJMLLJ8L2ndty/aTK35LyutS0yz67/BNRTTg01JLAa6+9Jrp27VqjfUgWWdpayyG3X6NV/WouW97MTGl/ZdtTM+TB+R53bt4Ra2buEOPa5oqmPifNLyd0okvwbjFjQI74Y2Ve9Q9iy/WTa1OSrU24aWk1e71cammJyCZsJvtTQkKCSEtLE0OGDBH16tUTbdu2FZ9++mmlr7l165YoKioyPfLz86W5mLb+hyuHm0tZtgYk06bZt70tTVvGwMpa06IxsFq4UJ436Rq4WnBVLJq4SQxvtl7UVV0yOy1/3BAPN/hNfD5ynTi771zND2ZLkCPnpiR7fmhY+ix4QnMsEVXAYOhParVaqNVqMWXKFLFjxw4xb9484e/vL7766iurr3nrrbcEgAoPp9YMOTDJ1m72/mqW+ld2ZmblAeOPPzr/Ju2gPKCC3WfFp8PXigH1twg1bpqdRpjqghjZfJ1YPPk3ce3sNUmOJ4SwPcj59Vf5BgxVBc3lv1vl3y9bg25HBnoOzi0jUiIGQ3/y9fUVnTt3Nlv20ksvifvvv9/qaxxWM2TLf9ihoYabjpz+I7T3V7PUv7IzM4UIC6v4+rAwwzpn/6qXuDnu4E/HxHsP5YjOtfYIFXRmu23mc1xMaJ8j1v57l7hz84405S/P1uv3xhvSBrlSsxY02/pZcGSXf1vK7qFNvESu5KxgyMs1mUq2a9iwIRITE82WJSQk4OTJk1Zfo1arUbt2bbOHJIwjCAN3B1U0UqkMj//+F+jVy/VJv2UZp4EoX2Yjlcow6J9xGgh7t6+MMRH74sWK6y5dMvy1Ncl69WpDgnBNGMtTPtnWmBielVXlLvSlemyavxevdcpFnF8eEgY0w+QVPbD5WisIeOG+wAN4+8Fc7M06gqMljTFzWw90e6kNfPwd1F9B6qkvXJXwP3iwYZJXW1g658GDDYn9jRqZL4+KcuzgpxJ8pojIxRwaakngiSeeqJBAnZaWVqG2qDJOGWdITs1iltj7q1mKX9m2Nt+sXGl7jUBNfm3XIGfmxsUbYumbW8SzcWtFfdU5s5f5okT0Cdsq5g5dK05tPVO9stWErTVDv/7q+qYkqc6lslpCZzZXyTkPi8gDsJnsT7///rvw8fER77zzjjhy5Ij47rvvRGBgoPj2229t3ofDRqB2t/wAe4O4mgZ9tt7YZs60PRiqSZOHnTfaC39cFF/9bb0YHLlZBOGq2Sa1cUUMbbxRfP/yRnHlxBX7y1Jdlj539uTLuLIpydbzk3vAVhYTt4kcisFQGUuXLhVJSUlCrVaL+Pj4KnuTleesi+kW7A3iahL02ZqI/eKLtgdDNbkh2lie5fe9KXrU2SG8ccdsVSOvM2JMUq5YOX2bKLlaYt+xpVBZXoo9QY7cazblHrCVxS79RA7lrPs3J2olx8nNBVJSqt7uo4+A8ePt339Ojn0D6NlYnh7IwVoY9tvK/w9o7juD1NERaDcs3nEToFbFlgmBAdsngJXj4JZlVWMyW5ew9TNu72eViAA47/7NYIgcx9YZzo8eBWJjrW9nTXo68MQTdpdHnD4NlYXj6KHCKTTCyNrZeLjnNTw8LgbNejS2ff+OYryO1kZYLjtTPCDvIMcecg/YANs/43l58is7kRtw1v1b9tNxkBsz9r4bMsRwUyh7szDWaMyaBfj5Wd+uMnb0eio+VYyfZ+zDmZIXME68AQEVvHD3OHoAKgjU/c/bWPNie5v36xT2TjXhKTUQEk+D4hC2fsYZCBHJmuy71pObs7W7s7XtLLGxa//pbQX45Il1eCh8G8Kj/TH03w9gwvm/YwgWoQDmgZRXdDRUmZkIfnGEPWfnHPbO70bO5aou/UQkGTaTkXPY2uRh3E6rNfyitvZr28JNRugF9muPQjv3NLSb62Hr9ZZm6+/xzYOm7QmkPhOGTk/HwXvLJnk3wRgxL8U9uEOzHpGbYc6QhBgM2UFO/6HbkESru63Dxvn7oP3qMrS7Y3CstInZLu6vtRepXS9C81JjxPdv5sTCS4h5KUSkUMwZIudbtAgYMwY4f/7usqgoQ06EK6r6Bw8GNJoKwdmNyyVYOWULtItuY9mxBFwQbUwvUeMWetXbi9SHbmLQxHg0aN3K+eWWGvNSiIgcijVDZPDqq8CMGZbXqVQuz304f/AClv7rILQr/LCqsBVuItC0rq7qMgY03Q/NI97o+0oSgiODXVZOh3KX7uZERBJhM5mEGAxVYeFC4PHHK98mOtrpzTBHVh2HdvZxaNfXxabiJOhx99hNvE9Bk3QMmuG1kfxCEnwDfZ1WLquc0cQop2ZMe7hruYnIpRgMSYjBUCV0OqBBA+DChaq3dXCCrr5Uj23fHET2f89DuyMKB0qam62/N+AgNJ3OIvWFhmg95B7XDYBoiaVaG1c2McoJrw0RVRNzhsg51q+3LRACHNJ1u6S4BDn/3ovs9BtYcvgeFOjv9gDzwR10r7sXmp5X8fD4WDTpkgAgQfIy1Ji10aGNs5YruXs1rw0RuQEGQ0pnT4BjxyCHlblyogjL/7UP2Uu8sOJUS1zFfaZ1tXAV/aL2QTNIj/6TWqJuTDtJjukwOp2h1sNSBasQhnyrtDRDIrjSmoV4bYjITTAYUjpbA5x69aoc5LAyJzefhnbmUWjXBGPt5VYoRZe7RfAqxMNxf0AzNAA901pDXbtztY/jdPaODq0kvDZE5CYYDCldcrIhf6OymxYAzJ1r1693oRfYs+gPZH9SAO2WCOy8mQDg7gi9ieqj0LQ7Bc0z4egwIhFePg2qeQIuxtGhreO1ISI3wWBI6cqOYWMtl37SJMP6KpTeKsX6uXuR/XUxtPticUIXByAOAKCCHl1q74Um+TI045qiRe/mAJpXuj+3YGvNmkRNjG6F14aI3AR7k5GBpR4/9eoBH38MPPaY1ZddK7yGX2buRXamDj8db4nLoq5pnT9uok+DPdA8dBsDJ8ajfst6jjwD1+Do0Nbx2hBRDbE3GTmXldGeLd2kCvecw9IPDiF7RQBWn2+FEtzN8QlTXcSg2APQDPFD7/FJCKrfSboyynGsGo4ObR2vDRG5CdYMkU0OLf8fsv99EtqNYdhyrSUEvEzrYn1OQNMmD5oRdfHA31rCx98BMbbcx6px5OjQcgwC7cGRs4momjjoooQkuZjufkOyk+62Dlu+PIDszy9Cu6sJ/rgTY7a+Q9B+aDqfh2ZMI7TUNHfsAIjWxqqpZAZ7l3DEZ0TuQaCtFPb9MVHqeRNJhMGQhGp8MT3lhlSFm5duYvWsvdD+eAtL/kjAOXE3x8cXt9EzbA80vW/g4VdaoNF9Tkp6NeadWOvt5sl5J+4SBJJlCvl/g8iRGAxJqEYX09q8XR5yQ7p45BJ+mnEA2ct88EtBK9xAkGldbRRhQJN90GhUeOiVlghpHOL8AubmAikpVW/n4KlCnE7JQaAnYCBLJAkmUMvBokXAE09YXufGI+jmrcuH9qP/ITsnBBuKkqBDV9O6KO8z0CQegWZYLXR/sRX8anWpZE9OoNSxajhgofviyNtEbofBkDVZWZV2KQfgNjckoRfYkX4I2k/PIntrJPbeugdAtGl9a//D0HQogOa5CLQbFg+VV6TrClueUseqUWoQ6AkYyBK5HQZDlhh/2dnKlTckKwmat6/dxto5e6FNvwbtgRY4pbs7yakXdOhWZw80PYqhGd8MMd3uDo4oO8YRsqsaq6YGU4U4XHWSaJUaBHoCBrJEbofBUFnGm9bq1VVPT1GWq25IFhI0b9Sqh/kBaZh2fiyK0N60PBDX8VDkXmgGlGLApESEtbjXFSW2n7uPVVPdJFpPCAKVioEskdthArWRpZuWLaKjXZPE+meCphACZTu16/98NgSLsFGVjIfvOQjN4/7oldYKAaEBzi2jlNxxrJqaJtEaXw9YDgKZhCtPHHmbSDLsTSahKi+mtZuWLTIznXpDEnqB/VmH0fipbqhVcr7M0IdltgFwu24D+Jw+Ae8AP6eVzeHcacwWqXqDuWMQSAxkiSTCYEhClV7Mqm5a1nh7AxkZVSdZS0B3W4eN8/dB+9VlZO+OQXRpHnKhwO7m7kTKIQHcKQikuxjIEtUYu9Y7S1U9P6z5/nubZnKvrhsXbmDlzL3QLrqNpccScVG0Ma3rglzbdsIETXPODCqkTKL19mZQ647smO+PiFyLwZC9AYMDf9md238eyz44BO0KP6wsbI1buDvJaV3VZQyM2Q/NYG/071wfeNSGHTJB8y5njwbMJFoCGMgSuQkGQ7bejN54A+jVS/JfdkdWHYd29nFo19fFxuJWELjbO6iJ9ymktjoGzfDa6Pp8EnwD/xwcUadjTyN7WMsJO33asNwR+RvsDUZE5DaYM+Tknh/6Uj22fnUA2s8vQLsjCgdKmputvzfgIFLvPwvN8w3Resg91idArW6CptLyT1w5rQWTaImIasRZOUMQClBUVCQAiKKiIssb/PijEIbblflDpTI8MjNrdPxbRbfE8mm/i9EJa0VDrwKzQ/jgtuhVd7v4z5BccWLTKft2nJkpRFSUeZmjo62X19L2UVE1Pj9Zy8mx/N6Wf+TkOOb49r5HRERkUuX9WyJsJsvKAiZMsLwuKqra+UGX865g+Yz90C71ws+nknANHUzrauEq+kXtQ+rDevSb2BJ1Y9pVr+z2JGi6oqlIDlw9GjCTaImIZE/ZzWRVjS+0cKFdPcZObj4N7cyj0K4JxtrLrVAKX9O6hl6FeDjuD6QOC0TKy62grq2u7unYT8kzoCt11nsiIg/AcYYkZPFiShAgCL3A7oV/QDuvANotEdh5M8FsfaL6KFLbn4Lm2Xq4b3gCvHwsDZHoBEoOCDgaMBGR2+I4Q45WzZml79y4g/Wf7IP2m2Jo98XihO7uJKcq6NGl9l6kdrsMTVoMmvdqDqC5xd07laubilzJ3ec2IyIih1NuMGRHgHD1zFX8MnMftIt1+Ol4S1wWdyc59cdN9GmwB6n9bmPgpATUS2hTyc5cROlj3gwebMiJsjTOEEcDJiJSPOUGQzbe+Ce/UISPivxwG51Ny8JVFzAw9iBSH/ND7wmtEBjeqZI9yICrxryRUzd+JjITEZEVLkpiqb7p06dDpVIhLS2tZjsyBggqy+P46KHCSURjRtHfcBtqxPqcwIT2uVj3n90ovFUXXx5JhubdTggMD6xZOZzB2FQEVDxfRzUVZWUZcnVSUoBhwwx/mzY1LHcV42jATzxh+MtAiIiI4GbB0NatW/Hpp5+idevWNd+Ztzd0Mz8yDPxSbpUeACCwwacHFrT7D/ZlHsaRksaYua0Hkl9sA2+/MjdRnc6QoJyRYfir09W8bI5gbCpq1Mh8eVSU9N3qjb30yudkGbvxuzIgIiIiKsdtepNdu3YN7dq1w9y5c/H222+jbdu2mDVrlk2vLZuN7lvqi18/2gvtjyVYeiQeXcR6zMY4ROPujVuv8oKX0N/dQXg4MHduxRnqnT3flRQc3XSl5G78REQkKXatL2fEiBEIDQ3FRx99hB49elQaDJWUlKCkpMT0vLi4GNHR0RgY8SvWnL0fNxBkWheCIgxovBvP3LcHXeoehPrzudYLMWkS8K9/Gf5tbYwipU+1oORu/EREJCl2rS/j+++/x44dO7B161abtp8+fTqmTZtWYfmysx0ABCHK+ww0iUeQ+lQwuo1Jgl+tboCui6FGozIzZgAdOwKPPGKoEbIURwphCIjS0gwJu0qr/VByN34iInJLsg+G8vPzMW7cOKxcuRL+/v42vWbKlCmYUGaKDWPN0Kud1+MvY5vh3ifiofKKNH9RVeMOGY0ZA9Sta/sYRcnJyurBpPRu/ERE5HZkHwxt374d586dQ/v27U3LdDod1q1bhzlz5qCkpATe5YILtVoNtbridBevr0i2Xs1ma03F+fOGpiBbaLXA8OHulVNUU67qxk9ERFRNsu9N1qtXL+zduxe7du0yPe677z48+eST2LVrV4VAqNocUVMxa5byelS5ohs/ERFRDcg+GAoODkZSUpLZIygoCGFhYUhKSpLuQMnJhl5jtujRo9IxiqBSWb/ZG2tL0tLk2w2/pqx14w8PN+RahYZ67rkTEZHbkX0w5DTe3obu81WJjjYEQ5XVfghR+c2+bE6Rpxo8GDh+3NBrLC3NEAidP2+oFZLDAIxERER/cstgKDc31+Yxhuzy2GOG7vPWqFR3m3gqG8TQ1tGxPb1Hlbc3cOmSIXC8cMF8nac3FxIRkdtwy2DIof71L2DhQqBePfPl0dEVxw4qW/uRnm74m5dn6FJvC0/vUaXTVT4EAeDZzYVEROQW3GbQxZqo1qBNNRmp2TgKc1U9qjx9FGYOwEhERDXAQRddzTipZ3VfO3u2oRnImENkpKQeVRyAkYiI3ACbyRzFmROjyhUHYCQiIjfAZjJHc/TEqHLG5kIiIqoBNpN5ipo0t7k7NhcSEZEbYDMZORabC4mISOZYM0SON3iwYbgBpTYXEhGRrDEYkpqSc4Qqo+TmQiIikjUGQ1LKyjIMMqikWeqJiIjcHHOGpJKVZUgUVtos9URERG6OwZAUOO0EERGR22IwJIX16yvWCJWlhFnqiYiI3BSDISlw2gkiIiK3xWBICpx2goiIyG2xN5kUkpMNvcaqmnbigQcMM7mz2z0REZFssGZICsZpJ4C700wYGZ8PHQrExgIpKcCwYYa/TZuylxkREZGLMRiSSmXTTkycCHzwAbvdExERyRBnrZda+RGoH3jAUCNkrbcZZ24nIiKyiLPWu6vy007k5tre7Z7TVRARETkdm8kcjd3uiYiIZI3BkKOx2z0REZGssZnM0Wztdp+c7PyyyVn53CsOQ0BERA7CmiFHs6Xb/axZvNGXlZVlGHaAwxAQEZETMBhyhsq63S9aZFhPBllZhuEGOAwBERE5CbvWOxObfiqn0xlqgDgMARERgV3rPVP5bvdkbv16DkNAREROx2Yykg8OQ0BERC7AmiFHYZOY/TgMARERuQBrhhyBvaGqxzgMQfled0YqFRAdzWEIiIhIUgyGpMbeUNXHYQiIiMgFGAxJSacDxo2zPLiicVlammE7sozDEBARkZMxZ0hK7A0ljcGDAY2GOVdEROQUDIakxN5Q0uEwBERE5CRsJpMSe0MRERG5HQZDUmJvKCIiIrfDYEhK7A1FRETkdhgMSY29oYiIiNyK7IOh6dOno0OHDggODkb9+vWRmpqKw4cPu7pYlRs8GDh+HMjJAdLTDX/z8hgIERERyZDse5OtXbsWY8eORYcOHVBaWorXX38dffr0wYEDBxAUFOTq4lnH3lBERERuQSWEpREC5ev8+fOoX78+1q5di27dutn0muLiYoSEhKCoqAi1a9d2cAmJiIhICs66f8u+Zqi8oqIiAEBoaKjVbUpKSlBSUmJ6Xlxc7PByERERkXuSfc5QWUIITJgwAV27dkVSUpLV7aZPn46QkBDTIzo62omlJCIiInfiVs1kY8eOxU8//YQNGzYgKirK6naWaoaio6PZTEZERORG2ExWzksvvYQlS5Zg3bp1lQZCAKBWq6FWq51UMiIiInJnsg+GhBB46aWXsHjxYuTm5iImJsbVRSIiIiIPIvtgaOzYsUhPT4dWq0VwcDAKCwsBACEhIQgICHBx6YiIiMjdyT5nSGVlnq8vv/wSI0eOtGkf7FpPRETkfpgz9CeZx2pERETk5tyqaz0RERGR1BgMERERkaIxGCIiIiJFYzBEREREisZgiIiIiBSNwRAREREpGoMhIiIiUjQGQ0RERKRoDIaIiIhI0RgMERERkaIxGCIiIiJFYzBEREREisZgiIiIiBSNwRAREREpGoMhIiIiUjQGQ0RERKRoDIaIiIhI0RgMERERkaIxGCIiIiJFYzBEREREisZgiIiIiBSNwRAREREpGoMhIiIiUjQGQ0RERKRoygqGFi4EcnMBnc7VJSEiIiKZUFYw9OyzQEoK0LQpkJXl6tIQERGRDCgrGDI6fRoYMoQBERERESk0GBLC8DctjU1mRERECqfMYAgwBET5+cD69a4uCREREbmQcoMho4ICV5eAiIiIXIjBUMOGri4BERERuZCPqwvgMioVEBUFJCe7uiRERETkQsqsGVKpDH9nzQK8vV1aFCIiInItZQZDUVHAokXA4MGuLgkRERG5mLKayT77DIiNNTSNsUaIiIiIoLRg6LHHgNq1XV0KIiIikhFlNpMRERER/YnBEBERESma2wRDc+fORUxMDPz9/dG+fXus58jRREREJAG3CIZ++OEHpKWl4fXXX8fOnTuRnJyMfv364eTJk64uGhEREbk5lRDGWUvlq1OnTmjXrh0++eQT07KEhASkpqZi+vTpVb6+uLgYISEhKCoqQm0mUBMREbkFZ92/ZV8zdPv2bWzfvh19+vQxW96nTx9s2rTJRaUiIiIiTyH7rvUXLlyATqdDRESE2fKIiAgUFhZafE1JSQlKSkpMz4uKigAYIkwiIiJyD8b7tqMbsWQfDBmpjFNo/EkIUWGZ0fTp0zFt2rQKy6Ojox1SNiIiInKcixcvIiQkxGH7l30wFB4eDm9v7wq1QOfOnatQW2Q0ZcoUTJgwwfT8ypUraNKkCU6ePOnQiyk3xcXFiI6ORn5+vqJypXjePG8l4HnzvJWgqKgIjRs3RmhoqEOPI/tgyM/PD+3bt8eqVavwyCOPmJavWrUKGo3G4mvUajXUanWF5SEhIYr6EBnVrl2b560gPG9l4Xkri1LP28vLsSnOsg+GAGDChAkYPnw47rvvPnTu3BmffvopTp48ieeff97VRSMiIiI35xbB0F/+8hdcvHgR//jHP1BQUICkpCQsX74cTZo0cXXRiIiIyM25RTAEAGPGjMGYMWOq9Vq1Wo233nrLYtOZJ+N587yVgOfN81YCnrdjz9stBl0kIiIichTZD7pIRERE5EgMhoiIiEjRGAwRERGRojEYIiIiIkVzy2Bo7ty5iImJgb+/P9q3b4/169dXuv3atWvRvn17+Pv7o1mzZpg3b16FbTIzM5GYmAi1Wo3ExEQsXrzYUcWvNnvOOysrC71790a9evVQu3ZtdO7cGb/88ovZNgsWLIBKparwuHXrlqNPxS72nHdubq7Fczp06JDZdp72fo8cOdLiebds2dK0jTu83+vWrcOgQYMQGRkJlUqF7OzsKl/jCd9ve8/bU77f9p63p3y/7T1vT/l+T58+HR06dEBwcDDq16+P1NRUHD58uMrXOeM77nbB0A8//IC0tDS8/vrr2LlzJ5KTk9GvXz+cPHnS4vZ5eXno378/kpOTsXPnTvz973/Hyy+/jMzMTNM2mzdvxl/+8hcMHz4cu3fvxvDhw/H4449jy5YtzjqtKtl73uvWrUPv3r2xfPlybN++HSkpKRg0aBB27txptl3t2rVRUFBg9vD393fGKdnE3vM2Onz4sNk5tWjRwrTOE9/v2bNnm51vfn4+QkND8dhjj5ltJ/f3+/r162jTpg3mzJlj0/ae8v2297w95ftt73kbufv3297z9pTv99q1azF27Fj89ttvWLVqFUpLS9GnTx9cv37d6muc9h0XbqZjx47i+eefN1sWHx8vJk+ebHH7V199VcTHx5stGz16tLj//vtNzx9//HHx0EMPmW3Tt29fMXToUIlKXXP2nrcliYmJYtq0aabnX375pQgJCZGqiA5h73nn5OQIAOLy5ctW96mE93vx4sVCpVKJ48ePm5a5w/tdFgCxePHiSrfxlO93WbactyXu+P0uy5bz9pTvd1nVeb894fsthBDnzp0TAMTatWutbuOs77hb1Qzdvn0b27dvR58+fcyW9+nTB5s2bbL4ms2bN1fYvm/fvti2bRvu3LlT6TbW9uls1Tnv8vR6Pa5evVphsrtr166hSZMmiIqKwsCBAyv8snSlmpz3vffei4YNG6JXr17IyckxW6eE9/vzzz/Hgw8+WGGUdjm/39XhCd9vKbjj97sm3Pn7LQVP+X4XFRUBQKWTsDrrO+5WwdCFCxeg0+kqzFYfERFRYVZ7o8LCQovbl5aW4sKFC5VuY22fzlad8y5v5syZuH79Oh5//HHTsvj4eCxYsABLlixBRkYG/P390aVLFxw5ckTS8ldXdc67YcOG+PTTT5GZmYmsrCzExcWhV69eWLdunWkbT3+/CwoK8PPPP+PZZ581Wy7397s6POH7LQV3/H5Xhyd8v2vKU77fQghMmDABXbt2RVJSktXtnPUdd5vpOMpSqVRmz4UQFZZVtX355fbu0xWqW8aMjAxMnToVWq0W9evXNy2///77cf/995ued+nSBe3atcN//vMf/Pvf/5au4DVkz3nHxcUhLi7O9Lxz587Iz8/HBx98gG7dulVrn65S3TIuWLAAderUQWpqqtlyd3m/7eUp3+/qcvfvtz086ftdXZ7y/X7xxRexZ88ebNiwocptnfEdd6uaofDwcHh7e1eI9s6dO1chKjRq0KCBxe19fHwQFhZW6TbW9uls1Tlvox9++AHPPPMMfvzxRzz44IOVbuvl5YUOHTrI5pdETc67rPvvv9/snDz5/RZC4IsvvsDw4cPh5+dX6bZye7+rwxO+3zXhzt9vqbjb97smPOX7/dJLL2HJkiXIyclBVFRUpds66zvuVsGQn58f2rdvj1WrVpktX7VqFR544AGLr+ncuXOF7VeuXIn77rsPvr6+lW5jbZ/OVp3zBgy/GEeOHIn09HQMGDCgyuMIIbBr1y40bNiwxmWWQnXPu7ydO3eanZOnvt+AobfG0aNH8cwzz1R5HLm939XhCd/v6nL377dU3O37XRPu/v0WQuDFF19EVlYW1qxZg5iYmCpf47TvuM2p1jLx/fffC19fX/H555+LAwcOiLS0NBEUFGTKqp88ebIYPny4afv//e9/IjAwUIwfP14cOHBAfP7558LX11csWrTItM3GjRuFt7e3eO+998TBgwfFe++9J3x8fMRvv/3m9POzxt7zTk9PFz4+PuLjjz8WBQUFpseVK1dM20ydOlWsWLFCHDt2TOzcuVOMGjVK+Pj4iC1btjj9/Kyx97w/+ugjsXjxYvHHH3+Iffv2icmTJwsAIjMz07SNJ77fRk899ZTo1KmTxX26w/t99epVsXPnTrFz504BQHz44Ydi586d4sSJE0IIz/1+23venvL9tve8PeX7be95G7n79/uFF14QISEhIjc31+xze+PGDdM2rvqOu10wJIQQH3/8sWjSpInw8/MT7dq1M+uWN2LECNG9e3ez7XNzc8W9994r/Pz8RNOmTcUnn3xSYZ8LFy4UcXFxwtfXV8THx5t9ueTCnvPu3r27AFDhMWLECNM2aWlponHjxsLPz0/Uq1dP9OnTR2zatMmJZ2Qbe877/fffF7GxscLf31/UrVtXdO3aVfz0008V9ulp77cQQly5ckUEBASITz/91OL+3OH9Nnadtva59dTvt73n7Snfb3vP21O+39X5nHvC99vSOQMQX375pWkbV33HVX8WkIiIiEiR3CpniIiIiEhqDIaIiIhI0RgMERERkaIxGCIiIiJFYzBEREREisZgiIiIiBSNwRAREREpGoMhIiIiUjQGQ0RERKRoDIaIiIhI0RgMEZFbysjIgL+/P06fPm1a9uyzz6J169YoKipyYcmIyN1wbjIicktCCLRt2xbJycmYM2cOpk2bhs8++wy//fYbGjVq5OriEZEb8XF1AYiIqkOlUuGdd97BkCFDEBkZidmzZ2P9+vUMhIjIbqwZIiK31q5dO+zfvx8rV65E9+7dXV0cInJDzBkiIrf1yy+/4NChQ9DpdIiIiHB1cYjITbFmiIjc0o4dO9CjRw98/PHH+P777xEYGIiFCxe6ulhE5IaYM0REbuf48eMYMGAAJk+ejOHDhyMxMREdOnTA9u3b0b59e1cXj4jcDGuGiMitXLp0CV26dEG3bt0wf/5803KNRoOSkhKsWLHChaUjInfEYIiIiIgUjQnUREREpGgMhoiIiEjRGAwRERGRojEYIiIiIkVjMERERESKxmCIiIiIFI3BEBERESkagyEiIiJSNAZDREREpGgMhoiIiEjRGAwRERGRojEYIiIiIkX7f+UKQz58uPSQAAAAAElFTkSuQmCC\n",
+ "image/png": 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SC/pq+te//oWVK1eiR48emDRpEpKSknD9+nUcPXoUy5cvx8cff4yYmBisXLkSmZmZeOWVV3RTM2RmZmL69Ono27cv7rnnHgCa4GrRokVITk5G27ZtsWXLFrzzzjtGA5P6Cg0NRf/+/fHKK6+gYcOGWLBgAfbv3292eP0nn3yCwYMHY9CgQRgzZgyio6Nx6dIl7Nu3D1u3bsV3333nkPoS2cTFCdxEkrR9+3YxduxYkZCQIJRKpfD39xctWrQQjzzyiFi1apVe2dGjR4uGDRsa3M/evXvFgAEDRGBgoGjatKm47777xPHjxwUA8eqrr+qVXbp0qWjbtq3w8/MTzZs3F2+++aZ49dVXzY4mE0KI0tJS8fLLL4ukpCTh5+cngoKCRFpampgyZYreSCAAYuLEiXXqaWifM2fOFFFRUcLLy6vOSCFDPvvsM9GyZUvh5+cnWrVqJRYuXChGjx6tN5pMCM2Q+HfffVe0a9dO+Pv7i0aNGonk5GQxfvx4cfDgQSGEZhTYPffcI+Li4oRSqRQhISGiT58+YunSpXr7unbtmvjnP/+pe9+QkBDRv39/sX79er1yCxcuFF27dhUNGzYUAQEBIjExUTzyyCNi8+bNujJ9+vQRqampdY7L0DFkZ2eL5ORk4evra/C7rO38+fNi0qRJIiEhQfj6+org4GDRqVMn8dJLL4nS0lJx6tQpERYWJvr37683ykqtVothw4aJJk2a6Eb2Xb58WYwbN06EhYWJBg0aiNtuu02sXbtW9OnTR/Tp00f3Wu0Ir5pD4IW4OQ1C7dGH2nPt/Pnzum3a82XBggUiMTFR+Pr6iuTkZLF48WK91xoaTSaEEDt27BAjRowQYWFhwtfXV0RERIj+/fuLjz/+2OTnReRsCiGEcFUgRkRE0qVQKDBx4kTMnz/f1VUhciiOJiMiIiJZYzBEREREssYEaiIiMohZFCQXbBkiIiIiWWMwRERERLLGYIiIiIhkTRY5Q2q1GqdOnUJgYKDBZROIiIhIeoQQuHr1qtl1COtLFsHQqVOnEBsb6+pqEBERkQ2KioocNss6IJNgSLuEQFFRkUXLKBAREZHrlZSUIDY21uBSQPYki2BI2zXWuHFjBkNERERuxtEpLkygJiIiIlljMERERESyxmCIiIiIZI3BEBEREckagyEiIiKSNQZDREREJGsMhoiIiEjWGAwRERGRrDEYIiIiIlljMERERESyxmCIiIiIZI3BEBEREckagyEiIiKSNQZDREREJGsMhoiIiEjWGAwRERGRrDEYIiIiIllzeTC0Zs0aDBs2DFFRUVAoFMjLyzNadvz48VAoFJg3b57T6kdERESezeXBUFlZGdq1a4f58+ebLJeXl4eNGzciKirKSTUjIiIiOfBxdQUGDx6MwYMHmyxz8uRJPP300/jll18wZMgQJ9WMiIiI5MDlLUPmqNVqjBo1CjNmzEBqaqqrq0NEREQexuUtQ+a89dZb8PHxwaRJkyx+TUVFBSoqKnSPS0pKHFE1IiIi8gCSbhnasmUL3n//fSxatAgKhcLi12VmZiIoKEj3Exsb68BaEhERkTuTdDC0du1anDt3Ds2bN4ePjw98fHxw7NgxTJs2DfHx8UZfN3PmTBQXF+t+ioqKnFdpIiIiciuS7iYbNWoU7rjjDr1tgwYNwqhRozB27Fijr1MqlVAqlY6uHhEREXkAlwdDpaWlOHTokO7xkSNHsH37dgQHB6N58+YICQnRK+/r64uIiAgkJSU5u6pERETkgVweDG3evBn9+vXTPZ46dSoAYPTo0Vi0aJGLakVERERy4fJgqG/fvhBCWFz+6NGjjqsMERERyY6kE6iJiIiIHI3BEBEREckagyEiIiKSNQZDREREJGsMhoiIiEjWGAwRERGRrDEYIiIiIlljMERERESyxmCIiIiIZI3BEBEREckagyEiIiKSNQZDREREJGsMhoiIiEjWGAwRERGRrDEYIiIiIlljMERERESyxmCIiIiIZI3BEBEREckagyEiIiKSNQZDREREJGsMhoiIiEjWGAwRERGRrDEYIiIiIlljMERERESyxmCIiIiIZI3BEBEREckagyEiIiKSNQZDREREJGsMhoiIiEjWGAwRERGRrDEYIiIiIlljMERERESyxmCIiIiIZI3BEBEREckagyEiIiKSNQZDREREJGsMhoiIiEjWGAwRERGRrDEYIiIiIllzeTC0Zs0aDBs2DFFRUVAoFMjLy9M9V1VVheeffx5paWlo2LAhoqKi8Mgjj+DUqVOuqzARERF5FJcHQ2VlZWjXrh3mz59f57ny8nJs3boVr7zyCrZu3Yrc3Fz89ddfuPvuu11QUyIiIvJECiGEcHUltBQKBZYsWYKMjAyjZTZt2oRbb70Vx44dQ/PmzS3ab0lJCYKCglBcXIzGjRvbqbZEREQyoVIBa9cCp08DkZFAr16At7fD39ZZ928fh+3ZQYqLi6FQKNCkSROjZSoqKlBRUaF7XFJS4oSaEREReaDcXODZZ4ETJ25ui4kB3n8fGD7cdfWyI5d3k1nj+vXreOGFF/Dggw+ajBAzMzMRFBSk+4mNjXViLYmIiDxEbi5w7736gRAAnDyp2Z6b65p62ZnbBENVVVUYOXIk1Go1FixYYLLszJkzUVxcrPspKipyUi2JiIg8hEqlaREylE2j3TZ5sqacm3OLbrKqqiqMGDECR44cwW+//Wa231CpVEKpVDqpdkRERB5o7dq6LUI1CQEUFWnK9e3rtGo5guSDIW0gdPDgQRQUFCAkJMTVVSIiIvJ8p0/bt5yEuTwYKi0txaFDh3SPjxw5gu3btyM4OBhRUVG49957sXXrVixbtgwqlQpnzpwBAAQHB8PPz89V1SYiIvJskZH2LSdhLh9aX1hYiH79+tXZPnr0aMyaNQsJCQkGX1dQUIC+FjbLcWg9ERGRlVQqID5ekyxtKFRQKDSjyo4ccdgwe9kMre/bty9MxWMSmgaJiIhIPry9NcPn771XE/jUvB8rFJp/581zynxDjuY2o8mIiIjIyYYPB77/HoiO1t8eE6PZ7iHzDLm8ZYiIiIgkbPhwID3dJTNQOwuDISIiIjLN29vth8+bwm4yIiIikjUGQ0RERCRr7CYjIiKim1y0Qr0rMRgiIiIiDRmsUG8Iu8mIiIhINivUG8JgiIiISO5ktEK9IQyGiIiI5M6aFeo9EIMhIiIiuZPRCvWGMBgiIiKSOxmtUG8IgyEiIiK569VLM2pMuwBrbQoFEBurKeeBGAwRERHJnXaFeqBuQORhK9QbwmCIiIiIZLNCvSGcdJGIiIg0ZLBCvSEMhoiIiOgmD1+h3hB2kxEREZGsMRgiIiIiWWM3GRERkS1kuLq7p2IwREREZC2Zru7uqdhNRkREZA0Zr+7uqRgMERERWUrmq7t7KgZDRERElvLU1d1VKqCwEMjO1vwrs2COOUNERESW8sTV3Zn/xJYhIiIii3na6u7MfwLAYIiIiMhynrS6O/OfdBgMERERWcqTVnf31PwnGzAYIiIisoanrO7uiflPNmICNRERkbU8YXV3T8t/qgcGQ0RERLZw99XdtflPJ08azhtSKDTPu0P+Uz2xm4yIiMgUT52Dx5Pyn+qJwRAREZExublAfDzQrx/w4IOaf+PjPWfIuafkP9WTQghDbWOepaSkBEFBQSguLkbjxo1dXR0iInIH2jl4at8mta0mnhQsqFSSzH9y1v2bwRAREVFtKpWmBcjY0HNtPs2RI5IIGjyVs+7f7CYjIiKqjXPwyApHkxEReSKJdnu4DU+Yg8cDzoHq69VOeR8GQ0REnoYLb9afu8/B48bnQNm5MqyYswv5OdVYejjGKe/p8m6yNWvWYNiwYYiKioJCoUBeXp7e80IIzJo1C1FRUQgICEDfvn2xZ88e11SWiEjquPCmfbjzGmRueA6c33cBC8euxd0RGxEa7oXhb3fDl4dvw2UEO+X9XR4MlZWVoV27dpg/f77B599++23MnTsX8+fPx6ZNmxAREYEBAwbg6tWrTq4pEZHEceFN+3HXOXjc6Bw4tOoY5gwrRK+gHYhIaYpxi3rhh7NdcR0BiPcpwuQOq7Esc6dzKiMkBIBYsmSJ7rFarRYRERHizTff1G27fv26CAoKEh9//LHF+y0uLhYARHFxsT2rS0QkLQUFQmhueaZ/CgpcXVP3kZMjREyM/ucXG6vZLkUSPgfUKrX4c9Ee8VLPApGq/KtOlToG7BWz+xWIHd8dEGqVWgjhvPu3pHOGjhw5gjNnzmDgwIG6bUqlEn369MH69esxfvx4g6+rqKhARUWF7nFJSYnD60pE5HKekPQrNe62BpnEzoHK0koUfrAL+VmlyN/bCifVKQBSAADeqEbfpjuR3v8q0qe1QPPurQG0dkq9apN0MHTmzBkAQHh4uN728PBwHDt2zOjrMjMzMXv2bIfWjYhIctw96Veq3GkNMgmcAyUnSvDTO7uRny/w47E2KEEn3XMNUYrB0buQcbcad81IRdOEjg6rhzUkHQxpKWr11woh6myraebMmZg6darucUlJCWJjYx1WPyIiSeDCm+Sic+DU1jNY+u5fyFvRAL9dbIsq9NA9F+51Dne32o+MkQHo/2wa/ANv1bS0/fETcEwaLW2SDoYiIiIAaFqIImtEsefOnavTWlSTUqmEUql0eP2IiCRFm/R7772am17Nm6GUk37didTn7nHSOSDUAvuX/428D4qQ93so/ixrAyBC93wr3yPI6HAMGeNC0PXRVHj59NY8IdEh/y4fTWZKQkICIiIisHLlSt22yspKrF69Gj169DDxSiIimeLCm47jLou2OugcUFWq8PtHO/HcrYVI8j+KlGGJeHFF3xuBENCt0S5kDirEvh//xoHKBLy1sS+6P5EGL58boYaEh/y7fG2y0tJSHDp0CADQoUMHzJ07F/369UNwcDCaN2+Ot956C5mZmfjiiy/QsmVLvPHGGygsLMSBAwcQGBho0XtwbTIikh2pt2C4G2ct2mrP780O+7p26RpWzduFvG8q8MPBZJwTzXTP+aECtzfbifQB13D3jCREtjfeY2PrWm9Ou387dKyaBQoKCgSAOj+jR48WQmiG17/66qsiIiJCKJVK0bt3b7Fr1y6r3oND64mIyGbV1XWH19f8USg0w+2rq+v3PoaG8cfEOH0Y/8VDl8T/xq8Vw6M2iIa4qledIFwRD8atE99OWS+Ki6y4p9o45N9Z92+Xtww5A1uGiIjIZoWFmi4xcwoKbB915qyWJyOO/X4C+XMPI++3xlhzJQ2qGinFMd6nkJ5yEBkPB6L3hDbwa+Rn/RtkZ2u6Fs3JygIeeED30Fn3b0knUBMREbmco+fuMTdrtEKhmTU6Pd1uXZ1CLbDju7+Q//Fp5G2MwPZryQBurgOW5v8X0jufQsb4cHR8MBkKr6j6vaEEhvybwmCIiIjIFEffyNeuNZ5LA2gCoqIiTbl6zHdUfb0aaxfsQv7/lSBvVyKOqZIAJAEAvKDCbUG7kN7nCtKfTUBi/1YAWtn8XnVIfNoHBkNERESmOPpG7sCWp7JzZfjl3V3Iy6nGj0dScEl00D0XgHIMjNiFjCFVGDItGc1at7d6/xaT+LQPDIaIiIhMcfSN3M4tT+f2nMcP7+xH3k9K/HouDdfRTfdciOIihiXuRcZ9fhgwNQ0NQrvaUmPbaIf8G5pnaN48l077wARqIiIiSxiaMDA2tv43cu2wc3MtT7WGndd0cOVR5L9/FHlrgrH+ahuIGtMIJvgcR0bbv5Expil6PJ4KH38Xt4NYMeTfWfdvBkNERESWsnbuHkvLa0eTAYZbnmqNJlNXq7H5//Yh77/nkb81BnsrWujtrlODvUjvdg4ZE6LQ5p6WUHgZWcJK4vNRMRiyIwZDRETkcLUDiwsXgClTLF96wkzLU2VpJQre34m8rHIs3d8Sp9Q3u818UIW+wTuRcXsp7p7WErFdLRj9Za+lMRwYUDEYsiMGQ0QkC1L+K1/KdbMHQ4GFIebmDar1ORXHtcVP7+1HXh7wU1EqShCkK9oIVzE4ZrdmBfjn2qBJXFDd/Zmqrz3mNXLUWmM3PoeSw4cR9NhjDIbsgcEQEXk8iS6ACUDadbMHY4GFMWZygE5uPo2lcw4ib2UDFFxsiyrcnOQwwuss7m51ABkPBKD/5LZQNrZhUXIbl8aow1ETRdY4X0oABAEMhuyBwRAReTQXz15skpTrZg/mAgtTbsxYLdQCe384jPwPTyBvfTNsKkvVK5bsdxjpHYqQ8Vgobh2TcnPhU1vZY0ZtewVUtdU6X5wVDHFoPRGRO3PB7MUeUTd7MTdhogn7/7cRn88A8nbE41BVCwCaJGgF1OjWaA/Sb7uI9GeaI/muRACJ9quzPeY1csREkabOFwdjMERE5M6cNHuxTaRcN3uxdQkOAE9+0RWr0ReAZgX4O5rtRMad1zBsejIi2qbZqYIG2GNeI0dMFFmPwLK+GAwREbkzR6+bVR9Srpu92LAEhxoKnEAMdiEND8X/jozhXhg0rQ0Co7o4oIIG2GNGbUcsUeLC84DBEBGRO5PyAphSrpu9mAksBICaM/yooYACAldGTcKZjxvDt0FPp1VVxx4zajtiiZKDBy0va2f1zMIiIiKX0t6UFEYm1VMoNHPVWHpTUqk0CbbZ2Zp/VSrp1E2KvL0h3psHITSBT01qA8UVsTFQ5OSg7f+mw7eBrzNqaJh2aYzoaP3tMTGWJbVrAyqg7vdryxIlubnAq69aVtYBOJqMiMjdWTl7scn92HsIvL3qJjFV5VVY+9Fu5P2vBPl7EtFJ9Sfex7OIxc3P7mpAGMpfmI3w3snSnV+pvvM/2WOJEhMj0zi03o4YDBGRx6vvTcmRQ+AdtaaXk5WeKcUvc3YhL0eFH4+m4rJoqnsuAOUYHLENj3fcih79lWjcqZW0Ah9HTnpZ332bGOrPYMiOGAwROYmnzzIsdbZ+/o6aM8YedXOxs7tvrAD/sxK/nmuLCvjrngtVXMCwFvuQcZ8f7piShgahDVxYUxMsbfFz1XeUnQ08+KDBpxgM2RGDISIn8PRZhj2ZPSbhkyIbb+5//XIE+f85hry1wdhQawX4W3yOIaPdEc0K8E+0gbefxAM6S1v8rL1+7Rk4SaBliKPJiMg8c7/4jP3CPXlSs91N80JkwxOHwFtxc1dXq7Hpy73I//wClm6OQmjVKUTiNHwBKCDQqcFeZPQ4h/QJ0UhNbwGFV5xzj8VWlk56qVYDI0ZYfv3a+w8fcyPTnEHIQHFxsQAgiouLXV0VIveTkyNETIwQml9Tmp+YGM12IYSorq77fM0fhUKI2FhNOZKm2bONf381fwoKXF1Ty+TkaM47Q+eiQiFETo64Xnxd/PTaJjG+9WoR6XVaAELcgxxxHPrnclVY5M1z3d0UFFj2vTZrZvn1a8FnaxPtfmvtu1gzSM/h9292kxGRcZY0sQcHe2YXi1xYurZWTAxw9Kj083zMHI8AcNE7DC1U+1GMmwnQD+IrfIVRAPTnBXLrUW8mcnGsVlCgacFxZG6ZgRankuhoBJ086fD7N+cZIiLDzDWxA5om9pMnLdufO3WxyImlSyA8/rj0AyHA7PEoAISqzqE9diDS6wyeTFmDn2ZvxFdRL0CBWoEQoH+u12fOJVew52SWp09bt7yKLYYP1wTcBQVAVpbm3127bNuXlZgzRESGWfqL7/x5y/bnzrMMezJLg9SWLR1bDzsRJ0/VDWgM+OzxP3HLgt7w8onQJPC+aiKod9c11CyZJbpxY6C42Py+IiOdk1vm7a3/GZeU2L4vK7BliIgMs/QXWrNmpmcZBjRdaSqV+/1lLQcesGSGqlKFtfN3YFrnQjz8iGW3tRYP3govnxtlPTGBHDA9SzSgCZDMBUI1Zwn3gHPFGAZDRGSYpb/QoqNN/8IFgEuXgDvu0OQb5ObapXpkJWPLbLjpkhnXLl3D0pc24tFWaxHhfxm9n2mHuVv64mv1fTiBaINLYQAwfDwefJM3uuyGJWovq+Gm54pFHJqeLREcTUZkA+0oMUMjR4yNMjE1qsweI04sqXNBgRBZWZp/OYJNw9yIQCMjeRz+fVnpwl8XxaLH1oqMyA0iAGV6VW2quCQeTlgrvp++XpR/9pV1x2Ptue6OtNfGV18JERpq2Siz2Ni6n5WTzxVn3b8ZDBGRcdb+4quuFuLXX4UIDnb+UHtzN3y5snQotKHPz9DN0Bp2CE7/Xn1cvJdRKPoEbRNeqNarXnPvIjGpXaFY9e5WUVlWWfe4rTkeNwkI683S4fbvvWf8+3LEuWIEgyE7YjBEVA/W/uKz9JetPeescdTcJ+7O2jmg7NmyZmNwqlapxZav9op/9i4Qbf3316lyO//94tU+BWJr1j6hVqnNH781x2PNue6urZBZWZZdn1lZpvfjpON31v2b8wwRkXnWTL1v6dwmWVnAAw/Yp26OXlfLXblqmQ0rF32tKq/Cmg+2Y/cnv+PgUV/sFqlYi15QwxveqEavJruQ0a8E6VMTEX9bjP3qaYgl57o7Lz3jZkuvOOv+zaH1RGRe7eGupjg7GdWauU8k8MvdqVwxSsrCJSCudumPX+btQ16uGoqjf+MNvIjbcfN7vOAVht39JyFtwVMIadnBfvUzx9y57u5Lz1gy3D4mxj2ToOuBo8mIyL6cPeLEU4dF24MrRklZGJwOb/4n7pvbHeVHz+JLjEY09F8TKs6j76pXELKr0H51qy9LJyKV8hQSpobb1x49JiMMhojIvpz9y9aTh0XXlyuGQlsYdIbiIlp6/42Fvk9Cobcu/A1SDC4cPQOzsxgbbh8TI/2WLQdhMERE9ufMX7aePPdJfbmgFUAdFm5RuTdeU+PAimNoUnXe+IzRUgsuPKkV0tDSF0eOyDIQAhgMEZGjOOuXLZv9TXNCYFpRUoGf/rUJ41uvQeyAZBQhBmpjIc6N4DRh5kgozp6x7A2kElx4WiukNj/qgQc0/8r1GgETqInIkaxJvK4P7Q3f0AifefNk+9euzvDhQHq65SMCLXDlWDGWv70beUu98NOJNihFFwCAF1T4Eo/gJbwBASMrwGuDU0uDhr17NaOg6lnnemPyscfi0Hoi8hzWTAFAVivaeApL5xxE3qpGKLzUFtXw1T0X5XUar0Z/jkeKP4B/yTnDO4iN1Q9OtdMiGAsuapPC8HXtaDJAv85Gpg2g+nHW/ZvBEBGRnJkIIIVaYPeSg8j/6BTyNoRhS3mK3ktTlIeQ0ekEMp4IQ6cGe+F1/wjjQc3s2cBLLxmes8dQcGGIVAIOQ/MM1Q70yC4YDN1QXV2NWbNmYfHixThz5gwiIyMxZswYvPzyy/DysizlicEQkZOxhcY9GLipi+gY7L1zCj7f1hH5OxPwd3Wc7jkF1OgRuBsZvS8h/dl4tBwQr3nC3MSXABAcDHz7reHcFEPBhTFSmUST57hTOO3+7dD5re3g3//+twgJCRHLli0TR44cEd99951o1KiRmDdvnsX74HIcRE7ENcLcg5ElTFRQCBUU4h7kCEAIJa6JoWEbxWej14gzu84Z3pelS7CYOhe0yzu8/LLzl3MhyXLW/VvyCdQbNmxAeno6hgwZAgCIj49HdnY2Nm/e7OKaEdmBp/116e6z88qFSgXVxGfgJUSdMV9eEFBDgf96P4WHJ4dj4PR2aBRx680ClZXAggXA4cNAYiIwYYJ1o72MnQvaZHtPGr5ObkPyQ+tvu+02rFq1Cn/99RcAYMeOHVi3bh3uuusuF9eMqJ5yczVdC/36adby6tdP8zg319U1s40nzM7r4f4uPI656YV4NugLeJ85ZXR+Hy8IhKjOYfjQKjSKaHTzieeeAxo0AKZMAebP1/zboAGQn295JcydC542fJ3cguRbhp5//nkUFxcjOTkZ3t7eUKlUeP311/GAiQUeKyoqUFFRoXtcUlLijKoSWc4TW1C4RpjkCLXA1qz9yPvkLPI3R2HX9VYAmmMkbGh9ee454J136pZRqYBvvgEaNQLKyiwbFWbqXODwdXIByQdD33zzDb766itkZWUhNTUV27dvx+TJkxEVFYXRo0cbfE1mZiZmz57t5JoSWcjChSyRnu5eXWbs3nAuI12sVeVVWD1/F/K+uor8vS1xQtUaQGsAgDeq0afpTtyXehpYZ8F7aFtfKiuBuXNNly0vv3n+Wjoux9C5oJ1E89576+6Lk2iSozg0I8kOYmJixPz58/W2vfbaayIpKcnoa65fvy6Ki4t1P0VFRUygJumwNNnU3RJEPfW4pMhAknpZozAxt9nrIghX9D7uhrgq/hG9Xvxv/Fpx8dAlzWujo01/RwqFELGxmqRmIYR47z3LvtsxY+omz9t6LhhKxI+NZSK+zDCB+oby8vI6Q+i9vb2hVquNvkapVEKpVDq6akS28dQWFHZvOMeNLlZRK/nZv/Q8ni19GWuRjN8VvXB3q31IH+GP2yenISC4u95rTbbcGGp9OXzYsro1aqRZgqWwELjvPuDyZePvER2tad3KzjY8eMABs2YTGSP5YGjYsGF4/fXX0bx5c6SmpmLbtm2YO3cuHn30UVdXjcg2npogyu4Nh9v/w0FEPfgkGom6q7x7QUAAyG46ET4nj8E7oLd+AVPdszVFR9ed5Tkx0bIKJiZqvt/iYsDYPHDac+PaNeCOO25uNzS7tLOWcyHZk/yki1evXsUrr7yCJUuW4Ny5c4iKisIDDzyAf/7zn/Dz87NoH5x0kSTF3BIEUplUzlZSmp3XzacuUFersXHhHuR9fhF52+IQWXUMhehn/oUFBXWDiMJCzYhFc+bM0Xx/NT+nykrNqDFTIwG9vTV5Q8uWmW59atQIKC2tu10qs0uTpHDSRTvipIskOdoJ72pPeqfd5u55EdoJ9LKyNP9qc0+cyU0nf7x2+Zr4cdaf4vHk1SLc66xe9R/G/yzLxcnKqrvjrKz6TYw4Y4bp18yYofmezeUMeXtbnqtEssecISJP5umrrLu6e8PNpi64fOQKfnx7D/J/8MJPJ9NQdmMFeABojGIMiduNjHsUGNIjGBhhwQ4NdbFa0+1q6HN6+23Nv3Pn6rcQeXsDU6dqni8sNL+khqnWJU6/QC4i+W4ye2A3GUmWm3fjSJK5dbIk0g15fMNJ5M85hPzfArH6cpreCvDRXqeRnvIXMh5qhD5Pp8Gv0Y2UgPp0sVq7QryxfRmagVqbspCdrZlAtL6ysgATc8mRfDjr/m1Vy1BRURFiY2MdVRci+XF1C4onkujkj0ItsCv3IPIWnEL+H+HYeq01gGjd86nKg8jofFKzAvzDraHwMtCSU58kdVOvNVhhI5+Tn59mHixD7JX0726DB8jtWbUcR3JyMl555RWUlZU5qj5ERPUjoakLqq9XY/X72zGl42okKovQ7r5WeLWgL7Zeaw0F1OjVeAfeHVqIg78ew+7rLfHvdX3R+ZEUKLyMLZSBm12s0dH622NizHf/GXutKeY+J5VK0z2Wna35f0zMzcCsNoXCdGucQqFJtuf0C+RkVrUMrVy5ElOmTMHnn3+O119/HWPHjnVUvYjkhd1l9mNpq8LZs5rP3c6fc/mFcqyYswt531Vh2d+tcVG01z3nj2sYGLET6XdWYuj0ZISltrPtTeozB4/2tR98oFlbzBxTn6ehkYMhIYZnotYGSFOnAu++q/k/p18gqbAl6/rLL78UMTExon379qLADWaT5WgykjQ3HfUkWdoRTbVH6lk6asoG5/aeF5+PWSPujvhD+KNc7y2CFRfF6MS1Ive5DaL0bKkdDtBOzH1O5kZ2aUdEGnodIERIiPHZozm7NFnIWfdvmxOor127hszMTMyZMwcDBw7EO++8gxYtWtg3UrMTJlCTZBkb9cQ5V+pH+7kCls22bMPnfGjVMeTPO4L8NU3xe0kbqHGzNSPepwgZaX8jY3QQeo5vAx9/iQ7cNfY5mftcLElSj44GFi0Czp0z3HLF1lCygLPu3zYHQ+Xl5di6dStycnLwn//8B76+vpg4cSJmzZqFwMBAe9ezXhgMkSS5yagnt2WoC8cQCz9noRbY8tU+5H16Dnmbo7GnoqXe8x0D9iG921lkTIhC2vCWpvN+pMSWSTItncDR0OSPRFaQ5Giyjz/+GJs2bcKmTZuwb98+eHt7o23btpg4cSLat2+PxYsXIyUlBUuWLEHnzp0dVWcizyDRUU8ew9LcGBOfc2VppWYF+MWlyN/bCifVKQBSAGhWgO/bdCfS+19F+rQWaN795urwbsWW/CMJJakT2YNVwdDrr7+Obt26YfTo0ejWrRs6d+6styDqo48+ijfeeANjxozB7t277V5ZIo9izxsKuxwM8/YGwsMtK3vjcy45UYKf3tmN/HyBH4+1QQk66Yo0RCkGR+9Cxt1q3DUjFU0TOjqi1s5n7RQPnrq+HsmW1fMMmTNu3Di88sorNleISDbsdUMx1M1haNFLOVKpNKPGLLD0s3P4aNImrLrQDlXoodse7nUOd7faj4yRAej/bBr8m3R3VG3dR69emnPM3OSPHCJPbsLuM1ALIbBmzRr06dPHnrutF+YMkSTZY8FWJmAbZ2HOkBoKnEAMEnBElwTdyvcIMjocQ8a4EHR9NBVePlZNySYPtiZfE1lB8gnU7oTBEElWfW4o7p6A7ciuPSNBogBQM61ZfePRvfgepxu1RHrPi8iY1BzJd91in3p4OluSr4mswGDIjhgMkaTZekNx5xE9juzaMxck1nDOKxzbez6NtP88jsj2FuYWkT7mq5EDSXI0GRE5gK2zCbvriB5zK8p/+y0QGlr3s7Dwplvy9XI0tiAQuj4rE2Evz8BAQwua8uZuOa6vRx6AwRCRFNhyQ3HHET0qlaZFyFCDtHbbyJGacloxMZoVzLOzjbYkHfv9BPLnHkZ+QSAiLhdjsQVV8W8VVzfIqU+LlbVBFIMuIslgNxmRu7JHArZ2P866KVvatWcBAQUAgel+72Nu5STd9j4oRCFs6D6sTzK6tUEURwASWcRZ928OkSByV97empsnUHeVcEsXvczN1QRU/foBDz6o+Tc+XrPdEezYZaeAgIACz1a+Cz9cw6SGn2FZx1ew+J1TmqUgTK2cXntldEtarCZP1m+x0tIGUbW75rTdfrU/S2vLE5HDsWWIyN3ZmoDtimH5dmwZqknVNATely/e3BASAly8aHzl9NrHZmsyurUj+tx9BKAl2P1HdsSWISKyzPDhwNGjmht1Vpbm3yNHTAcy9WkJsYVKpQk4Tp7UJEfbmV4gBACXLmn+DQ7W3x4TYzjIszUZ3ZolVWwp726c3dJIZCdMoCbyBMYSsI39le7MddEsXTDVnoTQtLIEBAC//mp85XQtW5PRrQ2i3HUEoCXMjRLkJIwkYQyGiDyVqSTdigrL9lHfm7KJyQ8B/QkQq+ENL6js11wthObYvb01o9FMsXV5CWuDKHccAWgJcy2NCoWmpTE9nV1mJEnsJiPyROaSdA8etGw/9bkpm7hBasaBKXAWzfAgvsLtWIk3Gr6u225XlgR01iaj1+z2a9bM8mRtbdBlTXK3O/D07j/yeAyGiDyNJflA//2v9SOurGXmBukFgXCcx6Ppl5BztAv+Wfo8FDk5UMRE6xeMjQVmzNAEETU1a2ZZPSwN6IYP13TlRNd6/9p5RjXzYh5+GDh/3nhrEqAfRNljBKAUeXL3H8kCgyEiT2PJX+knTgBPPKF5bOeb8snNp/HRA2uQOex3i8rfcX8omsQFaR4YSwZ/++2620+c0IwaM8aWgM5cMrqxFjdDjCVrWxp0uRNP7f4j2WDOENkHh9NKh6V/fbdsqbn5GsorsmKhTaEW2LfsMPLmn0De+mbYVJYKIBJ9oMZMS3ZQ+wZpLBm89vbcXM3weaMVE7YFdKaS0Y21uGk1awa8954m0DF1Ddi6BItU2ZpzRSQRDIao/jibrrRY81d637423ZRVlSr88fke5C28hLwd8ThU1QJACwCAAmp0a7QHd/VUoWpLBHwvnrXPDbJmwB0WBkyaZLp8SIjm2OzFXIsboOkyi462bASeJ63ppe3+u/dew88LoVlmxV2DPfJ8QgaKi4sFAFFcXOzqqnienBwhFAohNL/ubv4oFJqfnBxX11B+qquFiIkx/L1ov5vYWE05K5RfLBdLX94oxrVaI5opzunt0g/XxV3N/hSfjlotTu84e/NF2vOjdl2sPT9ycjTHZOh4TP0UFFh1jCZlZVn2nllZ9ntPdzNjhvHPhb8PyAbOun+zZYhsx+G00lTzr3RjMzBb2H108eAl/PjOXuT/6IOfT6WhHLfqnmuiuIIhcXuQMdwLg6a1QWBUl7o70ObH1Kcrztj8NZawZ8Iu82JMU6k0i+mawt8HJFFcjoNsZ+sSBlIghxwnG5fpOLpOuwJ8Y6y5kgZVjd70WO+TSE85hIxRgeg9MQ2+DXwtq4utn7e55SvMsee5Z6+FcT2VO/8+IMly1v2bLUNkO3cdTiuXHCcLk3SFWmD7NweQ/8kZ5G2MxI7rSQBuDmNv638AGbeeRvoT4ejwQDIUXrVGQVnC1vwYS/J0DHFEwq4dW9w8krv+PiACgyGqD3fsNpDbkgFGgpCq8iqs/Wg38v+vBHm7E3FclQwgGQDgBRV6Be1CRr9ipE+5BQm9kwAkOa/ONVuR9u61/vWODEzs0e3nqdzx9wHRDewmI9u5W7eBHFYMN6H0TCl+mbML+bkqLDuSisuiqe65AJRjUOROZAypxpDprRGaZGL+HkeyxzpmFnQF1pvUulmlUB93+31AboHdZCR97tZtYO3ipFK4wdTT2d3n8cM7+5H3sxK/nmuLCnTXPRequIBhLfYh4z4/3DElDQ1Cu7mwprAtUVqh0AxlX7TI/GKs9iSlYfFS6fZ1t98HRDU5dKyaRHBovYMZGvYcGyu9YbTWDI02dEwxMdI7JgP+WnFEvH1XgegRuEMooNI7hESfo2JapwKx5oPtorrCuqH1DqWdDsCaYfOcvkGaU1u4y+8DcgvOun+zm4zswx1aUSwd7TJ7NjBrVt0WCu1ftxLLK1JXq7H5//Yh77/nkbclFvsqE/We79xgLzJ6nEP6hGikpreAwsvOC6Hag6XfTU3O6A6TMil3+7rD7wNyC866fzMYIvmwJKchOlrz3MmThvchkbyHipIKFPxnF/Kzy5G/vxVOqyN0z/mgCv2CdyJjQCnuntYKMV3cIGE1Oxt48EHz5V5+GUhJ4Q0W4FB2kgXmDBHZmyU5DY8/Drz6qvF91M4rcqLi48VY/s4e5OcDy4va4Co6654LRAkGx+5GRjoweHoqmsR1cmrd6s3SEUa3384buxaHshPZDYMhkhdzQ6MrKizbj5NuMCc2ncbSOX8hb2UjFF5KQxV66J6L9DqD9OS/kP5AA/SblAZl4x4m9iRxUlno0526dziUnchu3CIYOnnyJJ5//nn89NNPuHbtGlq1aoXPP/8cnTq52V+/JA2mJiMsLLRsHw66wQi1wJ78Q8hfcBJ568OwuTwFwM33au13GBmdipA+LhRdRqfAyyfC+M7ciRRGIkllVJalpBJAEnkAyecMXb58GR06dEC/fv3w1FNPISwsDIcPH0Z8fDwSExPN7wDMGSIruGCuFFWlCus/3Y38RZeRtyMBh6vjbr4d1OgeuBsZvS4hfVIcWg1KsMt7SpaNS4jY5X0NDeuXaNK8jrbegOEAUqr1JrIQE6hveOGFF/D7779j7dq1Nu+DwRBZxQk3mGuXrmHlnJ3I/64SPxxKxnnRTPecEtdxR9hOZNxZgWEzkhHeppmJPXkgZ3dVSXlUliVcFUASOQGDoRtSUlIwaNAgnDhxAqtXr0Z0dDQmTJiAxx9/3OhrKioqUFEj96OkpASxsbEMhshy338PTJgAnD9/c1s9bzAXD17Csrf3Iu9HH6w4nYZyNNQ911RxGUMT9iB9uDcGTUtDo4hG9TwAspgnjMpyp1wnIitwNNkNf//9Nz766CNMnToVL774Iv78809MmjQJSqUSjzzyiMHXZGZmYvbs2U6uKXmM3FxgyhT9QCg0FJgzx+pA6MiaIuS/9zfyCoKwtjgNatyme6659wlktDmM9FGN0eupNvBtcJuJPZHDeMKoLCnNiE3khiTfMuTn54fOnTtj/fr1um2TJk3Cpk2bsGHDBoOvYcsQ2ayeuSNCLbAtez/yPz2LvD8jsfO6/gKn7fwPIKPraaSPj0D7+5OkOQGi3HhCyxCRh2LL0A2RkZFISUnR29a6dWvk5OQYfY1SqYRSqXR01cjTqFSa3AtDfx8IoQmIJk/WjESr0QVRVV6FNR/uQv5XV5G/JxHHVa0BtAYAeKMavZrsQka/EqRPTUT8bU5eAZ7M46gsItmTfDDUs2dPHDhwQG/bX3/9hbi4OCOvILKRFQu5liZ3xs/v7EL+EhWWHW2DK6KjrlgDlGFQ5C5kDK3GkBkpCGnZwQmVJ5tJYVg/EbmU5IOhKVOmoEePHnjjjTcwYsQI/Pnnn/j000/x6aefurpq5GkszAl5++51+OfVbnorwDdTnMfdLfcjfYQSd0xJQ0Cwi1eAJ+uYm4yTo7KIPJrkc4YAYNmyZZg5cyYOHjyIhIQETJ061eRosto4tJ4sYmHuSF8UYDX6ooXvUWS0O4r0scHo/lgqvP3YcuD2OCqLSFI4tN6OHPJh8pem51GpIOLjgRMnoUDdy0INBc4pwvHF7V8h/Zk4tB6aaD4BmucJEZHNmEAtZe42bT+ZVFFSgd/m7UT+19dQdXI2/ovHIKCAV42ASABQQCBi1lOY+VJfywIanidERG6BLUPWctdp+6VAQq0kV44VY/nbu5G31As/nWiDUgTqnnsQX+E/3lMRojpv+MWWBDQ8T4iI6o3dZHZktw/T3aftdyUJtJIUbTyFpXMOIm9VIxReaotq+Oqei/I6jfTWB5H+QAP0fSYNyoY+wOuvA6++WndH5gIanidERHbBYMiO7PZhcnI227iolUSoBXYvOYj8j04hb0MYtpTrz1eVojyEjE4nkPFEGDo9lAwvH6+bT9YnoOF5QkRkF8wZkiJPmLbf2WycyNDmt6tU4fdPdiP/S80K8H9XtwLQCoBmBfgegbuR0fsS0p+NR8sBLQC0MLwjK+YcqhPQ8DwhInIrDIasERlp33JyUJ+gwkLlF8qxcu4u5H1XiWWHW+OCaKd7TonrGBi+A+l3VmLo9GSEt2lr2U7rE9DwPCEicisMhqzBafut56BWkgsHLmLZO/uQ96MvVpxJwzV01T3XVHEZwxL2IONeHwycloaGYV1N7MmIgwctK2cooOF5QkTkVhgMWYPT9lvPjq0kfxceR/68v5FX2ATraq0AH+d9Ahlph5ExOgi3PdkGPv71WAE+NxeYNct0GVMBDc8TIiK3wgRqWxgaGRUby2n7DdEmIptrJTGQiCzUAluzbqwAvykKu6630nu+fcB+ZHQ9g4ynItH23lb2WQHeXOJ0TTk55ofX8zwhIrIZR5PZEWegdjHtaDLAcCtJjdFkVeVVWD1/F/K+uoqle1ugSBWtK+6NavRpuhPp/a4ifWoi4nrG2L+ulo4Emz0b+Oc/zZfjeUJEZDOOJpM6b2/LE37lfkM0swjm1W4D8PPUDcjLVWP58VS9FeAbohR3Ru9C+lAVhsxIRXBiRwNvYEeW5i61bGlZOWvOEyIicgkGQ44mgckGJWH4cM3w+RtB4aVyf+SsaoIlTzbCqvN+qKyxAnyY4jzubrUP6SP8cfvkNAQEdzexYzvjSDAiItlhN5kjcUkGPfuX/438D44jb10INpamQuDmJIctfY8go/0xZIwLQdexKa5bAb4eOU5ERGRfzBmyI5cEQ3JaksFIN6C6Wo2NC/cgf+FF5G1rjgOVt+i9rGvD3UjveQEZz8Qi+a5b7JMAbQ9W5DgREZHjMGfI3TlhskFJMNANeK1xGBYFPoPZp5/AWXWabrsvKnF76A6kD7iGu6e3QlTHNq6osXlmcpwYCBEReRYGQ44ihyUZbrSgCCFQs01HWXIe40v+iZVIwSrcjiFxu5FxjwJ3TmuDxjFdXFZdq9TKcZJl4jsRkUwwGHIUT0vErdUVVuQdjyYPP4lGtQIhAPCCgACwOGgCvI8dgV9QT1fUuP44EoyISBYYDDmKJy3JkJsL8eyzUNToMlIiFIG4YPQlCgABxWeBbRsZUBARkaR5mS9CZqlUmsn6srM1/6pUN5dkAG4m3mq5yZIM1dersefRORD/+AdErfynUBOBkB537gYkIiJZYDBUX7m5mlFj/foBDz6o+Tc+XrNdm4gbHa3/mpgYyY5IKr9QjryZGzGmxTpEBVxC4y/mQaDuiWLxieMu3YBERCRbHFpfH5bOIyTxGajP77ugWQH+Jz+sPJOGa2gAAOiDQhTCgqUpDPGkqQOIiMglOLRe6lQqzdBrQ7GkEJpgYPJkzYgkCSbiHv7tGPLfP4K8wqb4vaQN1LiZuxTvU4SMtL/xeJsNwP/ZsHM36QYkIiICGAzZzs3mERJqgS1f7UPep+eQvzkauytaAojTPd8xYB/Su51FxoQopA1vCYVXLFAoLAuGmjUDzp+/+Zjz8RARkRthMGQrN5hHqLK0UrMC/OJSLN3XEidUKQBSAGhWgO/bdCfS+19F+rQWaN69NYDW+juwdETcoUPA+vWWdwNKvNuQiIjkhcGQrSQ6j1DJiRL8PGc38pYILD/WBsXopHuuIUoxOHoXMu5W464ZqWiaYGAF+NqByty5wP33awIfQ0tTzJsH+PmZb/3S7jc/H/jqK+BCjdFocly4loiIJIMJ1LaS0IKep7efxdJ3DiBvRQB+u9AWlVDqngv3Ooe7W+1HxsgA9H82Df5N/I3vyMDSGoiJAR54QDNtQM3tsbGWd4UZ2m9NXPPLfbBVj4iciAu12pHDR5MBTl3QU6iFZgX4+UXIWxeKjWVt4AUVemEtInEaPt5AdMcwpD8Whq6PpsLLx4KB8OZGxn37LRAaav1N0Nh+a+PoM+kzFiyzVY+IHITBkB059MM0dIMw1Wpi41/W6mo1/vh8D/I+v4j87XH4qypB99w9yMVHigkIF2dvvsCam5S2lctUy40tgYq5/RpSUCCJhHOqxdJpJIiI7IjBkB05/MO0NMCx8i/r61euY9W8Xcj7+hp+OJiMs+ow3XN+qMCA0G14NfK/6LxrYZ31way6SRUWaiaLNMfaQMXS/daUlaXpliPpcFSwTERkBucZcieWzCNk7C/rkyc1228ELZePXMGPb+9B3g9e+PlkGspwc5X3IBRrVoAf7oWhKX8jYPYLwC4jNyhDcx0Z46iRcbaMpOOM1dLjZtNIEBFZi8GQM5iZoFFAgdKHn8JwZSwKrnSACjdXeY/xPoX0lIPIeDgQvSe0gV+jnjcCq1Hm83AsvUk5amScNeXdaeFauXGDaSSIiOqDwZAzmPnLWgGBwGvnUHWtDCr4IM3/L6R3PoWM8eHo+GAyFF5RNwubCqyMMXeTsnQ+IWsDFXP7rc2eM1Zz1JP9SHQaCSIie+FCrc5g4V/MMzquwqFVx7DzWiu8trYvOj3cGgqvWtlA5rosDDF3k/L21uQtATdzjbTqs7SGqf3WFBtr3wRcU4vnkvW0Qa2x71Ch0HyHbNUjIjfFYMiBys6VYcnzfyBz2gXzhQEMmXM7EvvHmS5kTVeENTep4cNvDp+vKSamfoHK8OGa10dH629v1kyTz1RQoEm8tWcgdO+9dQNGbW4WAyLrOSpYJiKSCI4ms7Nze85j2bv7NSvAn22L6wiAF1Q4inhE4yS8UM8JGq0ZoaVQWB7IGBrpFhoKLFgA3HefZe9nijO6rTjqybGsnUaCiKieOLTejhz9YR5adQz5844gb01T/F6SBlGjwe0Wn2NIb3sE4zpsRcrC6Zoh8PWZoNHczNda1swz5ClzyDhqigC6iblYROREHFovYepqNbYs3q9ZAX5LNPbUWgG+U4O9yOh+DulPRaHNPS2h8IoD0Be4K97wPEPW/GWt7bK4996664VpzZ4NvPSSZTcpMyPdLB6eLwUc9eR4lkwjQUTkZhgMWaiytBKFH+xC3uIyLN3XEifVN1eA90EV+gbvRMbtpbh7WkvEdr35nJ7hwzVBRX3/stbm4dijy8KT5pDhqCciIrKB2wVDmZmZePHFF/Hss89i3rx5Dn2vkhMl+Omd3cjLA5YfT0VJjRXgG+EqBsfs1qwA/1wbNInrZHxHNdnrL2t7BVae1JriqCkCiIjIo7lVMLRp0yZ8+umnaNu2rcPe4+Tm01g65yDyVzbAbxfbogo9dM9FeJ3F3a0OIOOBAPSf3BbKxt0dVg+L2COw8qTWFFNdiBz1RERERrhNMFRaWoqHHnoI//3vf/Hvf//bbvsVaoF9yw4jb/4J5K8PxZ9lbQDcvPEn+x1GeociZDwWilvHpMDLJ9xu7y0JntaaYqwL0drcLCIikg23CYYmTpyIIUOG4I477jAbDFVUVKCiokL3uKSkRO95VaVKswL8wkvI3xGHg1UtALQAACigRrdGe5DR6yLSn2mOpMGJABLtfTjS4YmtKfbqQiQiIllwi2Do66+/xtatW7Fp0yaLymdmZmL27Nl1tv/8+masyPPF0oPJOC9udrX5oQJ3NNuJjDuvYdj0ZESkpty4kW4ECo97/o3UE1tTOOqJiIgsJPl5hoqKitC5c2esWLEC7dq1AwD07dsX7du3N5pAbahlKDY2FkAxAM08BU0UVzAkbg8yhnth0LQ2CIwK1BQ2NLGcNXP2uDPOIUNERBLCSRdvyMvLwz333APvGjdllUoFhUIBLy8vVFRU6D1niPbDjPbah3tSzyJjVCB6T0yDbwNf/YKeMvkgERGRB2AwdMPVq1dx7NgxvW1jx45FcnIynn/+ebRp08bsPrQf5pXLVxDUJMhwIS7lQEREJCmcgfqGwMDAOgFPw4YNERISYlEgVJMi53sgMdFw948nTT5IREREFpPXqvWPPaZZuyo+vu7q5Z40+SARERFZTPItQ4YUFhbWbwcnT2pyg2rmAHnS5INERERkMXm1DGlp06QmT9bkCgE3Jx/UJkvXplBo1v5yl8kHiYiIyCLyDIYA/Rwg4Obkg0DdgMhdJx8kIiIis+QbDGnVzAHSTj4YHa1fJibmZpeaSgUUFgLZ2Zp/tS1LRERE5JbcMmfIrmrnAJlaykHOEzISERF5KMnPM2QPunkKoJ1/GtbPG8QJGYmIiJzKWfMMybObzNocIJVK0yJkKG40lIxNREREbkOewZA2Byg93bL8H2smZHQV5jIRERHZRF45Q599dnMG6vz8ustvGMv/kfqEjMxlIiIispm8Wobuu0+zlEZ+vib/p3Zrj3YyxtqzU0t5QkZtLpOlx0JERER65JVAXVyMxg0bWr8gq3YR15MnDecNuWoRVy4uS0REHowJ1I5iS/6PqydkNJYP5A65TERERBInv2DI1vwfSyZkdITcXE3rT79+wIMP6i80K/VcJiIiIjcgrwRqoH75P6YmZHQEY3MbafOBZs2ybD9cXJaIiMgo+eYMSS3/pzZL8oGiozXHcOqUtI+FiIjIBswZchRz+T9CAP/4h6b1x5Vz9ViSD3TiBPDEE5rHXFyWiIjIJvILhgDj+T9eNz6OefP0c3NcwdI8n5YtXZPLRERE5CHkGQwBmiDh6FGgoECzlAZQtyXIlXP1WJPbVPNYsrI0/x45wkCIiIjIAvLLGard5yjVuXqkOrcRERGRkzBnyFmkOlePq+c2IiIikgkGQ1Keq8dVcxsRERHJiPzmGapNyuuOAc6f24iIiEhmGAz16qVpaTGXm9Orl/PrpuXtrVlgloiIiOyO3WTMzSEiIpI1BkMAc3OIiIhkjN1kWszNISIikiUGQzUxN4eIiEh22E1GREREssZgiIiIiGSNwRARERHJGoMhIiIikjUGQ0RERCRrDIaIiIhI1hgMERERkawxGCIiIiJZYzBEREREssZgiIiIiGSNwRARERHJGoMhIiIikjXJB0OZmZno0qULAgMDERYWhoyMDBw4cMDV1SIiIiIPIflgaPXq1Zg4cSL++OMPrFy5EtXV1Rg4cCDKyspcXTUiIiLyAAohhHB1Jaxx/vx5hIWFYfXq1ejdu7dFrykpKUFQUBCKi4vRuHFjB9eQiIiI7MFZ928fh+3ZQYqLiwEAwcHBRstUVFSgoqJC97ikpMTh9SIiIiL3JPluspqEEJg6dSpuu+02tGnTxmi5zMxMBAUF6X5iY2OdWEsiIiJyJ27VTTZx4kT8+OOPWLduHWJiYoyWM9QyFBsby24yIiIiN8JuslqeeeYZLF26FGvWrDEZCAGAUqmEUql0Us2IiIjInUk+GBJC4JlnnsGSJUtQWFiIhIQEV1eJiIiIPIjkg6GJEyciKysL+fn5CAwMxJkzZwAAQUFBCAgIcHHtiIiIyN1JPmdIoVAY3P7FF19gzJgxFu2DQ+uJiIjcD3OGbpB4rEZERERuzq2G1hMRERHZG4MhIiIikjUGQ0RERCRrDIaIiIhI1hgMERERkawxGCIiIiJZYzBEREREssZgiIiIiGSNwRARERHJGoMhIiIikjUGQ0RERCRrDIaIiIhI1hgMERERkawxGCIiIiJZYzBEREREssZgiIiIiGSNwRARERHJGoMhIiIikjUGQ0RERCRrDIaIiIhI1hgMERERkawxGCIiIiJZYzBEREREssZgiIiIiGSNwRARERHJGoMhIiIikjUGQ0RERCRrDIaIiIhI1hgMERERkawxGCIiIiJZYzBEREREssZgiIiIiGSNwRARERHJGoMhIiIikjUGQ0RERCRrDIaIiIhI1hgMERERkawxGCIiIiJZc5tgaMGCBUhISIC/vz86deqEtWvXurpKRERE5AHcIhj65ptvMHnyZLz00kvYtm0bevXqhcGDB+P48eOurhoRERG5OYUQQri6EuZ07doVHTt2xEcffaTb1rp1a2RkZCAzM9Ps60tKShAUFITi4mI0btzYkVUlIiIiO3HW/VvyLUOVlZXYsmULBg4cqLd94MCBWL9+vYtqRURERJ7Cx9UVMOfChQtQqVQIDw/X2x4eHo4zZ84YfE1FRQUqKip0j4uLiwFoIkwiIiJyD9r7tqM7sSQfDGkpFAq9x0KIOtu0MjMzMXv27DrbY2NjHVI3IiIicpyLFy8iKCjIYfuXfDAUGhoKb2/vOq1A586dq9NapDVz5kxMnTpV9/jKlSuIi4vD8ePHHfphSk1JSQliY2NRVFQkq1wpHjePWw543DxuOSguLkbz5s0RHBzs0PeRfDDk5+eHTp06YeXKlbjnnnt021euXIn09HSDr1EqlVAqlXW2BwUFyeok0mrcuDGPW0Z43PLC45YXuR63l5djU5wlHwwBwNSpUzFq1Ch07twZ3bt3x6efforjx4/jySefdHXViIiIyM25RTB0//334+LFi/jXv/6F06dPo02bNli+fDni4uJcXTUiIiJyc24RDAHAhAkTMGHCBJteq1Qq8eqrrxrsOvNkPG4etxzwuHnccsDjduxxu8Wki0RERESOIvlJF4mIiIgcicEQERERyRqDISIiIpI1BkNEREQka24ZDC1YsAAJCQnw9/dHp06dsHbtWpPlV69ejU6dOsHf3x+33HILPv744zplcnJykJKSAqVSiZSUFCxZssRR1beZNcedm5uLAQMGoFmzZmjcuDG6d++OX375Ra/MokWLoFAo6vxcv37d0YdiFWuOu7Cw0OAx7d+/X6+cp33fY8aMMXjcqampujLu8H2vWbMGw4YNQ1RUFBQKBfLy8sy+xhOub2uP21Oub2uP21Oub2uP21Ou78zMTHTp0gWBgYEICwtDRkYGDhw4YPZ1zrjG3S4Y+uabbzB58mS89NJL2LZtG3r16oXBgwfj+PHjBssfOXIEd911F3r16oVt27bhxRdfxKRJk5CTk6Mrs2HDBtx///0YNWoUduzYgVGjRmHEiBHYuHGjsw7LLGuPe82aNRgwYACWL1+OLVu2oF+/fhg2bBi2bdumV65x48Y4ffq03o+/v78zDski1h631oEDB/SOqWXLlrrnPPH7fv/99/WOt6ioCMHBwbjvvvv0ykn9+y4rK0O7du0wf/58i8p7yvVt7XF7yvVt7XFrufv1be1xe8r1vXr1akycOBF//PEHVq5cierqagwcOBBlZWVGX+O0a1y4mVtvvVU8+eSTetuSk5PFCy+8YLD8c889J5KTk/W2jR8/XnTr1k33eMSIEeLOO+/UKzNo0CAxcuRIO9W6/qw9bkNSUlLE7NmzdY+/+OILERQUZK8qOoS1x11QUCAAiMuXLxvdpxy+7yVLlgiFQiGOHj2q2+YO33dNAMSSJUtMlvGU67smS47bEHe8vmuy5Lg95fquyZbv2xOubyGEOHfunAAgVq9ebbSMs65xt2oZqqysxJYtWzBw4EC97QMHDsT69esNvmbDhg11yg8aNAibN29GVVWVyTLG9ulsthx3bWq1GlevXq2z2F1paSni4uIQExODoUOH1vnL0pXqc9wdOnRAZGQkbr/9dhQUFOg9J4fv+/PPP8cdd9xRZ5Z2KX/ftvCE69se3PH6rg93vr7twVOu7+LiYgAwuQirs65xtwqGLly4AJVKVWe1+vDw8Dqr2mudOXPGYPnq6mpcuHDBZBlj+3Q2W467tjlz5qCsrAwjRozQbUtOTsaiRYuwdOlSZGdnw9/fHz179sTBgwftWn9b2XLckZGR+PTTT5GTk4Pc3FwkJSXh9ttvx5o1a3RlPP37Pn36NH766Sc89thjetul/n3bwhOub3twx+vbFp5wfdeXp1zfQghMnToVt912G9q0aWO0nLOucbdZjqMmhUKh91gIUWebufK1t1u7T1ewtY7Z2dmYNWsW8vPzERYWptverVs3dOvWTfe4Z8+e6NixIz744AP85z//sV/F68ma405KSkJSUpLucffu3VFUVIR3330XvXv3tmmfrmJrHRctWoQmTZogIyNDb7u7fN/W8pTr21bufn1bw5Oub1t5yvX99NNPY+fOnVi3bp3Zss64xt2qZSg0NBTe3t51or1z587ViQq1IiIiDJb38fFBSEiIyTLG9ulsthy31jfffINx48bh22+/xR133GGyrJeXF7p06SKZvyTqc9w1devWTe+YPPn7FkJg4cKFGDVqFPz8/EyWldr3bQtPuL7rw52vb3txt+u7Pjzl+n7mmWewdOlSFBQUICYmxmRZZ13jbhUM+fn5oVOnTli5cqXe9pUrV6JHjx4GX9O9e/c65VesWIHOnTvD19fXZBlj+3Q2W44b0PzFOGbMGGRlZWHIkCFm30cIge3btyMyMrLedbYHW4+7tm3btukdk6d+34BmtMahQ4cwbtw4s+8jte/bFp5wfdvK3a9ve3G367s+3P36FkLg6aefRm5uLn777TckJCSYfY3TrnGLU60l4uuvvxa+vr7i888/F3v37hWTJ08WDRs21GXVv/DCC2LUqFG68n///bdo0KCBmDJliti7d6/4/PPPha+vr/j+++91ZX7//Xfh7e0t3nzzTbFv3z7x5ptvCh8fH/HHH384/fiMsfa4s7KyhI+Pj/jwww/F6dOndT9XrlzRlZk1a5b4+eefxeHDh8W2bdvE2LFjhY+Pj9i4caPTj88Ya4/7vffeE0uWLBF//fWX2L17t3jhhRcEAJGTk6Mr44nft9bDDz8sunbtanCf7vB9X716VWzbtk1s27ZNABBz584V27ZtE8eOHRNCeO71be1xe8r1be1xe8r1be1xa7n79f3UU0+JoKAgUVhYqHfelpeX68q46hp3u2BICCE+/PBDERcXJ/z8/ETHjh31huWNHj1a9OnTR698YWGh6NChg/Dz8xPx8fHio48+qrPP7777TiQlJQlfX1+RnJysd3FJhTXH3adPHwGgzs/o0aN1ZSZPniyaN28u/Pz8RLNmzcTAgQPF+vXrnXhElrHmuN966y2RmJgo/P39RdOmTcVtt90mfvzxxzr79LTvWwghrly5IgICAsSnn35qcH/u8H1rh04bO2899fq29rg95fq29rg95fq25Tz3hOvb0DEDEF988YWujKuuccWNChIRERHJklvlDBERERHZG4MhIiIikjUGQ0RERCRrDIaIiIhI1hgMERERkawxGCIiIiJZYzBEREREssZgiIiIiGSNwRARERHJGoMhIiIikjUGQ0TklrKzs+Hv74+TJ0/qtj322GNo27YtiouLXVgzInI3XJuMiNySEALt27dHr169MH/+fMyePRufffYZ/vjjD0RHR7u6ekTkRnxcXQEiIlsoFAq8/vrruPfeexEVFYX3338fa9euZSBERFZjyxARubWOHTtiz549WLFiBfr06ePq6hCRG2LOEBG5rV9++QX79++HSqVCeHi4q6tDRG6KLUNE5Ja2bt2Kvn374sMPP8TXX3+NBg0a4LvvvnN1tYjIDTFniIjcztGjRzFkyBC88MILGDVqFFJSUtClSxds2bIFnTp1cnX1iMjNsGWIiNzKpUuX0LNnT/Tu3RuffPKJbnt6ejoqKirw888/u7B2ROSOGAwRERGRrDGBmoiIiGSNwRARERHJGoMhIiIikjUGQ0RERCRrDIaIiIhI1hgMERERkawxGCIiIiJZYzBEREREssZgiIiIiGSNwRARERHJGoMhIiIikjUGQ0RERCRr/w8aPlgkqRW6qAAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
@@ -1867,7 +1879,7 @@
},
{
"cell_type": "markdown",
- "id": "48ba87fe",
+ "id": "fe2faeda",
"metadata": {
"editable": true
},
@@ -1878,7 +1890,7 @@
{
"cell_type": "code",
"execution_count": 8,
- "id": "7522775d",
+ "id": "89600ea6",
"metadata": {
"collapsed": false,
"editable": true
@@ -1888,9 +1900,9 @@
"name": "stdout",
"output_type": "stream",
"text": [
- "[[4.40754621]\n",
- " [2.78752269]]\n",
- "[4.37713991] [2.77711437]\n"
+ "[[4.1509778 ]\n",
+ " [2.92461411]]\n",
+ "[4.13288373] [2.92817032]\n"
]
}
],
@@ -1915,7 +1927,7 @@
},
{
"cell_type": "markdown",
- "id": "90552e2f",
+ "id": "c277543b",
"metadata": {
"editable": true
},
@@ -1925,7 +1937,7 @@
},
{
"cell_type": "markdown",
- "id": "5d7c032c",
+ "id": "f929cf55",
"metadata": {
"editable": true
},
@@ -1937,7 +1949,7 @@
},
{
"cell_type": "markdown",
- "id": "ed86f1ba",
+ "id": "dff0af0d",
"metadata": {
"editable": true
},
@@ -1947,7 +1959,7 @@
},
{
"cell_type": "markdown",
- "id": "0386e23c",
+ "id": "3722fdb9",
"metadata": {
"editable": true
},
@@ -1961,7 +1973,7 @@
},
{
"cell_type": "markdown",
- "id": "b65523fc",
+ "id": "074790fe",
"metadata": {
"editable": true
},
@@ -1971,7 +1983,7 @@
},
{
"cell_type": "markdown",
- "id": "c62584ee",
+ "id": "3469f911",
"metadata": {
"editable": true
},
@@ -1984,7 +1996,7 @@
{
"cell_type": "code",
"execution_count": 9,
- "id": "e8d43667",
+ "id": "61a75ef6",
"metadata": {
"collapsed": false,
"editable": true
@@ -1994,15 +2006,15 @@
"name": "stdout",
"output_type": "stream",
"text": [
- "[[3.94107596]\n",
- " [2.96620033]]\n",
- "[[3.96670977]\n",
- " [2.94212937]]\n"
+ "[[4.0795449 ]\n",
+ " [2.86893619]]\n",
+ "[[4.04785727]\n",
+ " [2.89298533]]\n"
]
},
{
"data": {
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\n",
+ "image/png": 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jJsc1sHRf2hIZGYl27doBADp27IiOHTuiZcuWGDt2LPbv32/1c+bIPRAdHY1vv/3WbjlPXUPyTWwZIkVNnz4dOp0Ojz76KK5du+bSvgy/iKs+cJcsWWLyffXq1dGhQwfk5uaa/FV+4cIFfPLJJ3aPc8899+DPP/9EdHQ02rVrZ/blzIRvhjrLaRFp3Lgx6tWrh5ycHJPJ6Q4fPmwyqstQ17Nnz0Kn01msq6Vf7oGBgejYsSMWLlwIAPjuu+8AAHfddReuXLliNvqm6vGEEDh27JjF49188812z68qR66NoQ4//fQTkpOTLdahcjA0Y8YMFBQU4MMPP8TKlSvx/fffm7UOSZJk9pn67LPPcOzYMYfPRY6vvvrKZDSVTqfDypUrkZycjPj4eIuvady4MRo1aoTvv//e4jm3a9fOJPCVq3v37vjll1+MnwGD999/H5IkIS0tzeF92tKoUSM88cQT+PHHH7Fy5Uqr5Ry5B7p06YILFy7g888/N9ledYSep64h+Sa2DJGiOnfujIULF2LChAlo06YNRo0ahWbNmiEgIADFxcVYs2YNAMia9DAlJQXJycmYNm0ahBCIiorCJ598gs2bN5uVfeGFF3DnnXeiR48emDJlCnQ6HV5++WVUr14d586ds3mczMxMrFmzBrfffjsmTZqEFi1aoKKiAkeOHMGmTZswZcoUdOzY0aHrYAgS5s+fj4yMDAQHB6Nx48YWf/kGBATghRdewMMPP4z+/fvjkUcewfnz5zFz5kyzLoLBgwfjww8/xN13342JEyeiQ4cOCA4OxtGjR5GXl4e+ffuif//+WLx4MbZs2YLevXujQYMGuHLlirHl64477gCgz7FYunQpHn30URw4cABpaWmoqKjArl270KRJEwwePBidO3fGqFGjMHLkSOzZswe33347qlevjuLiYmzfvh0333wzxowZ49C1McxK/uGHH6JJkyaoUaMG4uLiTIKayp5//nls3rwZnTp1wmOPPYbGjRvjypUrOHToEDZs2IDFixcjPj4emzdvRnZ2Np599lnj1AzZ2dmYOnUqunbtiv79+wPQB1fLli1DSkoKWrRogb1792LOnDlWAxNX1a5dG926dcOzzz6L6tWrY9GiRfjtt9/sDq9fsmQJ7rrrLvTq1QsjRoxA/fr1ce7cOfz666/47rvvsGrVKofrMmnSJLz//vvo3bs3nn/+eTRs2BCfffYZFi1ahDFjxuCmm25y9jStmjp1KhYvXoysrCwMGjQIgYGBZmUcuQcyMjIwd+5cDBs2DC+++CJuvPFGfP755/jiiy+M+zLwxDUkH+XF5G3SsP3794uRI0eKpKQkERoaKsLCwsSNN94oHnzwQfHVV1+ZlM3IyBDVq1e3uJ9ffvlF9OjRQ9SsWVPccMMN4r777hNHjhwRAMSMGTNMyq5fv160aNFChISEiAYNGoiXXnpJzJgxw+5oMiH0w3WfeeYZ0bhxYxESEiIiIyPFzTffLCZNmmQyEgiAGDdunFk9Le1z+vTpIi4uTgQEBJiNFLLknXfeEY0aNRIhISHipptuEu+++67IyMgwGUkjhH648quvvipatmwpwsLCRI0aNURKSooYPXq0+OOPP4QQ+lFg/fv3Fw0bNhShoaEiOjpadOnSRaxfv95kX3///bd47rnnjMeNjo4W3bp1Ezt27DAp9+6774qOHTuK6tWri/DwcJGcnCwefPBBsWfPHmOZLl26iGbNmpmdl6VzyMnJESkpKSI4ONjie1nV6dOnxWOPPSaSkpJEcHCwiIqKEm3bthVPP/20uHjxojh+/LioW7eu6Natm8kIoYqKCtGnTx9Rq1Yt48i+v/76Szz00EOibt26olq1auK2224TBQUFokuXLqJLly7G1xpGPFUeAi/E9SHgVUcfGj5rp0+fNm4zfF4WLVokkpOTRXBwsEhJSREffvihyWstjSYTQojvv/9eDBo0SNStW1cEBweL2NhY0a1bN7F48WKb10sIy6PJhBDi8OHDYujQoSI6OloEBweLxo0bizlz5phcN8Nosjlz5tg9jr3jCXF9BJhhigVr5yv3Hjhy5IhIT08XNWrUEDVr1hQDBgwQGzZsMBtlKoRr15D8hyRElUVhiIhIEZIkYdy4cViwYIG3q+L3Zs+ejWeeeQZHjhzxWCsf+S52kxERkV8xBJcpKSm4du0atmzZgv/85z8YNmwYAyGyiMEQERH5lWrVqmHu3Lk4dOgQysrK0KBBAzz55JN45plnvF01Uil2kxEREZGmcWg9ERERaRqDISIiItI0BkNERESkaZpIoK6oqMDx48dRs2ZNh6ePJyIiIu8QQuDChQt210l0lSaCoePHjyMhIcHb1SAiIiInFBUVeXRaBE0EQ4YlDoqKimQt80BERETeV1paioSEBI+vE6eJYMjQNRYREcFgiIiIyMd4OsWFCdRERESkaQyGiIiISNMYDBEREZGmMRgiIiIiTWMwRERERJrGYIiIiIg0jcEQERERaRqDISIiItI0BkNERESkaQyGiIiISNMYDBEREZGmMRgiIiIiTWMwRERERJrGYIiIiIg0jcEQERERaRqDISIiItI0BkNERESkaV4PhrZt24Y+ffogLi4OkiRh3bp1VsuOHj0akiRh3rx5itWPiIiI/JvXg6FLly6hZcuWWLBggc1y69atw65duxAXF6dQzYiIiEgLgrxdgbvuugt33XWXzTLHjh3D+PHj8cUXX6B3794K1YyIiIi0wOstQ/ZUVFRg+PDhePzxx9GsWTNvV4eIiIj8jNdbhux5+eWXERQUhMcee0z2a8rKylBWVmb8vrS01BNVIyIiIj+g6pahvXv3Yv78+Vi2bBkkSZL9uuzsbERGRhq/EhISPFhLIiIi8mWqDoYKCgpw6tQpNGjQAEFBQQgKCsLhw4cxZcoUJCYmWn3d9OnTUVJSYvwqKipSrtJERETkU1TdTTZ8+HDccccdJtt69eqF4cOHY+TIkVZfFxoaitDQUE9Xj4iIiPyA14Ohixcv4uDBg8bvCwsLsX//fkRFRaFBgwaIjo42KR8cHIzY2Fg0btxY6aoSERGRH/J6MLRnzx6kpaUZv588eTIAICMjA8uWLfNSrYiIiEgrvB4Mde3aFUII2eUPHTrkucoQERGR5qg6gZqIiIjI0xgMERERkaYxGCIiIiJNYzBEREREmsZgiIiIiDSNwRARERFpGoMhIiIi0jQGQ0RERKRpDIaIiIhI0xgMERERkaYxGCIiIiJNYzBEREREmsZgiIiIiDSNwRARERFpGoMhIiIi0jQGQ0RERKRpDIaIiIhI0xgMERERkaYxGCIiIiJNYzBEREREmsZgiIiIiDSNwRARERFpGoMhIiIi0jQGQ0RERKRpDIaIiIhI0xgMERERkaYxGCIiIiJNYzBEREREmsZgiIiIiDSNwRARERFpGoMhIiIi0jQGQ0RERKRpDIaIiIhI0xgMERERkaYxGCIiIiJNYzBEREREmsZgiIiIiDSNwRARERFpGoMhIiIi0jSvB0Pbtm1Dnz59EBcXB0mSsG7dOuPPrl27hieffBI333wzqlevjri4ODz44IM4fvy49ypMREREfsXrwdClS5fQsmVLLFiwwOxnly9fxnfffYdnn30W3333HXJzc/H777/j3nvv9UJNiYiIyB9JQgjh7UoYSJKEtWvXol+/flbL7N69Gx06dMDhw4fRoEEDWfstLS1FZGQkSkpKEBER4abaEhERkScp9fwO8tiePaSkpASSJKFWrVpWy5SVlaGsrMz4fWlpqQI1IyIiIl/k9W4yR1y5cgXTpk3D0KFDbUaI2dnZiIyMNH4lJCQoWEsiIiLyJT4TDF27dg2DBw9GRUUFFi1aZLPs9OnTUVJSYvwqKipSqJZERETka3yim+zatWsYNGgQCgsLsWXLFrv9hqGhoQgNDVWodkREROTLVB8MGQKhP/74A3l5eYiOjvZ2lYiIiMiPeD0YunjxIg4ePGj8vrCwEPv370dUVBTi4uIwcOBAfPfdd/j000+h0+lw4sQJAEBUVBRCQkK8VW0iIiLyE14fWp+fn4+0tDSz7RkZGZg5cyaSkpIsvi4vLw9du3aVdQwOrSciIvI9mhla37VrV9iKx1Q0DRIRERH5IZ8ZTUZERETkCQyGiIiISNMYDBEREZGmMRgiIiIiTWMwRERERJrGYIiIiIg0zetD64mIiEjDdDqgoAAoLgbq1QNSU4HAQEWrwGCIiIiIvCM3F5g4ETh69Pq2+Hhg/nwgPV2xarCbjIiIiJSXmwsMHGgaCAHAsWP67bm5ilWFwRAREREpS6fTtwhZWmXCsC0zU19OAewmIyIiIs+qmhek05m3CFUmBFBUBOzYoUj1GAwRERGR51jKC4qKkvfaEyc8U6cqGAwRERGRZxjygqp2h507J+/1sbHur5MFDIaIiIjI/WzlBdkjSfpRZZ06ub9eFjCBmoiIiNyvoMB2XpA1kqT/d948xeYbYjBERERE7ldcLK9c1fyh+Hhg9WpF5xliNxkRERG5X7168sp99JG+BYgzUBMREZGquLpMRmqqvpXn2DHLeUOGvKCuXRUPfqpiNxkRERGZys0FEhOBtDRg6FD9v4mJjs0KHRioX1YDuJ4HZOCFvCBbGAwRERHRdatWAQMGuGeZjPR0ff5P/fqm272QF2SLJIQzY958S2lpKSIjI1FSUoKIiAhvV4eIiEidVq8GBg+2vgyGoWursNCxFh0nu9yUen4zZ4iIiIj0LT733We7jGGZjIICfa6PXIGBlsu7mpfkJgyGiIiItM4wQaJccofN22JpmY74eH2ekcLdZ8wZIiIi0jpHJ0iUO2zeGsMyHe7IS3IDBkNERERa50hLT0KCvjvLWbaW6TBsy8y0nrfkAQyGiIiItM6Rlh5Xh8Pba4WqnJekEAZDREREWmeYILHqfECVBQbqZ4t2NZ9HbiuUO/KSZGIwREREpHWBgcDcubZXmF+xwv5oMznktkK5mpfkAAZDREREWpebC0yaZPlnCQnAmjX6xGZ3sNcKJUmu5yU5iMEQERGRllkb2WXw2mvuHequwmU6GAwRERFpla2RXYA+OJkyxf0ju1S2TAcnXSQiItIqR0Z2OTLjtBzp6UDfvpyBmoiIiLzI2yO7rC3ToTB2kxEREWmVCkd2eQODISIiIq1S4cgub2AwREREpFUqHNnlDQyGiIiItExlI7u8gQnURERE9uh0qhj15DEqGtnlDV5vGdq2bRv69OmDuLg4SJKEdevWmfxcCIGZM2ciLi4O4eHh6Nq1K37++WfvVJaIiLQnNxdITATS0oChQ/X/Jibqt/sTw8iuIUP0/2okEAJUEAxdunQJLVu2xIIFCyz+/JVXXsHrr7+OBQsWYPfu3YiNjUWPHj1w4cIFhWtKRESaY2125mPH9Nv9LSDSKEkIW6uyKUuSJKxduxb9+vUDoG8ViouLQ2ZmJp588kkAQFlZGWJiYvDyyy9j9OjRsvZbWlqKyMhIlJSUICIiwlPVJyIif6LT6VuArE1KKEn6vJrCQu+3ovhpN55Sz2+vtwzZUlhYiBMnTqBnz57GbaGhoejSpQt27Nhh9XVlZWUoLS01+SIiInKII7Mze5NWuvE8SNXB0IkTJwAAMTExJttjYmKMP7MkOzsbkZGRxq+EhASP1pOIiPyQt2dnloPdeG6h6mDIQKoy94EQwmxbZdOnT0dJSYnxq6ioyNNVJCIif6P22ZltLbJq2JaZ6f5FVv2QqoOh2NhYADBrBTp16pRZa1FloaGhiIiIMPkiIiJyiNpnZ/aVbjwfoOpgKCkpCbGxsdi8ebNx29WrV7F161Z06tTJizUjIiK/p/bZmX2hG68qnQ7IzwdycvT/qqTVyuvB0MWLF7F//37s378fgD5pev/+/Thy5AgkSUJmZiZmz56NtWvX4qeffsKIESNQrVo1DB061LsVJyIi/5eeDqxcCURHm25Xw+zMau/Gq0rFid5eH1qfn5+PtLQ0s+0ZGRlYtmwZhBDIysrCkiVL8Ndff6Fjx45YuHAhmjdvLvsYHFpPREROyc3V5+VU7o6qUwdYtEifoOxNhqH/x45ZzhtS09B/Q6K3hXoKAFPwKgAJ2T/di9BmNxp/ptTz2+vBkBIYDBERkcOsPcANXWTebhkCrtcRMK2nmupoZ76mCkg4ingkoRAb3jyCXo8mGX/GeYaIiIi8xVdGaql9kdVz54CgIJuJ3gEQaIAiPNZ4E7o/nGS1nCcxGCIiIqrKl0ZqpacDhw4BeXnA8uX6fwsLvRcI9emDL6RekCRAio7CECyX9bK5M84jyEvLx3PVeiIioqo8MVLLk0tmGBZZ9YaLF4GaNSHB0Ir2icmPi6H+RG+2DBEREVXl7pFaKh5J5ZR//xufSvfoW39q1qgUCJkrQCrOVVfxfE1gMERERGTOnRMu+sOSGWVlgCTpgx8JkJa+iz741OZL/v5b35uoE4GIel/F8zWBwRAREZE5d0246CuJ2JY88QTWSv31wU9YqM3WHwAYO1Z/SoavsLBKP1R5ojeH1hMREVljaZ6hhAR9ICTnAZ6fr+8Ssycvzz05P67kJV27BoSE2A16KrtyBQgN9Vz9lHp+M4GaiIjImvR0oG9f5wMMJZfMsBS4xcfrW7isBW5DhmD2iiQ8jdkAggE7gdDkycBrr7lQR28metvAYIiIiMgWVx7gSi2ZYW2CSENekqErqqICCAys1PqTY3fXV68CwcGuVU/tmDNERETkKe5MxLbGXl6SEDg/YCQCJR2kwAC73WB9+pjm/vh7IAQwGCIiIvIcdyVi22JvgkgAtVCKVFifIPLq1evBz/r1zlfFVzEYIiIi8iRPj6SSmW9UD9fL3Xuv9lp/bGHOEBERkae5mohtgZAkBECgC+ohX0b5D76sh5zuTh/OrzEYIiIicjdrQ8hdGUn17LPo9mIa8tDtnw363J8CpKII8aiPYwiwlg9Upw4CUzs5f2w/x24yIiIid3Lj0hsVUsD1WZ9ffKFSIFSpDAIxEfq8JGEtUfv0aSA52Tdmu/YCBkNERGqk0+kn7MvJ0f+rxhmKyZyrS28sWIAO0rfGACgQFTaLt2unz/nJFekIWLMaUtW8JGfqoEGcgZqISG2cmTxPCzy56rs76HT6FiBrI7skSf8+Fhaa1FsnBSII8oNdnQ4IsNaUcfWq/hinTztUB6+Q8X4q9fxmyxARkZr4w6KenuALq77bG+IuBFBUBNx/Px6W3kZXKR+Bks5uIJSWZjryy2ogBAA7dlgPhCrXocD6MHtFqOz9ZDBERKQWvryopyf5SoAod0mNNWvwDkYhH2k4hET0h3n9KyquBz9btnigDu5Y/sNZKnw/GQwREamF3JYFb/9VryRfChCdWFKjPo5hNQZiVttck9Yfa3nQbquDq8t/OEul7yeDISIib6qcKP3VV/Jeo/Rf9d5M5vahAPHvtDtRhHhUwHIkYylBNwACARLw1KlM91xXJZb/cIVK308GQ0RE3lI1b+LFF+W9Tsm/6r2d26Hmbp8vv7w+7F0CquGKcYi7pYDIamOPOwMAJZb/cIVK308GQ0RE3mAtb8IWpf+qV0Nuh8q6fS5J1a8HQD3uMPv5WqRjIFbjGGwMcbfGXQGAp5f/cIXK3k8DDq0nIlKavSHYlhj+qlfqYebkMHGP1ePYMct5Jp6ux+7dkDq0l128RQvg++9hOmz85Elg0iT7L87Lc22G6qrUOBWBg++nUs9vBkNERErLz9d3NzkiIUHfvaHUX/Vy6+juB7glhhYqwPQB6qEA8bxUCzfgvOzydp+iOh0QEwOcPWu9THS0PmjydrDiLrYCMQfeT84zRETkrxztDqlTB3j9dWW7N9SU2+Hpbp8DB0xyf+wFQp07m877Q1XYyzNTYTceW4aIiJTmaMuQ0l1kgHdahux167ix2+eUVBcxOCW7vEtPSjW1snmaodWn6gWz9BnmDNRERH7E0aHn9oY/V+WN+VeUHqLt6VFrJ06YtP7YC4Q6dXJj64+aWtk8ydE5hAID9cHfkCH6f73YRchgiIjIFc48xG0Nf7bGG/OvPPKI9SRXwH1DtOWMWnPiOh+T6l8PgOrF2q1G5eDn669dOyUTKh1B5XYqnUNIDgZDRETOcmXoubW8CXuUaD0wBB4zZlj+uTtzO+S0JowaBQwYYP86X7hg0voTj2M2D+3W1h9b1D4Rorv4cAsYgyEiIme4Y1mB9HTg0CF9rsgzz8g7rqdbD+zNf5SVpR/27K7cJTmtCdZGYQkBIQSODMhEsHQVXSP2YjBy0AX5CLCy+KnHWn9sUftEiO7iwy1gDIaIiJzhri4BQ97EzJnebz2wFeAZ6vDOO+49poutBBKABijCMcQjH2nIwVCTBVB79VLJyC8VjqByOx9uAWMwRETkDHd3CbjaeuCO9cO8kfPhplaCOjht8n2CdAy50kBsHKWSFe0B05bA5cv1/7qzlc3bfLgFjMEQEfk3Ty0y6okuAWdbD9w1Euvjj+WVc2fOh53WhAqZuzF7tdpWtDdQ0Qgqj/DRFjDOM0RE/is3V9/tU7m1Iz5e/9erq7+UPblMhCPz6Tgyr4u9Y9arB5w+bb+s3Plw5J5Hbi7EgAEQkBBQaW13w2Kn5xCFKJwz+ZlD/GH+Hl/jpjmhuByHGzEYItIgdwUJco4BKLJMhBl3rh8md2LAOnX0Dzh7+5MRiFZuDOqPXMzHRCTgevkjSEAm5gEA1mCgvrwzj6zly/UtMeRzOOkika/yVLcMyeeOkV5yeLtLwJ05PnK7vh54QF4gZGFEmjh6FBUDBiJdyjXrFVuLdCTiELoiD0OwHF2RhwblhcgV6cgV6ZDWWLjOderIq7MKRy+RugR5uwJEfsWT3TIknyNBgqvdJ+npQN++3lkd3J1J3HIDhr59bf/cRiAqARAA5iETH6MvKmB6jfr1Bdas62p5v5auc6dOQHKy/a5KFY5eInVRfctQeXk5nnnmGSQlJSE8PBz/+te/8Pzzz6OiQm5aHZFCXJmAj9xL6cnfvJUU684kbjcNi94e3sNmIBoAgQYoQir0rVWVh72vWWfnulW9ziEhPjt6idRF9cHQyy+/jMWLF2PBggX49ddf8corr2DOnDl44403vF01ouuU6pYheXx48jeHuHNeFxeGRVee9XnhtUdkVT1/ebF75v3xdlcl+QXVB0M7d+5E37590bt3byQmJmLgwIHo2bMn9uzZ4+2qEV3nw2vy+CUfnvzNIe6e10VmYPF27LMmAVBlxfBCIOrv8/eQx6k+GLrtttvw1Vdf4ffffwcAfP/999i+fTvuvvtuL9eMqBIfXpPHL/nw5G8Oc3fLiJXAQhqQbgx+Rp18werLC5CKc+Fxygei/j5/D3mU6hOon3zySZSUlCAlJQWBgYHQ6XSYNWsWhtgYJllWVoaysjLj96WlpUpUlbRMK90yvsQQJFhKaJ83z79aDdydxB0YiFfGHsKTv46Q/ZLrXV6BQO4b+jw5SbI85YC/BKLkN1Q/z9CKFSvw+OOPY86cOWjWrBn279+PzMxMvP7668jIyLD4mpkzZyIrK8tsO+cZIo/x5AR85Bo3Tf6mBdYacyz5993F+O9nNoJ7SyMrExL8LxAlj+Kki/9ISEjAtGnTMG7cOOO2F198ER988AF+++03i6+x1DKUkJDAYIg8y9sT8BE5aMbteXi+QMZEi/9w+GnBQJRcpFQwpPpussuXLyMgwDS1KTAw0ObQ+tDQUISGhnq6akSmtNQtQz7LtPXHdiA0qdcveH1jU+cPZsjjIVI51QdDffr0waxZs9CgQQM0a9YM+/btw+uvv45///vf3q4akTlvTsBHZEFmj58x/8tmssubtv64EAgR+RDVd5NduHABzz77LNauXYtTp04hLi4OQ4YMwXPPPYeQkBBZ++DaZESkJY7k/szsmo8ZeV09VhciVzBnyI0YDBGRPxt553Es+yJOdnlZv/WZ70MqwIVaiYjIqsqTHtoLhF5v8z+TZS/sys3Vj45MSwOGDtX/m5jIJWXIbzEYIiLyAf26lVqd9dmSysHPpL3D5R+Ia+wpR6cD8vOBnBz9v1yux2scCoaKioo8VQ8iIqqicvDzcZ7tLoK347Mca/2xxJE19vggdw1b31TFoWAoJSUFzz77LC5duuSp+hARaVaH1ledbv15uGiG6xWQu8berFl8kLuCrW+q41AwtHnzZmzatAmNGjXC0qVLPVUnIiLNqBz87N5ve4TsCtzveuuPLXLXzpsxgw9yZznS+kaKcSgY6tSpE3bt2oWXXnoJzz33HFq3bo38/HwPVY2I/A67VhBTt8Lp1p/7xUrPVs6VtfP4IJdHbutbQYF7jsd7ThanEqgffPBB/P777+jTpw969+6N/v374+DBg+6uGxH5Ew3nSFQOfk6dtv1rdy36ebb1x5bUVP2M6Y5MVFSZux/k/khu65vccrZo+J5zlNOjyYQQ6NmzJ0aNGoX169ejefPmmDJlCi5cuODO+hGRP9BYjkRQkHC69aefWOfx+lkVGAjMn6//f9WKOxIgueNB7q/ktr650koHaO6ec5VDwdDixYvx0EMPoUWLFoiMjMQdd9yBr7/+GuPGjcOiRYuwf/9+NG3aFHv27PFUfYnI13gjR8ILXQOVgx+dznbg8Dnu9F7rjz2GNfbq1zfdHh8PZGXJ24erD3J/Zq/1TZKAhAR9OWcxL8lhDs1AnZCQgFtuucX41a5dO7MFUWfPno3ly5fjp59+cntlncUZqIm8KD9f3zxvT16eexb1zM21vFju/PluXSzX0Z4kUSGc737yBkszUAP6bpZjxyw/aCVJf60LC90zW7VSs2ArPdu2odUGML2Ohs/H6tWufVaVvuc8SLHnt3CzEydOiICAAHfv1iUlJSUCgCgpKfF2VYi0Z/nyyo0g1r+WL3f9WGvWCCFJ5vuWJP3XmjUu7V7OaRi+CtDZ9fNRI8M1rnqd3XSNTY4TH296jPh49+1f6ePIOW5CgnuOq+Q952FKPb/dPgN13bp1sWXLFnfvloh8lVI5Eh7oGqjc9SUr96fsqvFJc5vYLvs4PsVWN5qrLRoGSuW7eDOvJj0dOHRI3zqzfLn+38JC91w/pe45P8KFWonIs3Q6ZbpW3NQ14EhP1rdoj/Zit/wX+BNPdS0ZPi/Whp+76/Oi1HG8Qal7TgFcqJVIS/x5LhA5I5TmzXP9l7KTQ5Yttf4EQIcuyMdg5KAL8hGA6++HOHPW2Pqj2UAI0L9fXbsCQ4bo/3XXQ1WpeXiUnu9HSUrdc36EwRCRt2lhLhAlulYc6Bqw1fXVH7k4hETkIw05GIp8pEEXnwixJlf/R3Z0tOt1tcafgmJnz0WpeXiUnO/HG5S45/xIkLcrQH5G6VEZvs6Qs1C1KduQs+BPv7T69gUiI/UPRkDfmuDOFgXDkGUrXQMVkHAU8UhKsz5kuT9ysRoDEQAvvB8KjYJThCvnolS+ixbyatLT9fcdfyfb59H0bJXgaDKFWBuVsWqVEHl5+pELeXlClJd7u6bqUF5ufr2qjs5JSPCP6+XuETvl5ZY/U1ZGOukgCR0k0R9rLF7qP5Ds3ffDw6PgFOXquRjeB0v7cOf7oNRxyCVKPb8ZDJF7WPsFaOlLiWGrviAvT971ysvzdk1d4+4HvZXAyhDo9McacQSmPz+MBLNASOTnm+7XW++HLwbF1oJRd52LksP3lTgOOY3BkBsxGPIwe78A/eGvXXusPRxs8aO5QKxy94PeSmBVteUnAOWiC/LEYCwXXZAnAlAuilD/ep0svVfeej98LSi21crnznPx5Dw83jgOOUWp5zdzhsh19kZlVCWEPnM1M1Pfn+3r/dfO5kf4Q86CvRwxR0bs2JsJV6dD0YCJqA9hNvIjAAIVkDAPmfgYfVGBQGxFV4gPlwNDDfs9avu98tb74UuJvPZy3CZOlLcfOeeiVL4L82oITKAmd3Dml7QjD0E1cyUB2k7Cr3EuEFfWKPIUnQ6YNUsfRJw7d3171SDQxQe9EEDAP5FPFxQgH9YDqwAINEARdHmVP1NDrxew916tXOmd9+OPP+SV83ZQbG9SS0kCPvxQ3r7knoth+L6nKXUcUi0OrSfXufJLWqm/dj0xZNnVGY99dS6Q3FwgJgaYMcM0EALMZ+51orWl8rD3gEq/oerBhcBKpwNGjbL9Xk2ZAsyde70SlXnq/dDpgLfesl9ODUGxnFa+06eBOnU8uwgpkQcwGCLX2VuF2RYl/tr11Dw+7pi0zdfmAsnNBQYMAM6etfzzqkGgjBW6RUICAtNS7S55UQwXurFmzbJeZ0O9i4qA2rWVfT8KCvQBpD2PPOL9oFjuHy4PPKD/15cCfNI8BkPkOlstHNYo9ReiJ9cecleuhzvWKFJisj5DS5g9lYNAG5+NCkioEMCAonmogO2Ho+jXH/nl9gMri58pne56HewpLvbsmlGWjidHo0buP7aj5P7h0revbwX4RAA4mozcx9KoDG+OJvP0kGW1jAJSatVtuedrYdSVbpW84e6Gr0sIt36ujg6FdqTeSo/YUstnSA5H5+VxZoQlURUcWu9GDIYUVPUX4EcfeW/YqqcfNGqYtE3JyfrkDj3/56sL8kw2WRruXvnnokED+efsyGdKbr2jo5V/YKvhM+QIzstDCuPQevJNlkZlpKd7Z9iqp4csG7qABg7Ud9EIcf1nSuRHyBnd487pC2R2k1QAOIoEFCC1ynb9cHeDKwhFqCirVOKwvHo4OhRabvdOnz7ARx8p+xn19mfIUYYcN0vTE8ybxy4w8lmSEJZ+k/qX0tJSREZGoqSkBBEREd6uDiklP1+fLG1PXp5rw2otzV2TkKB/OHhy/hKlzs9Ap9Mnnlsbeg5AABCQMBCrsRbmD0YByeprPUZGvREQAFRUXP9e6TXBbH2G1BhgcA1CUohSz28GQ+S/7D0EDfPGFBa6/ou88sOhbl39tk8/1c+7cvr09XLufMjm5OhHx9mzfDkwZIjrxwNwbWUuAgcPBADzxUwBnEY0RuMtYyB0DUEIEuVuObZLDIn0gLxgzNAqo2TCLwMMIjNKPb85mqwqJUblkDKUmsen8kPsjz+AjAzgjjv0+64cCAHuGcVmoNCMyZXn/QkZnI6BWI1jMB0pdAZReBZZiMVJ5GKAMZlEFYEQYH0KA2vvvSFgsjVPlLsZupiHDNH/y0CISDFsGarM2WUVSN082QVhad/2uKtFykMtX5cuATVq2C4TAB1SUYB6KMaHGIqA8nLfeHhXDlxPngQmTbL/Gnd1MxKRw5RqGWICtYEryyqQunlq7SFrnxl7hHDPUiRuTL51dL5MHYIqHc89XXCKqJzgn5Mj7zVqWBOMiDyK3WSA68sqkPq5uwvi6lVg9GjXkoHd8ZB1ZAbrSl3AFz7JR6Ckszvrs0EFJJMx34onQXuCPyyUS0RuwZYhwL0ra5P/y80FHn0UOHPGtf04+5Ctmmjbt6/9lq/cXBQNmIiEfxY6rQngEOIxEfMtjvoCqo788oPgpyp7C+UC+nW2OnVStl5EpDi2DAGen4+G/Ieha6xqYrQjXFmKxNo6ax9/bNbydfKk/lDpUi4qBgxE/SorvtfHMazGQPSHPplbQIIo1/lX648tcpaROX0aSE52T8I7EakWgyGAzeUkj63uVLlcGcUmY521yiO/YmP1ic7zMRGAMLvZAyAQAIHc+IkQX36lH4JfUKCt7mBr3YyVuXMEIBGpEkeTAcrOR0O+S+4kh7Y4O4rN8Bm10p1bAQlHEY8kFJosetoF+ciHg3XW4gjKq1f1AZG1rk/+DiDyCs4zpCSl5qMh3+ZsN2mdOvoEfFdWP7eT1xYAgQYoQioKTLbXgxN1PnoUGDBAWy0hO3bYzgGrnDdIRH6HwZCBI6NySJvkdpPWrg1kZem7nfLy9EHU3LlOj2L77TdgSJq8oKYeivW5P0VHIQSQk+dC1+6oUdrpMmPeIJGm+UQwdOzYMQwbNgzR0dGoVq0aWrVqhb1797r/QOnpwKFD+geY4UHm7F/y5H8Mo49sjUWvU0ff3frccy4N46+c+9OkCVAMeUFNTl49fStGfLz8Oltz9iwwa5bjr/NFzBsk0jTV5wz99ddfaN26NdLS0jBmzBjUrVsXf/75JxITE5GcnCxrHy71OXK9IKrM2hpXLq5ltW8f0KaN9Z8HQIdDSER9HLO4JpjNnBZH1+WqLDpaP1Ozv3/mmTdIpErMGfrHyy+/jISEBCxduhQdOnRAYmIiunfvLjsQcom1YcxayqUgU27sTq3c+mMrEAKACgQiAUcRIMHxvDY5I6asOXtWG3kyzBsk0jTVB0Pr169Hu3btcN9996Fu3bpo3bo13n77bZuvKSsrQ2lpqcmXw2QMYyaNcrI7dccO0wDIHgEJInet6bw/zgZiVev85ZfADTfYrwSgnTwZ5g0SaZbqu8nCwsIAAJMnT8Z9992Hb7/9FpmZmViyZAkefPBBi6+ZOXMmsrKyzLbLbmazM4yZTeYEQFYXqqOpOqazPjt/XFmefx6YMcN+Oa0tVMqucSLVUKqbTPXBUEhICNq1a4cdO3YYtz322GPYvXs3du7cafE1ZWVlKCsrM35fWlqKhIQE+RdT7nwyWntI0HWWVquPj8fPo+aj+XPyWxAEJGDOHGDqVA9U0g6dDoiJ0XeFWeJrQb87gxgGRESqwJyhf9SrVw9NmzY12dakSRMcOXLE6mtCQ0MRERFh8uUQDrMlW6x0oVYcPYYmz11f3sIaUWnRUwjhnUAI0D/c33rLcvOVr+XJuDO/j7mCRJqj+mCoc+fOOHDggMm233//HQ0bNvTcQTnMlqzR6XBl9ERUWGhQNYzymodMBOD6/DwCEsTYcepc88uQJ2MYim/gS3ky7szvY64gkSapvpts9+7d6NSpE7KysjBo0CB8++23eOSRR/DWW2/hgQcekLUPh5vZOMyWqjA0lDi0vIWrt5aSXTW+2i3kzvw+5goSqQ67yf7Rvn17rF27Fjk5OWjevDleeOEFzJs3T3Yg5BQOs9W8DRssj/ySvbzF8uWuVUDprprAQLNV732CnWVKHFpGw537IiKfEuTtCshxzz334J577lH2oIbuAwtJsk4ttEmqJ2fkl9yZoF3qQjV01VRtWTJ01fhK95US3Jnfx1xBIs1SfcuQV3F5Dr+2bp3j8/7k3/yY7eUtJEm/Mn1qqnOV0un0AbilLjbDtsxM7awZZo878/uYK0ikWT7RMuRVhu4D8guOzPtzP1ZgBYZUCkz++dfQciNJlpfkcKUL1ZGuGn4ur6+9Zi+/T05w6s59EZFPYcsQ+bUPPnBi1ueYWAgBrBCDLT8UPTlTMbtqHOPO/D7mChJpFoMh8juVg5/hw22XHYuF5vP+nDhh/yCe6kL1dleNTqefdDQnR/+vL3THuTM49fSSHL54fYk0QPVD691BqaF55B2LFwNjxsgvL/DPX/lq/Oh7c1oHK7NqY/5838iTU/sM1L5+fYm8gMtxuJFPB0O+Ov+LhzmS+zMdszEbT6sz+LHEkJMEWM5J8sRoMmsj2Dx5TC3h9SVyCucZIi4LUMmcOU7k/vzT/TVbPOU7gRCg/OrpHMHmWby+RKrHYEituCyASfDzxBO2y87CU/rgp0Jcz/3xpQCoKiWndeBkg57F60ukegyG1Eijf0nOmOF8689TYrb+2jjSf6Z2Ss0KzRFsnsXrS6R62ppnaNUqIDlZ/Xk3cv+SfOMNICbGp3OJHIld/oMJmIAFQFkZEBIC47w/5Bpvj2Dzd7y+RKqnrQRqABGA+kZwVE2SPnYMGDbMsX2o7ZysmDwZmDtXfnlVj/zyF1yY2LN4fYmcxgRqT1JT3o2lJOnMTMf3o6ZzqqJy15e9QGgZMvRdX3+d94/cH1/AyQY9i9eXSPW0GQypJe/GWpL0mTOO70st5wRgyhTnc38yxHv6c6lVy+P1pEqUHsGmNby+RKqmzW6yyvLyvLPGk6Hp3FZuEGC+/pUceXn6HCIF5ydyJPfnI9yH+7AaOHJEv6gpqQfntfIsXl8ihyjVTaatBGpLvDWCw16StEHt2sDp047t++OP9etQeHCm28zM6y3/cpjm/qxySx0UobWHFxcm9ixeXyJVYjDkrREccoOwuXP1TevFxcDJk8CkSfZfM2+e+TZDTpELTfKOtP58hW7ohjzghx+Am2+GT4784vIJRESaoN1uMm+P4MjP1ydL21O5G0/OqJSAAOs5Qw6e89SpwGuv2a+igV+N/PLU8glaa2kiInIBR5N5khpGcKSm6gMTa80tkqTPp0lNvb7N3qgUIWwnT8uY6bZy4rO9QGgXOugTn7d/7V8jvzw16SWXVyEiUiVtBkNqGMHh7HBbW6NS5A7Jr9RF98QTzo/86iC+1QcHnTvLO66v8MTyCVxehYhItbQVDL3zjmfXeHKUs8Ntra1b1bevrMN2HVrPGPzMmWO77K9I0Qc/H6/3r9YfW9y9fIJGl1chIvIV2soZ8nCfo9PclUdiJ6eoAhKOIh5JKEQFrO/fmPuTl6fN3BZn8rmU3B8RkUYwZ0hL3LUgZ6WutwqY9nkZvs/EPLNA6BAa6lt/lr2nj6HWrNG3Tmk1t8WZfC5buFAnEZGqMRjyE9On/5P3MyAd6WI1jsG06+0o4jEQq7EW+q63yrk/DcVhfUtSRgZzWwD3L5/AhTqJiFSN3WQ+zFbCcwB0SEUB6qEYxaiHFbgfsTgFvPkm8Oijll9kb1Zsw9D8gweBHTv8vwvN0jxDCQn6QMiRnLNVq4BBg2yXSUjgQp1ERFUo9fxmMORDnnsOeOEF+eUdnvdHbm5LnTqms2L780SEruZzyV12ZdUqfcsbmePcTESaxeU4CIBjsz6fRRSi8BfwyivA44/D4Vmf5easVF0exA2zW6tW1eUTdDp90Cj3wezIsitkjrOAE5ECmDOkMlOnOj/vT5Q4p28FevxxeQczPNhzcvT/1q3rXKW1MjzcmUkTmTztPOavEZFCGAy5omow4WQg4Misz6WoqQ9+npvh2rw/lh7sGRlAdLRjzVEGzkxE6EucfTAzedo5nJuJiBTEYMhZzrQS/BM8reibg65SPgIlncOtPzXFBf3DICvLtbpberAfPw6cPavfvzMBEeCfLRyuPJjdPUxfKzwxCzgRkRUMhpzhRCtBupSLoqBEIC0Ng9cPRT7ScAiJ6A/zspdQTR/8PDJKXuuPIy1U9h7skqRvHao6K3adOtb3WZk/tnC48mB29zB9rWD3IhEpiMGQo2S2EryYpTN2faVLuViNgagP0wdqfRzDagzEWCy43vpTIVBNXNbv66237NfH0RYqOQ/2s2eBZctMl/s4elS7LRyuPpidXXZFy9i9SEQK4mgyR8lsJfhyZgGArgiADvMxEYAwizwD/hnttTDhFaCw3PHWAUMLVdXAzNLoLsPw5DVr5O371Cn9jNiVzZ+v368kmR7TUguHPw2HdseDOT1dv3acv1wTTzN0L1pZWsY455U/Bt9EpDi2DDlKZitBPejLpaIACThq+0I7k/vgSB5L5dajBQvk7d/Sg11uC4cz+VRq5q68H3ctu6IF7F4kIgUxGHKAEPoV3+UoRj1cQxDyIWMSQ8Dx3Ae5eSyzZlnOb7LG3oM9PR04dMi0C62w0DQQ8rfh0Hwwewe7F4lIIQyG7Fi79vqw94AAoACpKEK82UKoVeWvOIkgUa4PFuRwNPdBbvA0f778ofdyH+zWWjj8eTg0H8zeYS/4JiJyAy7HUYUQQFAQUFFhvUx/6BOiLeUBGUmS/iHZt6++i8he7oOj61LJXTrDEc6su1WZ3Drl5ZnO6uxL/CkXiohI5ZRajoMtQ9A/myu3/tgKhF7B48jFAARAICDAzuXLzNT/64kuFjl5LFFR8vY1frx7/uLWwnBo5v0QEfkdTQZDQgAjRlwPgLp1s12+wjDs/ZFReFzM0e8gL8921FR57hlPdLHIyWOZOFHevgYMcM+DncOhiYjIB/lcMJSdnQ1JkpBpaHVxQGTk9daf996zXu4rdLs+78/lvyEZJj2sPO+Po60gnsh9sBdkPf20snMD+ctsy25aZoWIiHyDT80ztHv3brz11lto0aKFW/dbFydxArH6lOhFi4AxW+y/yJlWkKoroLuDvflrHJkbyFWG1iqljucJXCWdiEhzfKZl6OLFi3jggQfw9ttv44YbbnB5f7+gibH15+Slmtdbf8aMkbcDNbWC2MpjUXoUlC+PuvLHaQGIiMgunxlNlpGRgaioKMydOxddu3ZFq1atMG/ePItly8rKUFZWZvy+tLQUCQkJKAEQAQDr1ulbU1xleHgClltB1PTwV3oUlK+NutLp9KP+rM3H5OyoPyIicppSo8l8optsxYoV+O6777B7925Z5bOzs5FlaVX3khLAnRfT0ApiqVvFlSHqnuCJLjo1Hc9VjizG6kvnRUREdqk+GCoqKsLEiROxadMmhIWFyXrN9OnTMXnyZOP3hpYhj+CaU/5BC9MCEBGRRaoPhvbu3YtTp06hbdu2xm06nQ7btm3DggULUFZWhsAqgUdoaChCQ0OVq6SvtYKQOU4LQESkWaoPhrp3744ff/zRZNvIkSORkpKCJ5980iwQInIKV0knItIs1QdDNWvWRPPmzU22Va9eHdHR0WbbiZzmD9MCEBGRU3xmaL1P4uR9vsWXpwUgIiKn+czQelcoNTTPBCfv812+Ni0AEZGfUur5zWDIEwzzD1W9tGqcf4iIiEiluGq9p3mqC0un07cIWYoxDdsyM9llRkREpBLaDIZyc/WzDaelAUOH6v9NTHTPcguOTN5HREREXqe9YMjT609x8j4iIiKfoq1gSIkuLE7eR0RE5FO0FQxlZ3u+C8sbq9lzCD8REZHTtBUMzZkjr5wrXViGyfsA84DIE5P3eTL/iYiISAO0FQzJ5WoXllKT93k6/4mIiEgDtDXPEACbsxQY1p8qLHRPy40nJ+/T6fQtQNa6/dx9LkRERApTap4h1a9NphhPdGF5cjV7R4bwe6oOREREfoDdZAa+tv4Uh/ATERG5BVuGnnkG6N7d99af4hB+IiIit9BuzpCv59QYcoaOHbM8b5Kvnx8REWke1ybzJE/kBylN6SH8REREfkqbwZCv5QdZo9QQfiIiIj+mrW6yd95BRHKy7+UH2ePJIfxERERewqH1nnDffYAHL6bXeHIIPxERkZ/TZjcZERER0T8YDBEREZGmMRgiIiIiTWMwRERERJrGYIiIiIg0jcEQERERaRqDISIiItI0BkNERESkaQyGiIiISNMYDBEREZGmMRgiIiIiTWMwRERERJrGYIiIiIg0jcEQERERaRqDISIiItI0BkNERESkaQyGiIiISNMYDBEREZGmMRgiIiIiTWMwRERERJrGYIiIiIg0TfXBUHZ2Ntq3b4+aNWuibt266NevHw4cOODtahEREZGfUH0wtHXrVowbNw7ffPMNNm/ejPLycvTs2ROXLl3ydtWIiIjID0hCCOHtSjji9OnTqFu3LrZu3Yrbb79d1mtKS0sRGRmJkpISREREeLiGRERE5A5KPb+DPLZnDykpKQEAREVFWS1TVlaGsrIy4/elpaUerxcRERH5JtV3k1UmhMDkyZNx2223oXnz5lbLZWdnIzIy0viVkJCgYC2JiIjIl/hUN9m4cePw2WefYfv27YiPj7dazlLLUEJCArvJiIiIfAi7yaqYMGEC1q9fj23bttkMhAAgNDQUoaGhCtWMiIiIfJnqgyEhBCZMmIC1a9ciPz8fSUlJ3q4SERER+RHVB0Pjxo3D8uXL8fHHH6NmzZo4ceIEACAyMhLh4eFerh0RERH5OtXnDEmSZHH70qVLMWLECFn74NB6IiIi38OcoX+oPFYjIiIiH+dTQ+uJiIiI3I3BEBEREWkagyEiIiLSNAZDREREpGkMhoiIiEjTGAwRERGRpjEYIiIiIk1jMERERESaxmCIiIiINI3BEBEREWkagyEiIiLSNAZDREREpGkMhoiIiEjTGAwRERGRpjEYIiIiIk1jMERERESaxmCIiIiINI3BEBEREWkagyEiIiLSNAZDREREpGkMhoiIiEjTGAwRERGRpjEYIiIiIk1jMERERESaxmCIiIiINI3BEBEREWkagyEiIiLSNAZDREREpGkMhoiIiEjTGAwRERGRpjEYIiIiIk1jMERERESaxmCIiIiINI3BEBEREWkagyEiIiLSNAZDREREpGkMhoiIiEjTGAwRERGRpvlMMLRo0SIkJSUhLCwMbdu2RUFBgberRERERH7AJ4KhlStXIjMzE08//TT27duH1NRU3HXXXThy5Ii3q0ZEREQ+ThJCCG9Xwp6OHTuiTZs2ePPNN43bmjRpgn79+iE7O9vu60tLSxEZGYmSkhJERER4sqpERETkJko9v1XfMnT16lXs3bsXPXv2NNnes2dP7Nixw0u1IiIiIn8R5O0K2HPmzBnodDrExMSYbI+JicGJEycsvqasrAxlZWXG70tKSgDoI0wiIiLyDYbntqc7sVQfDBlIkmTyvRDCbJtBdnY2srKyzLYnJCR4pG5ERETkOWfPnkVkZKTH9q/6YKh27doIDAw0awU6deqUWWuRwfTp0zF58mTj9+fPn0fDhg1x5MgRj15MtSktLUVCQgKKioo0lSvF8+Z5awHPm+etBSUlJWjQoAGioqI8ehzVB0MhISFo27YtNm/ejP79+xu3b968GX379rX4mtDQUISGhpptj4yM1NSHyCAiIoLnrSE8b23heWuLVs87IMCzKc6qD4YAYPLkyRg+fDjatWuHW2+9FW+99RaOHDmCRx991NtVIyIiIh/nE8HQ/fffj7Nnz+L5559HcXExmjdvjg0bNqBhw4berhoRERH5OJ8IhgBg7NixGDt2rFOvDQ0NxYwZMyx2nfkznjfPWwt43jxvLeB5e/a8fWLSRSIiIiJPUf2ki0RERESexGCIiIiINI3BEBEREWkagyEiIiLSNJ8MhhYtWoSkpCSEhYWhbdu2KCgosFl+69ataNu2LcLCwvCvf/0LixcvNiuzZs0aNG3aFKGhoWjatCnWrl3rqeo7zZHzzs3NRY8ePVCnTh1ERETg1ltvxRdffGFSZtmyZZAkyezrypUrnj4Vhzhy3vn5+RbP6bfffjMp52/v94gRIyyed7NmzYxlfOH93rZtG/r06YO4uDhIkoR169bZfY0/3N+Onre/3N+Onre/3N+Onre/3N/Z2dlo3749atasibp166Jfv344cOCA3dcpcY/7XDC0cuVKZGZm4umnn8a+ffuQmpqKu+66C0eOHLFYvrCwEHfffTdSU1Oxb98+PPXUU3jsscewZs0aY5mdO3fi/vvvx/Dhw/H9999j+PDhGDRoEHbt2qXUadnl6Hlv27YNPXr0wIYNG7B3716kpaWhT58+2Ldvn0m5iIgIFBcXm3yFhYUpcUqyOHreBgcOHDA5p0aNGhl/5o/v9/z5803Ot6ioCFFRUbjvvvtMyqn9/b506RJatmyJBQsWyCrvL/e3o+ftL/e3o+dt4Ov3t6Pn7S/399atWzFu3Dh888032Lx5M8rLy9GzZ09cunTJ6msUu8eFj+nQoYN49NFHTbalpKSIadOmWSz/xBNPiJSUFJNto0ePFrfccovx+0GDBok777zTpEyvXr3E4MGD3VRr1zl63pY0bdpUZGVlGb9funSpiIyMdFcVPcLR887LyxMAxF9//WV1n1p4v9euXSskSRKHDh0ybvOF97syAGLt2rU2y/jL/V2ZnPO2xBfv78rknLe/3N+VOfN++8P9LYQQp06dEgDE1q1brZZR6h73qZahq1evYu/evejZs6fJ9p49e2LHjh0WX7Nz506z8r169cKePXtw7do1m2Ws7VNpzpx3VRUVFbhw4YLZYncXL15Ew4YNER8fj3vuucfsL0tvcuW8W7dujXr16qF79+7Iy8sz+ZkW3u///ve/uOOOO8xmaVfz++0Mf7i/3cEX729X+PL97Q7+cn+XlJQAgM1FWJW6x30qGDpz5gx0Op3ZavUxMTFmq9obnDhxwmL58vJynDlzxmYZa/tUmjPnXdVrr72GS5cuYdCgQcZtKSkpWLZsGdavX4+cnByEhYWhc+fO+OOPP9xaf2c5c9716tXDW2+9hTVr1iA3NxeNGzdG9+7dsW3bNmMZf3+/i4uL8fnnn+Phhx822a7299sZ/nB/u4Mv3t/O8If721X+cn8LITB58mTcdtttaN68udVySt3jPrMcR2WSJJl8L4Qw22avfNXtju7TG5ytY05ODmbOnImPP/4YdevWNW6/5ZZbcMsttxi/79y5M9q0aYM33ngD//nPf9xXcRc5ct6NGzdG48aNjd/feuutKCoqwquvvorbb7/dqX16i7N1XLZsGWrVqoV+/fqZbPeV99tR/nJ/O8vX729H+NP97Sx/ub/Hjx+PH374Adu3b7dbVol73KdahmrXro3AwECzaO/UqVNmUaFBbGysxfJBQUGIjo62WcbaPpXmzHkbrFy5Eg899BA++ugj3HHHHTbLBgQEoH379qr5S8KV867slltuMTknf36/hRB49913MXz4cISEhNgsq7b32xn+cH+7wpfvb3fxtfvbFf5yf0+YMAHr169HXl4e4uPjbZZV6h73qWAoJCQEbdu2xebNm022b968GZ06dbL4mltvvdWs/KZNm9CuXTsEBwfbLGNtn0pz5rwB/V+MI0aMwPLly9G7d2+7xxFCYP/+/ahXr57LdXYHZ8+7qn379pmck7++34B+tMbBgwfx0EMP2T2O2t5vZ/jD/e0sX7+/3cXX7m9X+Pr9LYTA+PHjkZubiy1btiApKcnuaxS7x2WnWqvEihUrRHBwsPjvf/8rfvnlF5GZmSmqV69uzKqfNm2aGD58uLH8//3f/4lq1aqJSZMmiV9++UX897//FcHBwWL16tXGMl9//bUIDAwUL730kvj111/FSy+9JIKCgsQ333yj+PlZ4+h5L1++XAQFBYmFCxeK4uJi49f58+eNZWbOnCk2btwo/vzzT7Fv3z4xcuRIERQUJHbt2qX4+Vnj6HnPnTtXrF27Vvz+++/ip59+EtOmTRMAxJo1a4xl/PH9Nhg2bJjo2LGjxX36wvt94cIFsW/fPrFv3z4BQLz++uti37594vDhw0II/72/HT1vf7m/HT1vf7m/HT1vA1+/v8eMGSMiIyNFfn6+yef28uXLxjLeusd9LhgSQoiFCxeKhg0bipCQENGmTRuTYXkZGRmiS5cuJuXz8/NF69atRUhIiEhMTBRvvvmm2T5XrVolGjduLIKDg0VKSorJzaUWjpx3ly5dBACzr4yMDGOZzMxM0aBBAxESEiLq1KkjevbsKXbs2KHgGcnjyHm//PLLIjk5WYSFhYkbbrhB3HbbbeKzzz4z26e/vd9CCHH+/HkRHh4u3nrrLYv784X32zB02trn1l/vb0fP21/ub0fP21/ub2c+5/5wf1s6ZwBi6dKlxjLeuselfypIREREpEk+lTNERERE5G4MhoiIiEjTGAwRERGRpjEYIiIiIk1jMERERESaxmCIiIiINI3BEBEREWkagyEiIiLSNAZDREREpGkMhoiIiEjTGAwRkU/KyclBWFgYjh07Ztz28MMPo0WLFigpKfFizYjI13BtMiLySUIItGrVCqmpqViwYAGysrLwzjvv4JtvvkH9+vW9XT0i8iFB3q4AEZEzJEnCrFmzMHDgQMTFxWH+/PkoKChgIEREDmPLEBH5tDZt2uDnn3/Gpk2b0KVLF29Xh4h8EHOGiMhnffHFF/jtt9+g0+kQExPj7eoQkY9iyxAR+aTvvvsOXbt2xcKFC7FixQpUq1YNq1at8na1iMgHMWeIiHzOoUOH0Lt3b0ybNg3Dhw9H06ZN0b59e+zduxdt27b1dvWIyMewZYiIfMq5c+fQuXNn3H777ViyZIlxe9++fVFWVoaNGzd6sXZE5IsYDBEREZGmMYGaiIiINI3BEBEREWkagyEiIiLSNAZDREREpGkMhoiIiEjTGAwRERGRpjEYIiIiIk1jMERERESaxmCIiIiINI3BEBEREWkagyEiIiLSNAZDREREpGn/D+qH65X0+lk3AAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
@@ -2063,7 +2075,7 @@
},
{
"cell_type": "markdown",
- "id": "1ca83847",
+ "id": "967a83d3",
"metadata": {
"editable": true
},
@@ -2085,7 +2097,7 @@
},
{
"cell_type": "markdown",
- "id": "dcf3e808",
+ "id": "ba71e94a",
"metadata": {
"editable": true
},
@@ -2124,7 +2136,7 @@
},
{
"cell_type": "markdown",
- "id": "473b1af6",
+ "id": "02c72775",
"metadata": {
"editable": true
},
@@ -2137,7 +2149,7 @@
},
{
"cell_type": "markdown",
- "id": "3353fe2a",
+ "id": "11665768",
"metadata": {
"editable": true
},
@@ -2148,7 +2160,7 @@
},
{
"cell_type": "markdown",
- "id": "6e8e47c3",
+ "id": "0995d8db",
"metadata": {
"editable": true
},
@@ -2161,7 +2173,7 @@
},
{
"cell_type": "markdown",
- "id": "a2eeb6ad",
+ "id": "3cdc1697",
"metadata": {
"editable": true
},
@@ -2188,7 +2200,7 @@
},
{
"cell_type": "markdown",
- "id": "5a7a0f8b",
+ "id": "5af510b6",
"metadata": {
"editable": true
},
@@ -2203,7 +2215,7 @@
},
{
"cell_type": "markdown",
- "id": "b7b5884f",
+ "id": "490f4197",
"metadata": {
"editable": true
},
@@ -2213,7 +2225,7 @@
},
{
"cell_type": "markdown",
- "id": "6492d660",
+ "id": "219a6868",
"metadata": {
"editable": true
},
@@ -2226,7 +2238,7 @@
},
{
"cell_type": "markdown",
- "id": "584164f4",
+ "id": "8d3502b5",
"metadata": {
"editable": true
},
@@ -2241,7 +2253,7 @@
{
"cell_type": "code",
"execution_count": 10,
- "id": "42d97cf8",
+ "id": "2a2c6fab",
"metadata": {
"collapsed": false,
"editable": true
@@ -2266,7 +2278,7 @@
},
{
"cell_type": "markdown",
- "id": "ca9c6c58",
+ "id": "de5275cd",
"metadata": {
"editable": true
},
@@ -2306,7 +2318,7 @@
{
"cell_type": "code",
"execution_count": 11,
- "id": "d2921658",
+ "id": "1f118c97",
"metadata": {
"collapsed": false,
"editable": true
@@ -2349,7 +2361,7 @@
},
{
"cell_type": "markdown",
- "id": "84469eb8",
+ "id": "9250c537",
"metadata": {
"editable": true
},
@@ -2359,7 +2371,7 @@
},
{
"cell_type": "markdown",
- "id": "b4b94e7a",
+ "id": "54c13f2b",
"metadata": {
"editable": true
},
@@ -2370,7 +2382,7 @@
{
"cell_type": "code",
"execution_count": 12,
- "id": "71dcdb35",
+ "id": "250dbe92",
"metadata": {
"collapsed": false,
"editable": true
@@ -2381,20 +2393,20 @@
"output_type": "stream",
"text": [
"Own inversion\n",
- "[[3.95446837]\n",
- " [3.16961682]]\n",
- "Eigenvalues of Hessian Matrix:[0.31447174 4.32459186]\n",
+ "[[4.41170104]\n",
+ " [2.6431453 ]]\n",
+ "Eigenvalues of Hessian Matrix:[0.31228042 4.55571665]\n",
"theta from own gd\n",
- "[[3.95446837]\n",
- " [3.16961682]]\n",
+ "[[4.41170104]\n",
+ " [2.6431453 ]]\n",
"theta from own sdg\n",
- "[[3.91682433]\n",
- " [3.13655438]]\n"
+ "[[4.39272691]\n",
+ " [2.63430285]]\n"
]
},
{
"data": {
- "image/png": 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uspnbu8k2bdqEoUOHIioqCgqFAmq12nDuzp07eOmll9C2bVvUqVMHUVFReOyxx3D+/Hn3FZiIiCgjAxg2zDgQAoDcXN3xjAz3lIvs4vZgqLi4GO3atcPChQurnLt58yb27NmDV199FXv27EFGRgaOHz+OBx54wA0lJSIigq5r7PnnASGqntMfmzRJl448gtu7yQYNGoRBgwaZPBcSEoL169cbHfvwww/RpUsXnD17Fk2aNHFFEYmIiMpt3ly1RagiIYCcHF26vn1dViyyn9uDIVsVFhZCoVCgfv36ZtOUlpaitLTU8LqoqMgFJSMiIlnIy3NsOnI7t3eT2aKkpATTp0/HyJEjERwcbDbd3LlzERISYviJjY11YSmJiMirRUY6Nh25nccEQ3fu3MHDDz8MrVaLRYsWVZt2xowZKCwsNPzk5OS4qJREROT1evfWzRpTKEyfVyiA2FhdOvIIHhEM3blzB8OHD0d2djbWr19fbasQAAQGBiI4ONjoh4iIyCF8fXXT54GqAZH+9fvvc70hDyL5YEgfCJ04cQK//PILGjZs6O4iERGR3KWnA999B0RHGx+PidEd5zpDHsXtA6hv3LiBkydPGl5nZ2dj3759CA0NRVRUFIYNG4Y9e/bghx9+gEajQX5+PgAgNDQUAQEB7io2ERHJXXo6kJrKFai9gEIIUwsluE5WVhZSUlKqHB89ejRmzpyJ+Ph4k9dlZmair5VTFouKihASEoLCwkJ2mREREXkIVz2/3d4y1LdvX1QXj7k5ViMiIiIvJ/kxQ0RERETOxGCIiIiIZI3BEBEREckagyEiIiKSNQZDREREJGsMhoiIiEjWGAwRERGRrDEYIiIiIlljMERERESyxmCIiIiIZI3BEBEREckagyEiIiKSNQZDREREJGsMhoiIiEjW/NxdACIiIpIIjQbYvBnIywMiI4HevQFfX3eXyukYDBERERGQkQE8/zxw7lz5sZgYYMECID3dfeVyAXaTERERyV1GBjBsmHEgBAC5ubrjGRnuKZeLMBgiIiKSM41G1yIkRNVz+mOTJunSeSkGQ0RERHK2eXPVFqGKhABycnTpvBSDISIiIjnLy3NsOg/EYIiIiEjOIiMdm84DMRgiIiKSs969dbPGFArT5xUKIDZWl85LMRgiIiKSM19f3fR5oGpApH/9/vtevd4QgyEiIiK5S08HvvsOiI42Ph4Tozvu5esMcdFFIiIi0gU8qalcgZqIiIhkzNcX6NvX3aVwOXaTERERkayxZYiIiMiVvGEzVG+oQwUMhoiIiFzFlZuhOitg8cINXdlNRkRE5Aqu3Aw1IwOIiwNSUoCRI3X/xsXV/D28dENXhRCmdmbzLkVFRQgJCUFhYSGCg4PdXRwiIpIbjUYXjJjbA0yh0LWuZGfXvPVGH7BUfrzr1wyyd6q8K+vwF1c9v9kyRERE5Gyu2gzVmTvQe/GGrgyGiIiInM1Vm6E6M2Dx4g1dOYCaiIjI2Vy1GWpNA5bqBl178YaubBkiIiJyNldthlqTgMXSoGsX1UFbpsXvSw5hRvcsdG70Z43yshYHUBMRkWfw9LVt9AObAeMxPTUd2FyRfpBzbq7pcUPmBjlbO+jaSXW4c/MOsj7YD/VXN7DqcEvkavXBWhEADqAmIiJy3lRxV3LFZqj27EBvy6BrB9ahuKAYK6duw6hmvyGsbjEGzOiERQfvQa42EnVxHcNjt+Kzp3dYnV9NsGWIiIikzVlTxd3FFS1cphZGjI3VBUKVP6usLF1waUlmZvm+ZXbW4dKxy/h+3mGo1wZgXX4ySlDLcC5McRGprY4g7eFa6PdCMgKDA132/HZ7MLRp0ya89dZb2L17N/Ly8qBSqZCWlmY4L4TArFmzsHjxYly9ehVdu3bFRx99hMTERKvfg8EQEZGHcsPaNh7BmmDE2oBl+XJda5sly5YBI0bYXNQzW85B/c4pqDaEYHNhW2hRXoZmfmegbJeNtH+EovsTifANMC6fq57fbp9NVlxcjHbt2mHs2LF48MEHq5yfP38+3n33XSxduhQtW7bE7Nmz0b9/fxw7dgz16tVzQ4mJiMhlbJkqLpfd1q3dDsPaHegdPEtMaAUOqk5Aveg8VNvCsfdWAoAYw/n2tY5C2S0fyvFRSFK2gMKnqXXv70RuD4YGDRqEQYMGmTwnhMD777+Pl19+Gel/fcGff/45wsPDsWzZMjz99NOuLCoREbmaF69tYxdzXYb67TDs6TLUzxKzNOi6mlli2jIttv3fQaj/ewWqffE4VdYSQEsAgA806BVyAMqUQqRNaY64Xq0BtLatjE7m9mCoOtnZ2cjPz8eAAQMMxwIDA3HPPfdg69atZoOh0tJSlJaWGl4XFRU5vaxEROQEXry2jc0sDXRWKHQDnVNTbesy1A+6HjZMl4epWWKVB10DKC0qxYb390O1/BZWH2+NC9pkw7lAlGBA+B9IG3QbQ6cloHFCe+vL4waSDoby8/MBAOHh4UbHw8PDcebMGbPXzZ07F7NmzXJq2YiIyAUc0GrhNZzZZaifJWaq+63CoOuic0VY+9ZBqFTAjzlJuI67DUlDUIghcQeRlu6D+6a2Rd2IrraVwY0kHQzpKSpNDxRCVDlW0YwZMzB58mTD66KiIsTGxjqtfEREZAdrBvja2WrhlZzdZZiermtVqvSdXDhyBasf2wTVT7Xw68Vk3EYPwyWRPvlISziOtEfqoO/Etgio29O+93YzSQdDERERAHQtRJEVmkALCgqqtBZVFBgYiMDAQKeXj4iI7GTtIGDA6lYLr+eKLsO/Bl2f2nAG6neyoXrgELZeT4JAH0OSlv7ZUHY8g7QnGqHLmDbw8Yuw//0kQtLBUHx8PCIiIrB+/Xp06NABAHD79m1s3LgR8+bNc3PpiIjILvYMAjbTaiGLFiE9J3YZCq3AvhXHoP44H6rfo3CgpCWA8llenWsfhrJnAZTPxaL1/c2g8ImvQUWkx+3B0I0bN3Dy5EnD6+zsbOzbtw+hoaFo0qQJJk2ahDfffBMtWrRAixYt8Oabb6J27doYac2aCEREJC01GQRs7VRxW8riScGVg7sMNbc1+O0/B6D+vBDqA81wuqx8lpcvytC3wX6k9buO1BdbILZrGwBtHFodSRFulpmZKQBU+Rk9erQQQgitVitef/11ERERIQIDA0WfPn3EgQMHbHqPwsJCAUAUFhY6oQZERGS1zEwhdI/x6n8yM23Pu6xMd92yZbp/y8rMp125UoiYGOP3jInRHZc6U2WPjbWq7Dcv3xSrX9khxrbYJBopLhplUQvFQhm5TXz+5GZx+eQVF1TEMlc9v92+ArUrcAVqIiInsqWFxVmrHdsyBsmW7T2k2npkQ7munSnEmnkHoVrtg59y26IYdQ3nQhVXMLTZYSiH+6P/5Lao3ai2q2pgFdlsx+EKDIaIiJzEliAEsG8fLGvKYEtwY+32HqtW2VY3CTm/Jx+r3joO1bo6yLySjDL4G87F+uYiLfEklKOD0XtcW/gFuX3EjFkMhhyIwRARkRPYs4GqPhixNAjY2r3GbN27zNpgbNYsYOZMj9oc9tjaP6FacBbq3xphR3GS0bnEwBNI65wL5TPh6DiyNRQ+5penkRIGQw7EYIiIyMFqsoGqPogCTA8CtiXQsLWlydpuutBQ4MoV0+dsCdic2M0mtAK7vjgC1ScFUO+OxZHbzY3Od697AGm9L0P5Qhxa9I9zyHu6mmw2aiUiIg9Uk9WQHblukK0LEVq7Bo+5QAiwfqVnW7sQrXDn5h1s+ugAVF9ch/pQS+Rqy2d5+eM2/tZwP5QDb+KBqa0Q2b6tXe8hRwyGiIjIdjVdDdlR6wbZuhChNWv1hIYCly9bzrO6z8CBG6oWFxRj3TsHoPquDD9kJ+Kq6Gg4Vwc3cH/MASjTBO6fmoiQJp2tytMhpDq43A4MhoiIyHaOWA3ZEesG9eihy0ejqf59evQo/29La/U89xzw+uuW39tc3RywoerlE1fw/bzDUK/xx7r8triFboZzjRUX8UCLo1COCEK/SW0RVL+75bI6mrlWr/feAxo18rgAiWOGiIjIdo4eCG0ve2enmXqYx8bquulSU2tWNzvLdHZbLtRvn4R6QzA2XWsLTYX2iji/HCiTT0E5tgF6PJUE34C/3tcdrTPmWr1MqWG3IMcMERFROal1SdizGrIz6mBvd52lbrqarPRsZZlE7nkcXnUSqg/PQbU1HHtuJQCINpxvF3QMaV3zoBwXieRhLaHwqbThuBPGJFlUXauXKXZ0C7qFU5d0lAiuQE1EHk3KqyVbuxqyqXShoULMmlX9StGWOHNFa3tXerayTCN9lxsdUkAjegfvE++mZopTmWcsl02hqJqvQqH7cdbvhrWfd+Uyxcba9T1zBWoHYjcZEXkse9bycTVLLT6WulUaNgQWL7avHs7urrOnNctCmbRQ4BxiEI9s+KEM/cP+gHJQKYZObY2wxMbWlcneZQ1qytqlCUyxZSHNv3CdIQdiMEREHsmdDz1HsVSHilautC0g0gcqq1bpuq0qc2PAeOvTrxD05KMQAHwqHNdCV6YFjWcj5tEU3PdiEupF1bMtc2es4u3o9zbF1i1W4Lrnt4/lJERE5Ba2rOUjVZbqUNGkSdXPCqsoI0MXZKWklAdClQPCmBiXBkIFhy7i09GbMThsJ+o/OQwPYiVyEWOUpjQkDJovv8YLBf/EQ+92tz0QAmq+rEFN6Jcm0AeatrB2BqIbcAA1EZFUufOh5yi2lM2ahQwB891uWq3uX/20dRcMMs/elAPVO6egzmqALUVJ0KK34dxB/w74qP1SjOp9BgkdAuETE41ajiiTLcsaOHrQesWB87aIjdW9t0QxGCIikipHrOXjbraWzVLwZM0aPitXAm+/7ZRASGgF9n93HKpFeVDtiMT+klYAymd5dap9GMoeBUibEIM2Q5tD4RPv8DJYtXBkTAxw6VLVLkpHzDYzt4K4OQpF9bPvJIBjhoiIpEoqa/nUhC1jhgDL41xqOl7GjpYSzW0NtnxyEOqlV6He3wzZZU0M53xRhj71D0DZrwipU+5Ck+7R1eTkQJb2d3vxRV1A6MyB9xoNMGdO9QtU1mRwPFz4/HbqXDWJ4NR6IvJY+inUladRO3sKtSOZmwZuz/TrZcusm869bFn5NWVluinhkyYJ0bixVUsU3Lp6S3z/6g7xeMtNorGiwOiSINwUqRHbxdInNotLxy879rOyhbmp/998U/W4g6a6W10ORyybIDi13qHYMkREHq261ZLdPa3eWhkZwFNPmd7zy5bWCltbhkx9dmbeu7BzP6yZdxCqVT5Ym9sWxahrSNZAcRVD4g9BOcwPA6a0RZ2wOpbL4AqmWro2b3b9bDMnLQrKqfUOxGCIiDye1Fagtoe+W2XBAuNd4W0J7GzpOly1yqptIwSAiz7haKLNRilqGY7H+J5HWpsTSBtVD33Gt4V/bX+rqul21q4FZMdUd1fjdhxERFTOEZuaupuvL/Daa8DLL9sf2Fm7DQhg9bYRCgBh2gvohh0oCIiFsnMO0p4KQ+dRCVD4RNlURUnwhoH3LsaWISIi8jyWug7tWBzw/LT3EDVvkiNL6R5SHXhvR+smW4aIiMh7OLqbz8JGq5oz52Br7lGD2ttfHimxZxNdZ3PHprI2YMsQERE5l4sehDcv3cS6dw5A9c0dXP3zClYj1boLPWGJAntIZeB9DfbX4wBqB2IwRETkJo7aaNZMy9KVU1fxw7xDUP3gh5/zknELtQEAPtDgLJogEuer33dKShveOoO7B97XcH89BkMOxGCIiMgNHLXRrIkWjuu1GuNtn2mYUzwJmgojPpr6noMy+RSUY+ujZ+Pj8B35d90Jc486T1uiwNPUcJFMjhkiIiLPZstGs+ZmymVkQPzVslRxa9A6ty7hdUzDATTDyaAkKLuch3JcJNo91BIKH/3mqO2AAN+qXUWNGwOPPOKy/ctkzUP212MwRETWc3eTe015evk9TQ0ehNoyLX7/7wG0nvgMgoWo0tXlAwEBYEXjCfDPywF8W5rO28JAa3Iya6fvX7iguz/d9L1U25VKRGSQkaHr8khJ0S3olpKie52R4e6SWcfTy++JbFzv5vaN21g3dzeeTdyEmMACTH/6Kurfvmj2QaUA4H8xTxfoVEe/RtOIEbp/Xf3A1Wh03UXLl+v+1Whc+/7upN9UVqGoPt0LL7j1fmQwRESW6QfBVu7yyM3VHZd6QOHp5fdUlh6ECgW0UdH4bpUfHonbgrB6tzDwn53w8eE+yNNGoDlOWvc+bu5iqZbcg3D9NH/AckDkxvuRA6iJqHqOGgTrLp5efk9nZnd1/X89jOX4Bg8bjof7FCC15VE83W47Ovz6FhSXLll+D0fuseVIjppJ5w0s7RGnV+l+dNXzmy1DRFQ9WwbBSpGnl9/TpacD332HskYRRodzEIsHsRLf4GE09zuDFztnYcvHB5B7qyE+mXMJHb+ZbjkQUih0s8F693ZiBeyk0ZjfDkR/bNIk+XSZpacDp08D771XfTo33Y8cQE1E1fOQ2SBmeXr5PZTQChzIOAHVR+eh3tEG+2/loDc2IxJ5yEMkioMa4YEel/DGhBNITL0LCp+mugurCyJMcfVKytZyxEw6b+PrC4SHW5fWxfcjgyEiqp6nb/ro6eX3IJrbGmz79BBU/70C9R/x+LOsJQDdLC8faKCoH4JuKQqkTWmOpj1jTGdiKYjQa9wY+Phj6XYzMQg3TaL3I4MhIqqefhCspU0fpdhVAXh++SWu5FoJNiw4ANXyW1h9PAEFItlwLgi3MCBiP5SD72DI1AQ0atXBcobWBgfvvSfdQAiQ7EPf7SR6PzIYIqLqSXHTR1t4evklqPBsIX586xDUq4Afc9riBu42nKuvuIYhcQehHOaHgS+2RZ2wrrZlbm1wEB1tW76uJtGHvttJ9H7kAGoisuyvQbBVHkAxMZ4xI8bTyy8B+fsL8MkjmzCo8U40bloLIxf2wDc5PXAD9RDlk4dxSRuxft4eFNyogy/+7IX0+d1QJ6yO7W9kxXR8yQ6arqi6KeVyD8IleD9yaj0RWc/TV3D29PK72Mlfz0D1bjZUmxpi+41EVFwHunXAKaR1zIHyqcboPCoBPn4O/NvazHR8j5ySLpWd46XIivuRG7U6EIMhIhdxVrDBIMYlhFZgz7KjUH9yAaqd0ThU2sLofJc6B6HsdQlpzzVB6/ubObcw3hRE8PfXbgyGHIjBEJELmHp4xcTougpq8vByVr4EACgrKcPmRQeg/l8R1Aeb46ymfJaXH+6gb+h+KPvfwANTWiLmbhcP9mUQIXsMhv5SVlaGmTNn4quvvkJ+fj4iIyMxZswYvPLKK/Dxsa5ZlsEQkZM5a6Vdb1nBV2IP9VtXbmHd2/uh+uYOvv+zDa6IUMO52ijGfVEHoHxAg8HTEtEgvr7byknEYOgvc+bMwXvvvYfPP/8ciYmJ2LVrF8aOHYvZs2fj+eeftyoPBkNETuSs7S68ZRsNibRsXc2+hh/mHYRqtR9+zmuLmygf3NxQcRlDmx+GcngA+k9JRq3QWi4rF1F1XPX8lvzU+m3btiE1NRWDBw8GAMTFxWH58uXYtWuXm0tGRACct9KuN6zga65lS78hpZNbtnJ35UE9/zhUv9RD1tVkaNDLcK6J7zmkJZ2CckwIej2TBL8gic/OInIiyQdDvXr1wscff4zjx4+jZcuW+OOPP/Dbb7/h/fffd3fRiAio2Uq71XUfefoKvpb2plIodHtTpaY6tGXr6I9/QrXgLFRbGmNncSKA8nE+SYEnoOySi7Snw9FhRGsofMysAk0kM5IPhl566SUUFhaidevW8PX1hUajwZw5czBixAiz15SWlqK0tNTwuqioyBVFJZIne1fatdR95Okr+LqoZUtbpsXOzw9D/eklqPY0wbHbzQDoZnopoEX3egeh7HMFaS/E465+LQC0qDY/IjmSfDC0YsUKfPnll1i2bBkSExOxb98+TJo0CVFRURg9erTJa+bOnYtZs2a5uKREMmXPSrvWdB8NGaJrMaluV29fX6BHD8fUw1H0rV0rV1qX3o6WrTs37yDrg/1Qf3UD6sMtcV6bZDjnj9vo1+gPKAfewgPTWiMiObmanIgI8IAB1LGxsZg+fTrGjx9vODZ79mx8+eWXOHr0qMlrTLUMxcbGcgA1OZ7EZgm5jS2L5Fk7MHrJEuDeey2/d2amdMYMmWrtssTK8hcXFOOnt/ZD9Z0Wa84k4pqobzhXF9dxf+wBKNOA+6clITjGQ/8/x/uJKuEA6r/cvHmzyhR6X19faLVas9cEBgYiMDDQ2UUjuZPILCFJ0C+vb+rzqLxInrXdR1lZ1r23VMYMmWvtMseKvakuHbuM7+cdhurHAKy/kIwSdDecC1NcRGqrI0h7uBb6vZCMwGCJtZDZivcTuZHkg6GhQ4dizpw5aNKkCRITE7F37168++67+Mc//uHuopGcuXmWkCSlp+sGA1v6y97RwYsUxgxVN1jalGr2pjqz5RzU75yCakMINhe2hRblwVIzvzNQtstG2j9C0f2JRPgG9HFQBdyM9xO5meS7ya5fv45XX30VKpUKBQUFiIqKwogRI/Daa68hICDAqjy4zhA5lLesf+MuWVlASorldL/8AowZY3kskhQ+Z2vrpFdhWwmhFTioOgH1ovNQbQvH3lsJRknb1zoKZbd8KMdHIUnZAgofMxuYeireT1QNLrroQAyGyKGsffBJaSyLlOgfftYEOatWecaGncuXAyNHWk43YQLw4IPQdO2B7UuPQvXZFaj/iMepsqaGJD7QoFfIAShTCpE2pTnienn59HfeT1QNjhkikipPX//G3Xx9deNAhg3TBTWmghx995EtY5Hcycquuh03EvHZsz5YffwaLmjLZ3kFogT9w/ZDeX8phk5LQOOE9k4qqIM4cqAz7yeSAAZDRLby9PVvpMCWIMfasUjuZGF5AS2A84hGj6VPQgtduUNQiCFxB5GW7oP7prZF3YguLi60nRw90Jn3E0mATd1kOTk5iI2NdWZ5nILdZORQtnTzSOmBLUXeNJX6r0HAAoCiwu+FFrrWrmH4Dtt9eiAt4TjSHqmDvhPbIqCudeMeJcMZG+fyfqJquOr5bd22739p3bo1Xn31VRQXFzurPETSp+/mAcofAnrVzBIiE3x9deNARozQ/euhn9mpDWfw9n9D8c/At3FORBudy0cEvmoxE9P+ryXOlYZh0cE+GDCjk+cFQpa2FwF024tUt0imKbyfSAJsCobWr1+PdevWoUWLFliyZImzykQkffpunmjjBx9iYqQzqJecRmgF9i4/itf6ZKFt0Anc1a8ppq7pi7klkxGH03g6cAnUSa/gzJtfIvL2WYw6/hq6PZEEHz+b/pcrLbZsL2Ir3k/kZnbNJvvf//6Hl19+GY0aNcJ7772HvhIf4c9uMnIab+rmoWqVlZRhyycHoVpaCPWB5jijKZ/l5Ysy9G2wH2n9riP1xRaI7RrlxpI6ibUz5pYt07X02YP3E1Ui6dlkjz32GB566CHMnTsXgwcPxoABA/DWW2/hrrvucnT5iKRN381DXunWlVv45b0DUK0oxfcnE3BJtDecq4WbuC9yP9KGlGHIS4kIbd7RfQV1BVcMdOb9RG5i92wyIQQGDBiA69ev44MPPsDatWsxfvx4zJw5E/Xq1XNkGYmIXObamUKsmXcQqtU++Cm3LYpRPssrVHEFQ5sdhnK4P/pPbovajbq5saQuZs+GvEQewqZg6OOPP8bOnTuxc+dOHDlyBL6+vkhOTsb48ePRvn17fPXVV2jTpg1UKhU6d+7srDITETlU7q48rHr7ONTr6yLzSjLK0NNwLtY3F2mJJ6EcHYze49rCL6iXG0vqRrasD0XkYWwaMxQbG4tu3boZfjp37lxlQ9Q333wTy5Ytw8GDBx1eWHtxzBB5DW8aU+Hmuhxb+ydUC85C/Vsj7ChOMjqXGHgCaZ1zoXwmHB1Htpb2Fhiu/hxNrTNUYXsRIkfy2O04Lly4gKioKGhsnV7pRAyGyCtIeVdvWx/IbqiL0Ars+uIIVJ8UQLU7FkdvNzec84EGzwR9jvtaZaPDo4mIeeEhzwgy3fU74U1BOUmay57fwsG0Wq3IyspydLY1UlhYKACIwsJCdxeFyD4rVwqhUAih65wo/1EodD8rV7q3bDExxuWKiTFfJhfW5XbxbbF+3m4xvm2WiPY5b/R2/igVAxvuFD/1+pcoC4+0vvxSIeXfCSIHcdXzmxu1EkmdlHf1tnVFYhfUpbigGD+/fQDqlWX4ITsRV0UDw7k6uIH7Yw4g7QEt7p+WhPq7f3X8isquIOXfCSIH8thuMiliMEQeTaq7etvzQHZSXS6fuILv5x2Gao0/1uUnowS1DOcaKy7igRZHoRwRhH6T2iKofpD95ZcKqf5OEDmYpNcZIiIXkuqu3rasSKx/IDuwLme35UL99kmoNgRj87W20KB8llecXw6UyaegHNsAPZ5Kgm+Aiene1pZ/5kygXz/L42KcNY7GVL5S/Z0g8lAMhoikTqq7etvzQK5BXYRW4NCqk1B/lAvV1nDsuZUAoHz7hnZBx5DWNQ/KcZFIHtYSCh8Lm0pbW/7Zs3U/1Q1MdtZAZnP5Pvmkdddzp3ciq7CbjMiRnNE6INVdve3pqrGxLtoyLbZ/dgjqzy5DtS8OJ+/ElSeFFr2CD0CZchWpk5qhWd8mzil/5fJVHkfkjJ3crck3NBS4ckVavxNEDsYxQw7EYIhcwpnTnPUPRsD0YnfuGOhrb5BmoS53vvgav2Y3g+qrm1h1vDUuaMMMSQJQiv5hf0A5qBRDp7ZGWGJj55XfnNjY8jo5a9yRNfmGhgKXL5tfAFGqg7+JbOCxU+uliFPryelcMc3Z1BT22Fj3T6vX19GWepuoS3HdMPFOozkiGNeMsgrGNTGi6W/imxe2iqLcIseW/5tvqn5n1vxkZuquz8y0Lb21rM131izp/U4QOZCrnt8cM0RUUxqNrkXIVOuCELq/1CdNAlJTa9ZlkZ6uy0NKi92lp+taIEy1iFW3InF6Oi4074Fd077BoW1FWH+9Czbc6AftDV1dInwuILXVMSgfqY2U55MRULen6XxqIiMDmDzZvmv1443sGTdlTVeqtfm2aAGcPi2t3wmqGS5o6RYMhohqyp5ZVfaS4q7eNgRpf2adhfq9P6HKaoAtRW0h8JzhXAv/bCg7nEHa4w3R9R+J8PELd16ZzY3HsZZ+YLKtA8Kt7Uq1JV8p/k6QfaS8yryX45ghoppavhwYOdJyumXLgBEjnF8eCRFagT++PQ71f/Kg2hGJ/SWtjM53qn0Yyh4FSJsQgzZDm7tmDzBL43EsadxYF/RVHDNkzbipVausH2gt1UHz5DzOGojv4bjOEJGnsPav+BMnnFsOidDc1mDLJwehWnIN6gPNcLqsFQBdEOSLMvSpfwDKfkVInXIXmnRvA6CNawtoqSXPkkWLygMQa3dyB2zrSuUO8fLiqq52MsvH3QUg8ni9e+v+SldYaNWYOVP3158XKrlWgh9e+x2Pt9yMiKCruOe5dnh/7z04XRaLINxCasQOLH3iN1w4XoQNVztg4nf3oEn3aMsZO0NNFiKcOrV8JpyeftxUdKX6xMSU/zVvS1eqLfmSd7Dn94Mcii1DRDWl/yv+wQctp/Wiv+6unSnEj/MPQrXKB2tz26IYXQznGiiuYkj8ISiH+WHAlLaoE9bVjSWtxJ6FCBs3Bj76CHjoIdPnLY2bsnfFaCkOmifH44ribsdgiMgR0tOBWbOA1183n8aRA6nd5PyefKx++zhU62oj83Iy7qB8lleM73mktTmBtFH10Gd8W/jX7lVNTm6kb8mrbjxOdDSwdClQUGB9AFLdQOaarCLOAdLeT6qrzMsIgyEiR2nRwrp0HvbX3fGfs6F6/wzUvzXE9httAUQYziUEnIKycw7SngpD51EJUPhEua+g1rJmPM6CBbr9yBzFmgAsJkaXrjJOtfZ+Nfn9IIdgMERkibUPI0//6+6veorc8zh+8Da+2BgL1Z6mOFx6F4B4Q7KudQ5C2fsS0p5rglaDmgNo7rYi283e9ZHsZe+AaE61lgcOmHc7Tq0nqo4tDyMPng5dtvwblD07EUGFBYZjOYjB81iA7zEUKaH7oRxQjNSpLRHVMaKanDyMq1tdTP0+xcaaDsAsTbVesaJ8mj9bjLyDLb8fMsG9yRyIwRDZxZ51P6S4h5gZNy/dxLp3DuDskl8w4cKrAITR9FItAAWAmx//D3WeHuWeQnojawIwa9ZC0q9zpMcWI+/AblEjDIYciMEQ2awmG3BK+K+7K6eu4vt/H4J6jR9+zktGKQJxGnGIxjnT62yYqyf/h+1cWVlASopt10gw4CaqKS66SORONdliQ2LToXN2nIf6rRNQb6iHjVeToUH5LK+/+3yLWK2N9eQ4FuezZ5A9F+cjshuDISJTarruhxunQwutwJEfTkH14TmotoZh9802AMpnebUNOg5ll/NQjotEu7I7wKNWZKqvp7muw9xc3XFXt0p4awuVvYPsvWD5BiJ3YDBEZIqHzQzTlmmx47+HoP7sMlR7m+LEnbsA3AUAUECLHvUOQnnPFaS9EI/mf2sJoKXuwiwrg77ISOltGeDNLVSWplpb4mHLNxC5G8cMEZniATPDbt+4jcwF+6FedhOrjrZEnrZ8llcASnFv4/1Iu+8WHpiWgPCkxqYzsaWemzdbN44lM9P5rRJy2NTS3GB8a7jiOyByAVc9v7k3GZEp+nU/gKp7jrlx3Y8b+Tfw7eRteCRuC8Lq3cJ9r3TGx4f7IE8bgXoowsNNtuLr57biYk4p1hTcjSf/18d8IATYVk+pbBlgqYUK0LVQVZxp5YnM7U1W3e+cQqEbrM/F+Yhswm4yInNcvTCfGRePXMLqeUegXhuI9QXJKEV3w7lwnwKktjyKtBG18LdJyQgM7mH7G1hbT6l0HdZkcLunMTUY/9IlYPhw3XkuzkfkEOwmI7LEDYN0szflQP3uKagyG2BLURK0KH+/5n5noGyfDeUTDdF1bBv4BjioLJbqqdEA4eHA5cvm82jYELhwwbmfz/LlwMiRltMtWwaMGOG8criThJdvIHIkTq0nkgoXzAwTWoEDGSeg+ug8VNsj8UdJKwCxhvMdax1BWvcLUE6IRmLqXVD4NHV8ITxlQ1CptFC5k8SWbyDydB7RMpSbm4uXXnoJa9euxa1bt9CyZUt89tln6NSpk1XXs2XIBt46VVmCNLc12Lr4INRLr0L9Rzz+LCsPcHygQZ/6+5GWUoS0Kc3RtGeM+78baxcCdPbgXQ8Y3E5EjsGWob9cvXoVPXv2REpKCtauXYuwsDCcOnUK9evXd3fRvI83T1WWiJJrJfj13X04vHQHTuUE4ShaYTN6QwtfBOEWBkTsh3LwHQyZmoBGrTqUXyiF70YqA6i5qSUROZjkW4amT5+OLVu2YPPmzXbnwZYhK8hhqrKbFJ4txI9vHYJKrYD/uT/xb0xHLMqDmsu+jXFiyGS0XTwRdcLqVM1AKt+NVFqG9DhuhsjrcW+yv7Rp0wYDBw7EuXPnsHHjRkRHR2PcuHF48sknzV5TWlqK0tJSw+uioiLExsYyGDKnJvtwkUl5+y5g9VvHoPq5NjZcTsYdBECJDHyHYai8IWq1QY2Uvhspdk+5u+uQiJyKwdBfgoKCAACTJ0/GQw89hN9//x2TJk3CJ598gscee8zkNTNnzsSsWbOqHGcwZIbU/uL3UCfWn4b6/dNQbWqI7TcSjUKeNv7HsUXRCyG3L0Jh6mJzgYQrvhtbAgpzCwGaCujM5csAhois5LKeHSFx/v7+onv37kbHJk6cKLp162b2mpKSElFYWGj4ycnJEQBEYWGhs4vrmZYtE0L3aKv+Z9kyd5dUUrQardj1xWHxSq9MkRh4vMrH1aXOATF3YKY4suaUEJmZ1n3GmZnGb+Ls72blSiFiYozzionRHbflmthY42vM5Tt1qu3vR0SyVVhY6JLnt+QHUEdGRqJNmzZGxxISErBy5Uqz1wQGBiIwMNDZRfMenKpstbKSMmxedACqz4ugPnQXcjQJABIAAH64g76h+6HsfwMPTGmJmLuTyi9cvsO6N6g8+NiZ3429m65amtZtLt9z54C33qqan7s2eSUi+ovkg6GePXvi2LFjRseOHz+Opk2dsM6KXFnaFFKh0G0JoNHoFryTWdfGzQvXsWfyFzjwSwHWFnTEGgw2LIJYG8W4L+oAlA9oMHhaIhrEm1nuwd6gxprvJibG9u0Xarrpqrk1iarL1xx3bPJKRFSRU9udHOD3338Xfn5+Ys6cOeLEiRPiq6++ErVr1xZffvml1Xm4qpnNo61cKYRCofup2IWhf92woay6Ni6fvCL+9/Rm8e/6c0UOoo3qfg5R4sOIf4lV/9wubl6+aXxhWZmuq2vZMt2/ZWXlx2Niqn6+FT/n2Njy9BVV990oFPZ9D/Z22zkqX0e9HxF5NVc9vyUfDAkhxPfffy+SkpJEYGCgaN26tVi8eLFN1zMYspKpcR6hoeYf3vY+iCUq5/fz4sNhWaJfg93CF3eEEiuFBgqhqVR3rbm6Wxp/U5OgxppxOrZw1lgka/N19NgnIvJKrnp+S342mSNwnSEbVJzpc+wYMHu2+d2/vWDK/ZEfTkH1QQ7UWxtjZ3Gi4bgPNMhFDMKRb93sL2vXAqrJ2jiOnIXlrFlq1ubrqPcjIq/GqfUOxGDIDhkZwIMPWpfWgx5g2jItdn5+GKr/uwT13iY4druZ4ZwCWnSvdxDKPlcwIiUf0S9asclnZqYuKLG0FlB0NLB0KVBQAISF6Y4XFLhv/JWz1gyylK85XhBYE5HjcTsOch/9IFhrOXv7hRq6feM2Ni48ANWXxVh1pAXOa8tnefnjNvo1+gPKgbfwwLTWiEhO1p1Yvty6zPPydK015gIhQBcUnDsH3Htv+TH9VhruCiKdtaVFdfmawy00iMjNfCwnIY+j0ei6K5Yv1/1rrpvLnKys6h/ulUlwyv2N/BtYOXUbHo3fgrB6tzBgRif851AfnNdGoi6uY3jsViyfuBWXckqw9uLdeOrLPohIDivPwJbZX/YEg/rp5BkZtl/rKOnpuu676Gjj4zExNZvmbi7f2Fhg6lRd/o58PyKiGmI3mbep6YaeGRnAk08CV65Y936xsZLp2rh0uAA7p3yNQ1sLsa6oC37FvYYp8GGKi0htdQRpD9dCvxeSERhsYR0qS9tgAOV137zZvnEyUukactaK0FyBmohqiGOGHEg2wVBNN/Q0d311Vq5061/0p387B/U7p3B53S48dfN9ow1Q8xCJn5s9g7umpKH7E4nwDbDxgTttmulFAvWmTgXmz7d/nIyeB425IiJyJVc9v9lN5i0sLaIH6Ba1M9dlZutieb6+wDffuDwQElqBAyuP442/ZaFj7SOI7x2DTerLmHVzKqJh3IoTocjHmOyZ6BVx0vZASL/AZHW+/lqXTj9OBigPPG0h8TFXdqlpVy0RkQsxGPIW1gzizcnRpbPn+sq+/hp46CHbymgnzW0NtvxnP17snIUWgWeRPKwlXs/si723EuCH2/hYMQ6KyjvBA1BYEwSaY83nUfHzNDdOxhoSHHNVIxkZupaylBRg5Ejdv3Fx7h0fRURUDc4m8xbWti6YS2ft9Q0bAosXO71FqLSoFL++tx/qr29h1bEEFIhkw7lAlKB/2H4o7y9Fet8rqD/mgvmMKgaBtnRF2fN5Vt6zKywMGD0aOH/esVtpSJm9+50REbkRgyFvUdMNPa29fsUKoF8/69LaqOhcEX6cfxBqNfBjThKu427DuRAUYkjcQaSl++C+qW1RN6KL7oQtU+BtYe/nWXnPrg8+cPz0damq6X5nRERuwmBIqmydcVPTzVat3RDUwQN9Lxy8iFX/PgL1ulr49WIybqOH4VykTz7SEo4j7ZE66DuxLQLq9qyagbN2dXfUBqn67jNTM/ysWXXak9jSVcsB40QkIQyGpMie6fGWFtETArh1y/TCf+npzluEz4RTG85A9W42VJtCse16EgT6GM619M+GsuMZpD3RCF3GtIGPX0T1mTlrV3dHfh6Vu8+8dTp5TbtqiYjcxak7n0mER23Uqt/M096NUU1t6Fl5x/nq8nT0hqBCCK1GK3Z/eVi82jtTJAUer1KMzrUPiTn9M8Xh708KrUZr+xs4Y1f3ink7+PPwWtbuWM+d6YnIStyo1YE8Zp0hSwv9WbtIX8UuNv0g3txc6/N0wKJ4ZSVl+O3jg1B/Xgj1geY4oylfddgXZejbYD/S+l1H6ostENs1yqa8TarJBqiWcJFA6zhrvzMiki0uuuhAHhMMOWMncWftTm7CrSu3sP6d/VB/exurT7bBZdHQcK4WbuK+yP1IG1KGIS8lIrR5gxq9l0kMWtxPP5sMMN21yNlkRGQDbtQqR84Yc+HkcRxXs69hzfxDUH/vg59y26IYXQ3nQhVXMLTZYSiH+6P/5Lao3aibXe9htcozucj15DRgnIi8BoMhKXHGzCgn5Jm7Kw+r3j4O1fq6yLqSjDKUz/KK9c1FWuJJKEcHo/e4tvAL6mV9WeXC21uw5DJgnIi8BrvJpMQZYy4clOfRH/+E+oOzUP3WCL8XJxmdSww8gbTOuVA+E46OI1tD4WPHlhRyUdONdImIZITdZHLkjOntduapLdNi1xdHoP6/i1DtjsXR280BNDOc7173ANJ6X4byhTi06N8CQAtbaipPXJ2ZiEiS2DIkRc6YGWVFnndu3sHGhQeg/vI61IdaIldb3nXmj9v4W8P9SBtwE6nTWiGyfbj59/L2biB7OGqmIBGRjHA2mQN5XDAEOCegMJFn8eUS/Pz2Aai+K8MPp5NwTdQ3JK+DG7g/5gDSHtDi/mlJqN80xPJ7sBvINBfO6iMi8hbsJpM7Z8yM+ivPS8cu44e3jkA1YhfW5SejBOWzvBorLuKBFkehHBGEfpPaIqh+d+vzZzeQeVydmYhIshgMOZKEu4fObDmHVe+egmpDMDZdS4YW5bO84vxyoEw+BeXYBujxVBJ8A+zYRZ2bdFbPWXuoERFRjTEYchSJdQ8JrcChVSehWpgL9bZw7LmVAKB8Feh2QceQ1jUPynGRSB7WEgqf2Jq9ITfprJ6z9lAjIqIaYzDkCBLpHtKWabH9s0NQfXoZ6j/icPJO+SwvBbToFXwAypSrSJ3UDM36tgLQynFvzm6g6rlwI1wiIrINgyFrVNf95ebuodKiUmR+cACqr25i1fHWuKBtazgXgFL0D/sDykGlGDq1NcIS2zn8/Q3YDWQZV2cmIpIkziazxFL3lxtmCV0/fx1r3zoAVQbw49lEFKF8llcwCjG46UEo031w34tJqBdVzyHvaZGlxR0BoGFD4MIFtn5IeGwZEZGUcDaZFFjT/VVaal1eNeweunDwIlbPPwL1T7Xwy8Vk3EYPw7kInwtIbXUMykdqI+X5ZATU7VlNTk6i7wZ68EHzaS5fBlatYgsI91AjIpIUtgyZY+0ieUuWAPfeazm/X34B+vWzuswA8GfWWaje+RPqTQ2wpagtBHwM51r4Z0PZ4QzSHm+Irv9IhI+fTzU5uYhGA4SH64IeUzx5YUG25hARuRxbhtzN2tlRQPWzhPRGjwY++MC4VaTSA1b07IU/Mk5BtSgPqt+jcKCkJYAmhuSdah+GskcB0ibEoM3Q5lD4xNesjo62ebP5QAjw3BllEpspSEREjsVgyBxru7UKCszPEqro/HnjmWUmHrB5iMQbWAgVdA9YX5ShT/0DUPYrQuqUu9CkexsAbXRB1KaN0mul8MYZZRKZKUhERM4j32DIUreHtbOewsJ01z3/PPDll8ClS6bTVZhZdvt6CfzHPAIAqLi/ewTy8R2GYX79NxE5rBeGTGuDhi06GOdjqpWiUSNg0SLgoYesK7OzeNuMMi4kSUQkC/IcM2RNt4el2VEKBRAaCgQF6dLY4CIaoSEuwdQoH6FQQGFuXI25Vgq9qVOB+fNtKotDWfOZedKYIe4nRkTkVq4aMySBUbcupg8oKo8H0nd7ZGToXutnRwHli+Lp6bvDLl+2ORACgMZmAiEAUFQcV1NRda0Uem+9peu2cRdLnxngWQsLemO3HxERVSGvYMhStweg6/bQaHT/rV8kLzraOG10tG7NHGeq/IC1NKBbb9y48vK7g7nPLCbG88bXeFu3HxERmSSvMUNbt9q+f1Z6um5MSMXxRRqNddPpK1ModON7Ll60nLbyA9ba1oeLF90/W8vUZyaVQd624H5iRESyIK9gKD/funSVA49Ki+SVLf3C9g9O3020aBHwwgu2P2BtaX2QQreNNywsyP3EiIhkQV7dZBER1qUzEXjcvHQTqpe2Y3Tz36AcW9/299Z3Ew0bZt+4mt69da1K1mC3jeN4U7cfERGZJK/ZZFeuIDg52erZTpdPXMEP8w9D9YM/1uW3xS3UBgD4QIOzaIJInDcfTcbEAEuX6tYhMtVNZGpGW+PGwEcfmZ8i/+23wPDh1Vc2NtZzZmt5Eq5ATUTkcpxNZsbcuXOhUCgwadIk2y+2YrbTxWdfxYd//w1/a7AX4S2DMebTXliV3xW3UBtNfc9hUoeNyPzgICJeGFH9hzdihG77jREjdN1FlR+c6enAe+/pAiC9ixeByZPLZ7RV9tBDuunz5igU7LZxFn23n7nvk4iIPJZHtQzt3LkTw4cPR3BwMFJSUvD+++9bdZ016wwVBjbGbPEy3r79vNG1bYOOQ9nlPJTjItHuoZZQ+Cgs71sGWG6hMbdmkD5Iq64L5rvvdLPGKg7Ejo3VBULstiEiIi/hqpYhjwmGbty4gY4dO2LRokWYPXs22rdvb3cwpC3TYsen+7F/QRaOnlBgr6YdNqM3tPCFAlr0qHcQynuuIO2FeDT/W9OqGdZ0MT5rN4GtLphitw0REXk5btRayfjx4zF48GDce++9mD17drVpS0tLUVpaanhdVFQEAPjlrT1Yt9IHq461Qr62PYD2AIAAlOK+xnuQdt8tPDAtAeFJydUXpqaL8Vm7CWx1U+S9YbYWERGRBHhEMPT1119jz5492Llzp1Xp586di1mzZlU5/uDsjgB0kWU9FGFwk4NISwMGTU1CcMzd1heopovxcWVjIiIiyZB8MJSTk4Pnn38e69atQ1BQkFXXzJgxA5MnTza8LioqQmxsLBorLkLZah/SRtTC3yYlIzC4h32FqulifFzZmIiISDIkP2ZIrVZDqVTCt8J4GI1GA4VCAR8fH5SWlhqdM0Xf53jl4hU0aNSgagJ7xt/oB0ADphfjq24AtLdtaEpEROQEnFr/l379+uHAgQPYt2+f4adz58545JFHsG/fPouBUEW+ASbSZmToApOUFGDkSN2/cXHmp7fr1WQxPm/b0JSIiMiDSb5lyJS+ffvWaDaZQU2mt+vVZFaXqYUXOUWeiIgIAGeTOZ+lHewVCt0O9qmp1Qc3NZnV5S0bmhIREXkwjwyGsrKyap6JI6a3OwKnyBMREbmV5McMOQ2ntxMRERHkHAxxejsRERFBzsGQfq2gyrO59BQK3WBmc2sFERERkVeQbzDE6e1EREQEOQdDQM3WCiIiIiKv4JGzyRyK09uJiIhkjcEQwOntREREMibvbjIiIiKSPbYMmVKTLTaIiIjIozAYAoyDnxMngMWLdTvK68XE6GaecUA1ERGR12EwZGqz1Mpyc3UbunKGGRERkdeR95gh/a711QVCQPlmrpMm6VqRiIiIyGvINxiqbtd6Uypu3EpEREReQ77BkKVd683hxq1EREReRb7BkL1BDTduJSIi8iryHUBta1CjUOhmlXHjViIiIq8i32BIv2t9bq7lcUOVN27lOkREREReQ77dZNXtWl9ZxY1bMzKAuDggJQUYOVL3b1yc7jgRERF5HIUQ1k6n8lxFRUUICQlBYWEhgoODjU+aWmcoJgZ48kmgRQvjlh/9VPzKH5k+mOI6RERERA5T7fPbgRgMAdZ1e2k0uhYgczPQ9GOKsrPZZUZEROQArgqG5DtmqCJrdq23NBW/4jpElvIiIiIiyZDvmCFbWTsVn+sQEREReRQGQ9aydio+1yEiIiLyKAyGrKWfim9u5plCAcTGch0iIiIiD8NgyFrVTcWvvA4REREReQwGQ7ZIT9dNn4+ONj5ecR0iIiIi8iicTWar9HQgNZUrUBMREXkJBkP2sGYqPhEREXkEdpMRERGRrDEYIiIiIlljMERERESyxmCIiIiIZI3BEBEREckagyEiIiKSNQZDREREJGsMhoiIiEjWGAwRERGRrDEYIiIiIlmTfDA0d+5c3H333ahXrx7CwsKQlpaGY8eOubtYRERE5CUkHwxt3LgR48ePx/bt27F+/XqUlZVhwIABKC4udnfRiIiIyAsohBDC3YWwxcWLFxEWFoaNGzeiT58+Vl1TVFSEkJAQFBYWIjg42MklJCIiIkdw1fPb43atLywsBACEhoaaTVNaWorS0lLD66KiIqeXi4iIiDyT5LvJKhJCYPLkyejVqxeSkpLMpps7dy5CQkIMP7GxsS4sJREREXkSj+omGz9+PNasWYPffvsNMTExZtOZahmKjY1lNxkREZEHYTdZJRMnTsTq1auxadOmagMhAAgMDERgYKCLSkZERESeTPLBkBACEydOhEqlQlZWFuLj491dJCIiIvIikg+Gxo8fj2XLlmHVqlWoV68e8vPzAQAhISGoVauWm0tHREREnk7yY4YUCoXJ40uWLMGYMWOsyoNT64mIiDwPxwz9ReKxGhEREXk4j5paT0RERORoDIaIiIhI1hgMERERkawxGCIiIiJZYzBEREREssZgiIiIiGSNwRARERHJGoMhIiIikjUGQ0RERCRrDIaIiIhI1hgMERERkawxGCIiIiJZYzBEREREssZgiIiIiGSNwRARERHJGoMhIiIikjUGQ0RERCRrDIaIiIhI1hgMERERkawxGCIiIiJZYzBEREREssZgiIiIiGSNwRARERHJGoMhIiIikjUGQ0RERCRrDIaIiIhI1hgMERERkawxGCIiIiJZYzBEREREssZgiIiIiGSNwRARERHJGoMhIiIikjUGQ0RERCRrDIaIiIhI1hgMERERkawxGCIiIiJZYzBEREREssZgiIiIiGTNY4KhRYsWIT4+HkFBQejUqRM2b97s7iIRERGRF/CIYGjFihWYNGkSXn75Zezduxe9e/fGoEGDcPbsWXcXjYiIiDycQggh3F0IS7p27YqOHTviP//5j+FYQkIC0tLSMHfuXIvXFxUVISQkBIWFhQgODnZmUYmIiMhBXPX8lnzL0O3bt7F7924MGDDA6PiAAQOwdetWN5WKiIiIvIWfuwtgyaVLl6DRaBAeHm50PDw8HPn5+SavKS0tRWlpqeF1YWEhAF2ESURERJ5B/9x2dieW5IMhPYVCYfRaCFHlmN7cuXMxa9asKsdjY2OdUjYiIiJynsuXLyMkJMRp+Us+GGrUqBF8fX2rtAIVFBRUaS3SmzFjBiZPnmx4fe3aNTRt2hRnz5516ocpNUVFRYiNjUVOTo6sxkqx3qy3HLDerLccFBYWokmTJggNDXXq+0g+GAoICECnTp2wfv16KJVKw/H169cjNTXV5DWBgYEIDAyscjwkJERWv0R6wcHBrLeMsN7ywnrLi1zr7ePj3CHOkg+GAGDy5MkYNWoUOnfujO7du2Px4sU4e/YsnnnmGXcXjYiIiDycRwRDf//733H58mW88cYbyMvLQ1JSEn788Uc0bdrU3UUjIiIiD+cRwRAAjBs3DuPGjbPr2sDAQLz++usmu868GevNessB6816ywHr7dx6e8Sii0RERETOIvlFF4mIiIicicEQERERyRqDISIiIpI1BkNEREQkax4ZDC1atAjx8fEICgpCp06dsHnz5mrTb9y4EZ06dUJQUBCaNWuGjz/+uEqalStXok2bNggMDESbNm2gUqmcVXy72VLvjIwM9O/fH40bN0ZwcDC6d++On3/+2SjN0qVLoVAoqvyUlJQ4uyo2saXeWVlZJut09OhRo3Te9n2PGTPGZL0TExMNaTzh+960aROGDh2KqKgoKBQKqNVqi9d4w/1ta7295f62td7ecn/bWm9vub/nzp2Lu+++G/Xq1UNYWBjS0tJw7Ngxi9e54h73uGBoxYoVmDRpEl5++WXs3bsXvXv3xqBBg3D27FmT6bOzs3H//fejd+/e2Lt3L/75z3/iueeew8qVKw1ptm3bhr///e8YNWoU/vjjD4waNQrDhw/Hjh07XFUti2yt96ZNm9C/f3/8+OOP2L17N1JSUjB06FDs3bvXKF1wcDDy8vKMfoKCglxRJavYWm+9Y8eOGdWpRYsWhnPe+H0vWLDAqL45OTkIDQ3FQw89ZJRO6t93cXEx2rVrh4ULF1qV3lvub1vr7S33t6311vP0+9vWenvL/b1x40aMHz8e27dvx/r161FWVoYBAwaguLjY7DUuu8eFh+nSpYt45plnjI61bt1aTJ8+3WT6adOmidatWxsde/rpp0W3bt0Mr4cPHy7uu+8+ozQDBw4UDz/8sINKXXO21tuUNm3aiFmzZhleL1myRISEhDiqiE5ha70zMzMFAHH16lWzecrh+1apVEKhUIjTp08bjnnC910RAKFSqapN4y33d0XW1NsUT7y/K7Km3t5yf1dkz/ftDfe3EEIUFBQIAGLjxo1m07jqHveolqHbt29j9+7dGDBggNHxAQMGYOvWrSav2bZtW5X0AwcOxK5du3Dnzp1q05jL09XsqXdlWq0W169fr7LZ3Y0bN9C0aVPExMRgyJAhVf6ydKea1LtDhw6IjIxEv379kJmZaXRODt/3Z599hnvvvbfKKu1S/r7t4Q33tyN44v1dE558fzuCt9zfhYWFAFDtJqyuusc9Khi6dOkSNBpNld3qw8PDq+xqr5efn28yfVlZGS5dulRtGnN5upo99a7snXfeQXFxMYYPH2441rp1ayxduhSrV6/G8uXLERQUhJ49e+LEiRMOLb+97Kl3ZGQkFi9ejJUrVyIjIwOtWrVCv379sGnTJkMab/++8/LysHbtWjzxxBNGx6X+fdvDG+5vR/DE+9se3nB/15S33N9CCEyePBm9evVCUlKS2XSuusc9ZjuOihQKhdFrIUSVY5bSVz5ua57uYG8Zly9fjpkzZ2LVqlUICwszHO/WrRu6detmeN2zZ0907NgRH374IT744APHFbyGbKl3q1at0KpVK8Pr7t27IycnB2+//Tb69OljV57uYm8Zly5divr16yMtLc3ouKd837bylvvbXp5+f9vCm+5ve3nL/T1hwgTs378fv/32m8W0rrjHPaplqFGjRvD19a0S7RUUFFSJCvUiIiJMpvfz80PDhg2rTWMuT1ezp956K1aswOOPP45vvvkG9957b7VpfXx8cPfdd0vmL4ma1Luibt26GdXJm79vIQT++9//YtSoUQgICKg2rdS+b3t4w/1dE558fzuKp93fNeEt9/fEiROxevVqZGZmIiYmptq0rrrHPSoYCggIQKdOnbB+/Xqj4+vXr0ePHj1MXtO9e/cq6detW4fOnTvD39+/2jTm8nQ1e+oN6P5iHDNmDJYtW4bBgwdbfB8hBPbt24fIyMgal9kR7K13ZXv37jWqk7d+34ButsbJkyfx+OOPW3wfqX3f9vCG+9tenn5/O4qn3d814en3txACEyZMQEZGBjZs2ID4+HiL17jsHrd6qLVEfP3118Lf31989tln4vDhw2LSpEmiTp06hlH106dPF6NGjTKk//PPP0Xt2rXFCy+8IA4fPiw+++wz4e/vL7777jtDmi1btghfX1/x73//Wxw5ckT8+9//Fn5+fmL79u0ur585ttZ72bJlws/PT3z00UciLy/P8HPt2jVDmpkzZ4qffvpJnDp1Suzdu1eMHTtW+Pn5iR07dri8fubYWu/33ntPqFQqcfz4cXHw4EExffp0AUCsXLnSkMYbv2+9Rx99VHTt2tVknp7wfV+/fl3s3btX7N27VwAQ7777rti7d684c+aMEMJ7729b6+0t97et9faW+9vWeut5+v397LPPipCQEJGVlWX0e3vz5k1DGnfd4x4XDAkhxEcffSSaNm0qAgICRMeOHY2m5Y0ePVrcc889RumzsrJEhw4dREBAgIiLixP/+c9/quT57bffilatWgl/f3/RunVro5tLKmyp9z333CMAVPkZPXq0Ic2kSZNEkyZNREBAgGjcuLEYMGCA2Lp1qwtrZB1b6j1v3jzRvHlzERQUJBo0aCB69eol1qxZUyVPb/u+hRDi2rVrolatWmLx4sUm8/OE71s/ddrc76233t+21ttb7m9b6+0t97c9v+fecH+bqjMAsWTJEkMad93jir8KSERERCRLHjVmiIiIiMjRGAwRERGRrDEYIiIiIlljMERERESyxmCIiIiIZI3BEBEREckagyEiIiKSNQZDREREJGsMhoiIiEjWGAwRERGRrDEYIiKPtHz5cgQFBSE3N9dw7IknnkBycjIKCwvdWDIi8jTcm4yIPJIQAu3bt0fv3r2xcOFCzJo1C59++im2b9+O6OhodxePiDyIn7sLQERkD4VCgTlz5mDYsGGIiorCggULsHnzZgZCRGQztgwRkUfr2LEjDh06hHXr1uGee+5xd3GIyANxzBAReayff/4ZR48ehUajQXh4uLuLQ0Qeii1DROSR9uzZg759++Kjjz7C119/jdq1a+Pbb791d7GIyANxzBAReZzTp09j8ODBmD59OkaNGoU2bdrg7rvvxu7du9GpUyd3F4+IPAxbhojIo1y5cgU9e/ZEnz598MknnxiOp6amorS0FD/99JMbS0dEnojBEBEREckaB1ATERGRrDEYIiIiIlljMERERESyxmCIiIiIZI3BEBEREckagyEiIiKSNQZDREREJGsMhoiIiEjWGAwRERGRrDEYIiIiIlljMERERESyxmCIiIiIZO3/ATPeRV7/I8mtAAAAAElFTkSuQmCC\n",
+ "image/png": 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\n",
"text/plain": [
""
]
@@ -2481,7 +2493,7 @@
},
{
"cell_type": "markdown",
- "id": "6231b86f",
+ "id": "e0bdcd22",
"metadata": {
"editable": true
},
@@ -2494,7 +2506,7 @@
},
{
"cell_type": "markdown",
- "id": "8d50214c",
+ "id": "86fcc0af",
"metadata": {
"editable": true
},
@@ -2509,7 +2521,7 @@
},
{
"cell_type": "markdown",
- "id": "45d43ca3",
+ "id": "3b656ad4",
"metadata": {
"editable": true
},
@@ -2521,7 +2533,7 @@
},
{
"cell_type": "markdown",
- "id": "dcdd91bf",
+ "id": "ec7ef032",
"metadata": {
"editable": true
},
@@ -2539,7 +2551,7 @@
},
{
"cell_type": "markdown",
- "id": "c7519d1e",
+ "id": "842b17dd",
"metadata": {
"editable": true
},
@@ -2558,7 +2570,7 @@
},
{
"cell_type": "markdown",
- "id": "f4d4340d",
+ "id": "549a9b7e",
"metadata": {
"editable": true
},
@@ -2570,7 +2582,7 @@
},
{
"cell_type": "markdown",
- "id": "41ad532a",
+ "id": "310fe216",
"metadata": {
"editable": true
},
@@ -2586,7 +2598,7 @@
},
{
"cell_type": "markdown",
- "id": "eef8ae92",
+ "id": "e1b6edcb",
"metadata": {
"editable": true
},
@@ -2598,7 +2610,7 @@
},
{
"cell_type": "markdown",
- "id": "80481a6d",
+ "id": "49e7b650",
"metadata": {
"editable": true
},
@@ -2608,7 +2620,7 @@
},
{
"cell_type": "markdown",
- "id": "6aab8db7",
+ "id": "67564cfb",
"metadata": {
"editable": true
},
@@ -2620,7 +2632,7 @@
},
{
"cell_type": "markdown",
- "id": "dd6414d2",
+ "id": "ebb0e17a",
"metadata": {
"editable": true
},
@@ -2630,7 +2642,7 @@
},
{
"cell_type": "markdown",
- "id": "b76a8372",
+ "id": "6d0cfa1c",
"metadata": {
"editable": true
},
@@ -2642,7 +2654,7 @@
},
{
"cell_type": "markdown",
- "id": "07bbe6db",
+ "id": "e8252d81",
"metadata": {
"editable": true
},
@@ -2656,7 +2668,7 @@
},
{
"cell_type": "markdown",
- "id": "7a9a2ecf",
+ "id": "ed9da45e",
"metadata": {
"editable": true
},
@@ -2668,7 +2680,7 @@
},
{
"cell_type": "markdown",
- "id": "fe5a2bbc",
+ "id": "11c47009",
"metadata": {
"editable": true
},
@@ -2701,7 +2713,7 @@
},
{
"cell_type": "markdown",
- "id": "04540023",
+ "id": "7fd92874",
"metadata": {
"editable": true
},
@@ -2713,7 +2725,7 @@
},
{
"cell_type": "markdown",
- "id": "dfbf53a5",
+ "id": "5fa3a569",
"metadata": {
"editable": true
},
@@ -2731,7 +2743,7 @@
},
{
"cell_type": "markdown",
- "id": "32ac3869",
+ "id": "1534657f",
"metadata": {
"editable": true
},
@@ -2762,7 +2774,7 @@
},
{
"cell_type": "markdown",
- "id": "6f575b16",
+ "id": "85b9db6c",
"metadata": {
"editable": true
},
@@ -2777,7 +2789,7 @@
},
{
"cell_type": "markdown",
- "id": "274604c4",
+ "id": "0593ecb5",
"metadata": {
"editable": true
},
@@ -2795,7 +2807,7 @@
},
{
"cell_type": "markdown",
- "id": "cd679323",
+ "id": "8d8d8609",
"metadata": {
"editable": true
},
@@ -2807,7 +2819,7 @@
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{
"cell_type": "markdown",
- "id": "0a7f8e9d",
+ "id": "e22f9446",
"metadata": {
"editable": true
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@@ -2819,7 +2831,7 @@
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{
"cell_type": "markdown",
- "id": "48ba8fff",
+ "id": "1b88fbaa",
"metadata": {
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@@ -2837,7 +2849,7 @@
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{
"cell_type": "markdown",
- "id": "83140ab2",
+ "id": "558d9648",
"metadata": {
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@@ -2860,7 +2872,7 @@
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{
"cell_type": "markdown",
- "id": "61874dc3",
+ "id": "3711c9bc",
"metadata": {
"editable": true
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@@ -2878,7 +2890,7 @@
},
{
"cell_type": "markdown",
- "id": "24e19d86",
+ "id": "86d38c7e",
"metadata": {
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@@ -2890,7 +2902,7 @@
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{
"cell_type": "markdown",
- "id": "506f78ea",
+ "id": "8fee2361",
"metadata": {
"editable": true
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@@ -2902,7 +2914,7 @@
},
{
"cell_type": "markdown",
- "id": "cb4b8585",
+ "id": "705e9f9b",
"metadata": {
"editable": true
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@@ -2914,7 +2926,7 @@
},
{
"cell_type": "markdown",
- "id": "9b5b11b1",
+ "id": "281da053",
"metadata": {
"editable": true
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@@ -2926,7 +2938,7 @@
},
{
"cell_type": "markdown",
- "id": "92292a73",
+ "id": "e5ed01f4",
"metadata": {
"editable": true
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@@ -2938,7 +2950,7 @@
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{
"cell_type": "markdown",
- "id": "1a264832",
+ "id": "7ab5a8ef",
"metadata": {
"editable": true
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@@ -2955,7 +2967,7 @@
},
{
"cell_type": "markdown",
- "id": "6a307202",
+ "id": "f47fe0de",
"metadata": {
"editable": true
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@@ -2974,7 +2986,7 @@
},
{
"cell_type": "markdown",
- "id": "3285f010",
+ "id": "78c5a239",
"metadata": {
"editable": true
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@@ -2986,7 +2998,7 @@
},
{
"cell_type": "markdown",
- "id": "657349da",
+ "id": "23d5750c",
"metadata": {
"editable": true
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@@ -3004,7 +3016,7 @@
},
{
"cell_type": "markdown",
- "id": "65044ac7",
+ "id": "78629315",
"metadata": {
"editable": true
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@@ -3042,7 +3054,7 @@
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{
"cell_type": "markdown",
- "id": "dacf05cf",
+ "id": "39d7472b",
"metadata": {
"editable": true
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@@ -3054,7 +3066,7 @@
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{
"cell_type": "markdown",
- "id": "da4ad36e",
+ "id": "79a08e26",
"metadata": {
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@@ -3064,7 +3076,7 @@
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{
"cell_type": "markdown",
- "id": "f4c3e6c4",
+ "id": "2fca7cf2",
"metadata": {
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@@ -3076,7 +3088,7 @@
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{
"cell_type": "markdown",
- "id": "1c8bfd4a",
+ "id": "f55b402b",
"metadata": {
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@@ -3087,7 +3099,7 @@
{
"cell_type": "code",
"execution_count": 13,
- "id": "e1d91b8b",
+ "id": "83ffc6ab",
"metadata": {
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"editable": true
@@ -3154,7 +3166,7 @@
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{
"cell_type": "markdown",
- "id": "cd1158a5",
+ "id": "09c698dc",
"metadata": {
"editable": true
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@@ -3169,7 +3181,7 @@
{
"cell_type": "code",
"execution_count": 14,
- "id": "e2e9faff",
+ "id": "23ec9da1",
"metadata": {
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"editable": true
@@ -3206,7 +3218,7 @@
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{
"cell_type": "markdown",
- "id": "e4a83059",
+ "id": "c1d2dcbf",
"metadata": {
"editable": true
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@@ -3219,7 +3231,7 @@
{
"cell_type": "code",
"execution_count": 15,
- "id": "f65983d8",
+ "id": "0ff70c42",
"metadata": {
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"editable": true
@@ -3277,7 +3289,7 @@
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{
"cell_type": "markdown",
- "id": "1d369f97",
+ "id": "8ad0ae71",
"metadata": {
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@@ -3288,7 +3300,7 @@
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"cell_type": "code",
"execution_count": 16,
- "id": "46ea0652",
+ "id": "b9bf2265",
"metadata": {
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"editable": true
@@ -3325,7 +3337,7 @@
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{
"cell_type": "markdown",
- "id": "9cc6674a",
+ "id": "0fae646d",
"metadata": {
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@@ -3341,7 +3353,7 @@
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"cell_type": "code",
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- "id": "17813055",
+ "id": "44a8fa94",
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"editable": true
@@ -3379,7 +3391,7 @@
{
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- "id": "6da49540",
+ "id": "962c21ba",
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@@ -3413,7 +3425,7 @@
{
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- "id": "a8ff2c17",
+ "id": "83468113",
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@@ -3458,7 +3470,7 @@
{
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- "id": "ec67d4a3",
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@@ -3487,7 +3499,7 @@
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- "id": "742a2d68",
+ "id": "666db882",
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@@ -3534,7 +3546,7 @@
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{
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- "id": "e7be6348",
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@@ -3549,7 +3561,7 @@
{
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- "id": "c551058c",
+ "id": "3543f315",
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@@ -3589,7 +3601,7 @@
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- "id": "7a13b21d",
+ "id": "cc829644",
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@@ -3600,7 +3612,7 @@
{
"cell_type": "code",
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- "id": "19c7502b",
+ "id": "9dd71229",
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@@ -3622,7 +3634,7 @@
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{
"cell_type": "markdown",
- "id": "4450885d",
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@@ -3635,7 +3647,7 @@
{
"cell_type": "code",
"execution_count": 24,
- "id": "013fc7f8",
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@@ -3660,7 +3672,7 @@
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{
"cell_type": "markdown",
- "id": "8d360f7d",
+ "id": "2db7526b",
"metadata": {
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@@ -3671,7 +3683,7 @@
{
"cell_type": "code",
"execution_count": 25,
- "id": "e29a24eb",
+ "id": "314170c6",
"metadata": {
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"editable": true
@@ -3686,12 +3698,27 @@
},
{
"cell_type": "markdown",
- "id": "ad8fbbb7",
+ "id": "5aa6151e",
"metadata": {
"editable": true
},
"source": [
- "## Using Autograd with OLS\n",
+ "## Replace or not\n",
+ "\n",
+ "In the above code, we have use replacement in setting up the\n",
+ "mini-batches. The discussion\n",
+ "[here](https://sebastianraschka.com/faq/docs/sgd-methods.html) may be\n",
+ "useful."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "2d017a74",
+ "metadata": {
+ "editable": true
+ },
+ "source": [
+ "## Using Autograd\n",
"\n",
"We conclude the part on optmization by showing how we can make codes\n",
"for linear regression and logistic regression using **autograd**. The\n",
@@ -3701,7 +3728,7 @@
{
"cell_type": "code",
"execution_count": 26,
- "id": "904f65dc",
+ "id": "f784b385",
"metadata": {
"collapsed": false,
"editable": true
@@ -3761,20 +3788,155 @@
},
{
"cell_type": "markdown",
- "id": "ce338980",
+ "id": "9eb6dbe2",
"metadata": {
"editable": true
},
"source": [
- "### Including Stochastic Gradient Descent with Autograd\n",
- "\n",
- "In this code we include the stochastic gradient descent approach discussed above. Note here that we specify which argument we are taking the derivative with respect to when using **autograd**."
+ "## Same code but now with momentum gradient descent"
]
},
{
"cell_type": "code",
"execution_count": 27,
- "id": "de261f10",
+ "id": "408e6211",
+ "metadata": {
+ "collapsed": false,
+ "editable": true
+ },
+ "outputs": [],
+ "source": [
+ "# Using Autograd to calculate gradients for OLS\n",
+ "from random import random, seed\n",
+ "import numpy as np\n",
+ "import autograd.numpy as np\n",
+ "import matplotlib.pyplot as plt\n",
+ "from autograd import grad\n",
+ "\n",
+ "def CostOLS(beta):\n",
+ " return (1.0/n)*np.sum((y-X @ beta)**2)\n",
+ "\n",
+ "n = 100\n",
+ "x = 2*np.random.rand(n,1)\n",
+ "y = 4+3*x#+np.random.randn(n,1)\n",
+ "\n",
+ "X = np.c_[np.ones((n,1)), x]\n",
+ "XT_X = X.T @ X\n",
+ "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+ "print(\"Own inversion\")\n",
+ "print(theta_linreg)\n",
+ "# Hessian matrix\n",
+ "H = (2.0/n)* XT_X\n",
+ "EigValues, EigVectors = np.linalg.eig(H)\n",
+ "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
+ "\n",
+ "theta = np.random.randn(2,1)\n",
+ "eta = 1.0/np.max(EigValues)\n",
+ "Niterations = 30\n",
+ "\n",
+ "# define the gradient\n",
+ "training_gradient = grad(CostOLS)\n",
+ "\n",
+ "for iter in range(Niterations):\n",
+ " gradients = training_gradient(theta)\n",
+ " theta -= eta*gradients\n",
+ " print(iter,gradients[0],gradients[1])\n",
+ "print(\"theta from own gd\")\n",
+ "print(theta)\n",
+ "\n",
+ "# Now improve with momentum gradient descent\n",
+ "change = 0.0\n",
+ "delta_momentum = 0.3\n",
+ "for iter in range(Niterations):\n",
+ " # calculate gradient\n",
+ " gradients = training_gradient(theta)\n",
+ " # calculate update\n",
+ " new_change = eta*gradients+delta_momentum*change\n",
+ " # take a step\n",
+ " theta -= new_change\n",
+ " # save the change\n",
+ " change = new_change\n",
+ " print(iter,gradients[0],gradients[1])\n",
+ "print(\"theta from own gd wth momentum\")\n",
+ "print(theta)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "07f1dd70",
+ "metadata": {
+ "editable": true
+ },
+ "source": [
+ "We note indeed a considerable increase in efficiency here, we less iterations needed.\n",
+ "However, if we can invert the Hessian matrix, this is the preferred approach, as shown in the example here."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 28,
+ "id": "7eff4d61",
+ "metadata": {
+ "collapsed": false,
+ "editable": true
+ },
+ "outputs": [],
+ "source": [
+ "# Using Newton's method\n",
+ "from random import random, seed\n",
+ "import numpy as np\n",
+ "import autograd.numpy as np\n",
+ "import matplotlib.pyplot as plt\n",
+ "from autograd import grad\n",
+ "\n",
+ "def CostOLS(beta):\n",
+ " return (1.0/n)*np.sum((y-X @ beta)**2)\n",
+ "\n",
+ "n = 100\n",
+ "x = 2*np.random.rand(n,1)\n",
+ "y = 4+3*x+np.random.randn(n,1)\n",
+ "\n",
+ "X = np.c_[np.ones((n,1)), x]\n",
+ "XT_X = X.T @ X\n",
+ "beta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+ "print(\"Own inversion\")\n",
+ "print(beta_linreg)\n",
+ "# Hessian matrix\n",
+ "H = (2.0/n)* XT_X\n",
+ "# Note that here the Hessian does not depend on the parameters beta\n",
+ "invH = np.linalg.pinv(H)\n",
+ "EigValues, EigVectors = np.linalg.eig(H)\n",
+ "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
+ "\n",
+ "beta = np.random.randn(2,1)\n",
+ "Niterations = 5\n",
+ "\n",
+ "# define the gradient\n",
+ "training_gradient = grad(CostOLS)\n",
+ "\n",
+ "for iter in range(Niterations):\n",
+ " gradients = training_gradient(beta)\n",
+ " beta -= invH @ gradients\n",
+ " print(iter,gradients[0],gradients[1])\n",
+ "print(\"beta from own Newton code\")\n",
+ "print(beta)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "98ae5663",
+ "metadata": {
+ "editable": true
+ },
+ "source": [
+ "## Including Stochastic Gradient Descent with Autograd\n",
+ "In this code we include the stochastic gradient descent approach discussed above. Note here that we specify which argument we are taking the derivative with respect to when using **autograd**."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 29,
+ "id": "cd7caecf",
"metadata": {
"collapsed": false,
"editable": true
@@ -3858,57 +4020,287 @@
},
{
"cell_type": "markdown",
- "id": "ccd8829e",
+ "id": "87e8ab65",
"metadata": {
"editable": true
},
"source": [
- "### And Logistic Regression"
+ "Here we include momentum in the standard gradient descent approach."
]
},
{
"cell_type": "code",
- "execution_count": 28,
- "id": "cc5811d1",
+ "execution_count": 30,
+ "id": "3183015a",
"metadata": {
"collapsed": false,
"editable": true
},
"outputs": [],
"source": [
+ "# Using Autograd to calculate gradients using SGD\n",
+ "# OLS example\n",
+ "from random import random, seed\n",
+ "import numpy as np\n",
"import autograd.numpy as np\n",
+ "import matplotlib.pyplot as plt\n",
"from autograd import grad\n",
"\n",
- "def sigmoid(x):\n",
- " return 0.5 * (np.tanh(x / 2.) + 1)\n",
+ "# Note change from previous example\n",
+ "def CostOLS(y,X,theta):\n",
+ " return np.sum((y-X @ theta)**2)\n",
"\n",
- "def logistic_predictions(weights, inputs):\n",
- " # Outputs probability of a label being true according to logistic model.\n",
- " return sigmoid(np.dot(inputs, weights))\n",
+ "n = 100\n",
+ "x = 2*np.random.rand(n,1)\n",
+ "y = 4+3*x+np.random.randn(n,1)\n",
"\n",
- "def training_loss(weights):\n",
- " # Training loss is the negative log-likelihood of the training labels.\n",
- " preds = logistic_predictions(weights, inputs)\n",
- " label_probabilities = preds * targets + (1 - preds) * (1 - targets)\n",
- " return -np.sum(np.log(label_probabilities))\n",
+ "X = np.c_[np.ones((n,1)), x]\n",
+ "XT_X = X.T @ X\n",
+ "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+ "print(\"Own inversion\")\n",
+ "print(theta_linreg)\n",
+ "# Hessian matrix\n",
+ "H = (2.0/n)* XT_X\n",
+ "EigValues, EigVectors = np.linalg.eig(H)\n",
+ "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
"\n",
- "# Build a toy dataset.\n",
- "inputs = np.array([[0.52, 1.12, 0.77],\n",
- " [0.88, -1.08, 0.15],\n",
- " [0.52, 0.06, -1.30],\n",
- " [0.74, -2.49, 1.39]])\n",
- "targets = np.array([True, True, False, True])\n",
+ "theta = np.random.randn(2,1)\n",
+ "eta = 1.0/np.max(EigValues)\n",
+ "Niterations = 100\n",
"\n",
- "# Define a function that returns gradients of training loss using Autograd.\n",
- "training_gradient_fun = grad(training_loss)\n",
+ "# Note that we request the derivative wrt third argument (theta, 2 here)\n",
+ "training_gradient = grad(CostOLS,2)\n",
"\n",
- "# Optimize weights using gradient descent.\n",
- "weights = np.array([0.0, 0.0, 0.0])\n",
- "print(\"Initial loss:\", training_loss(weights))\n",
- "for i in range(100):\n",
- " weights -= training_gradient_fun(weights) * 0.01\n",
+ "for iter in range(Niterations):\n",
+ " gradients = (1.0/n)*training_gradient(y, X, theta)\n",
+ " theta -= eta*gradients\n",
+ "print(\"theta from own gd\")\n",
+ "print(theta)\n",
"\n",
- "print(\"Trained loss:\", training_loss(weights))"
+ "\n",
+ "n_epochs = 50\n",
+ "M = 5 #size of each minibatch\n",
+ "m = int(n/M) #number of minibatches\n",
+ "t0, t1 = 5, 50\n",
+ "def learning_schedule(t):\n",
+ " return t0/(t+t1)\n",
+ "\n",
+ "theta = np.random.randn(2,1)\n",
+ "\n",
+ "change = 0.0\n",
+ "delta_momentum = 0.3\n",
+ "\n",
+ "for epoch in range(n_epochs):\n",
+ " for i in range(m):\n",
+ " random_index = M*np.random.randint(m)\n",
+ " xi = X[random_index:random_index+M]\n",
+ " yi = y[random_index:random_index+M]\n",
+ " gradients = (1.0/M)*training_gradient(yi, xi, theta)\n",
+ " eta = learning_schedule(epoch*m+i)\n",
+ " # calculate update\n",
+ " new_change = eta*gradients+delta_momentum*change\n",
+ " # take a step\n",
+ " theta -= new_change\n",
+ " # save the change\n",
+ " change = new_change\n",
+ "print(\"theta from own sdg with momentum\")\n",
+ "print(theta)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "9ba705cd",
+ "metadata": {
+ "editable": true
+ },
+ "source": [
+ "### Similar (second order function now) problem but now with AdaGrad"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 31,
+ "id": "be7a85c7",
+ "metadata": {
+ "collapsed": false,
+ "editable": true
+ },
+ "outputs": [],
+ "source": [
+ "# Using Autograd to calculate gradients using AdaGrad and Stochastic Gradient descent\n",
+ "# OLS example\n",
+ "from random import random, seed\n",
+ "import numpy as np\n",
+ "import autograd.numpy as np\n",
+ "import matplotlib.pyplot as plt\n",
+ "from autograd import grad\n",
+ "\n",
+ "# Note change from previous example\n",
+ "def CostOLS(y,X,theta):\n",
+ " return np.sum((y-X @ theta)**2)\n",
+ "\n",
+ "n = 10000\n",
+ "x = np.random.rand(n,1)\n",
+ "y = 2.0+3*x +4*x*x# +np.random.randn(n,1)\n",
+ "\n",
+ "X = np.c_[np.ones((n,1)), x, x*x]\n",
+ "XT_X = X.T @ X\n",
+ "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+ "print(\"Own inversion\")\n",
+ "print(theta_linreg)\n",
+ "\n",
+ "\n",
+ "# Note that we request the derivative wrt third argument (theta, 2 here)\n",
+ "training_gradient = grad(CostOLS,2)\n",
+ "# Define parameters for Stochastic Gradient Descent\n",
+ "n_epochs = 50\n",
+ "M = 5 #size of each minibatch\n",
+ "m = int(n/M) #number of minibatches\n",
+ "# Guess for unknown parameters theta\n",
+ "theta = np.random.randn(3,1)\n",
+ "\n",
+ "# Value for learning rate\n",
+ "eta = 0.01\n",
+ "# Including AdaGrad parameter to avoid possible division by zero\n",
+ "delta = 1e-8\n",
+ "for epoch in range(n_epochs):\n",
+ " # The outer product is calculated from scratch for each epoch\n",
+ " Giter = np.zeros(shape=(3,3))\n",
+ " for i in range(m):\n",
+ " random_index = M*np.random.randint(m)\n",
+ " xi = X[random_index:random_index+M]\n",
+ " yi = y[random_index:random_index+M]\n",
+ " gradients = (1.0/M)*training_gradient(yi, xi, theta)\n",
+ "\t# Calculate the outer product of the gradients\n",
+ " Giter +=gradients @ gradients.T\n",
+ "\t# Simpler algorithm with only diagonal elements\n",
+ " Ginverse = np.c_[eta/(delta+np.sqrt(np.diagonal(Giter)))]\n",
+ " # compute update\n",
+ " update = np.multiply(Ginverse,gradients)\n",
+ " theta -= update\n",
+ "print(\"theta from own AdaGrad\")\n",
+ "print(theta)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "0e711ae2",
+ "metadata": {
+ "editable": true
+ },
+ "source": [
+ "Running this code we note an almost perfect agreement with the results from matrix inversion.\n",
+ "\n",
+ "Similarly, here is our implementation of RMSprop."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 32,
+ "id": "8b34e5b1",
+ "metadata": {
+ "collapsed": false,
+ "editable": true
+ },
+ "outputs": [],
+ "source": [
+ "# Using Autograd to calculate gradients using RMSprop and Stochastic Gradient descent\n",
+ "# OLS example\n",
+ "from random import random, seed\n",
+ "import numpy as np\n",
+ "import autograd.numpy as np\n",
+ "import matplotlib.pyplot as plt\n",
+ "from autograd import grad\n",
+ "\n",
+ "# Note change from previous example\n",
+ "def CostOLS(y,X,theta):\n",
+ " return np.sum((y-X @ theta)**2)\n",
+ "\n",
+ "n = 10000\n",
+ "x = np.random.rand(n,1)\n",
+ "y = 2.0+3*x +4*x*x# +np.random.randn(n,1)\n",
+ "\n",
+ "X = np.c_[np.ones((n,1)), x, x*x]\n",
+ "XT_X = X.T @ X\n",
+ "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+ "print(\"Own inversion\")\n",
+ "print(theta_linreg)\n",
+ "\n",
+ "\n",
+ "# Note that we request the derivative wrt third argument (theta, 2 here)\n",
+ "training_gradient = grad(CostOLS,2)\n",
+ "# Define parameters for Stochastic Gradient Descent\n",
+ "n_epochs = 50\n",
+ "M = 5 #size of each minibatch\n",
+ "m = int(n/M) #number of minibatches\n",
+ "# Guess for unknown parameters theta\n",
+ "theta = np.random.randn(3,1)\n",
+ "\n",
+ "# Value for learning rate\n",
+ "eta = 0.01\n",
+ "# Value for parameter rho\n",
+ "rho = 0.99\n",
+ "# Including AdaGrad parameter to avoid possible division by zero\n",
+ "delta = 1e-8\n",
+ "for epoch in range(n_epochs):\n",
+ " Giter = np.zeros(shape=(3,3))\n",
+ " for i in range(m):\n",
+ " random_index = M*np.random.randint(m)\n",
+ " xi = X[random_index:random_index+M]\n",
+ " yi = y[random_index:random_index+M]\n",
+ " gradients = (1.0/M)*training_gradient(yi, xi, theta)\n",
+ "\t# Previous value for the outer product of gradients\n",
+ " Previous = Giter\n",
+ "\t# Accumulated gradient\n",
+ " Giter +=gradients @ gradients.T\n",
+ "\t# Scaling with rho the new and the previous results\n",
+ " Gnew = (rho*Previous+(1-rho)*Giter)\n",
+ "\t# Taking the diagonal only and inverting\n",
+ " Ginverse = np.c_[eta/(delta+np.sqrt(np.diagonal(Gnew)))]\n",
+ "\t# Hadamard product\n",
+ " update = np.multiply(Ginverse,gradients)\n",
+ " theta -= update\n",
+ "print(\"theta from own RMSprop\")\n",
+ "print(theta)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "7a3b6455",
+ "metadata": {
+ "editable": true
+ },
+ "source": [
+ "## Introducing [JAX](https://jax.readthedocs.io/en/latest/)\n",
+ "\n",
+ "Presently, instead of using **autograd**, we recommend using [JAX](https://jax.readthedocs.io/en/latest/)\n",
+ "\n",
+ "**JAX** is Autograd and [XLA (Accelerated Linear Algebra))](https://www.tensorflow.org/xla),\n",
+ "brought together for high-performance numerical computing and machine learning research.\n",
+ "It provides composable transformations of Python+NumPy programs: differentiate, vectorize, parallelize, Just-In-Time compile to GPU/TPU, and more.\n",
+ "\n",
+ "Here's a simple example on how you can use **JAX** to compute the derivate of the logistic function."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 33,
+ "id": "2c30f41b",
+ "metadata": {
+ "collapsed": false,
+ "editable": true
+ },
+ "outputs": [],
+ "source": [
+ "import jax.numpy as jnp\n",
+ "from jax import grad, jit, vmap\n",
+ "\n",
+ "def sum_logistic(x):\n",
+ " return jnp.sum(1.0 / (1.0 + jnp.exp(-x)))\n",
+ "\n",
+ "x_small = jnp.arange(3.)\n",
+ "derivative_fn = grad(sum_logistic)\n",
+ "print(derivative_fn(x_small))"
]
}
],
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapteroptimization.py b/doc/LectureNotes/_build/jupyter_execute/chapteroptimization.py
index cb4459c01..0a4a034cd 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapteroptimization.py
+++ b/doc/LectureNotes/_build/jupyter_execute/chapteroptimization.py
@@ -250,7 +250,19 @@
# $\mathbb{R}$. Examples of convex sets of $\mathbb{R}^2$ are the
# regular polygons (triangles, rectangles, pentagons, etc...).
#
-# **Convex function**: Let $X \subset \mathbb{R}^n$ be a convex set. Assume that the function $f: X \rightarrow \mathbb{R}$ is continuous, then $f$ is said to be convex if $$f(tx_1 + (1-t)x_2) \leq tf(x_1) + (1-t)f(x_2) $$ for all $x_1, x_2 \in X$ and for all $t \in [0,1]$. If $\leq$ is replaced with a strict inequaltiy in the definition, we demand $x_1 \neq x_2$ and $t\in(0,1)$ then $f$ is said to be strictly convex. For a single variable function, convexity means that if you draw a straight line connecting $f(x_1)$ and $f(x_2)$, the value of the function on the interval $[x_1,x_2]$ is always below the line as illustrated below.
+# **Convex function**: Let $X \subset \mathbb{R}^n$ be a convex
+# set. Assume that the function $f: X \rightarrow \mathbb{R}$ is
+# continuous, then $f$ is said to be convex if
+# $f(tx_1 + (1-t)x_2) \leq tf(x_1) + (1-t)f(x_2)$
+# for all
+# $x_1, x_2 \in X$ and for all $t \in [0,1]$.
+#
+# If $\leq$ is replaced with a strict inequality in the
+# definition, we demand $x_1 \neq x_2$ and $t\in(0,1)$ then $f$ is said
+# to be strictly convex. For a single variable function, convexity means
+# that if you draw a straight line connecting $f(x_1)$ and $f(x_2)$, the
+# value of the function on the interval $[x_1,x_2]$ is always below the
+# line as discussed below.
#
# In the following we state first and second-order conditions which
# ensures convexity of a function $f$. We write $D_f$ to denote the
@@ -264,7 +276,7 @@
# is a convex set and $$f(y) \geq f(x) + \nabla f(x)^T (y-x) $$ holds
# for all $x,y \in D_f$. This condition means that for a convex function
# the first order Taylor expansion (right hand side above) at any point
-# a global under estimator of the function. To convince yourself you can
+# is a global under estimator of the function. To convince yourself you can
# make a drawing of $f(x) = x^2+1$ and draw the tangent line to $f(x)$ and
# note that it is always below the graph.
#
@@ -1742,7 +1754,14 @@ a*= b
a /=b
-# ## Using Autograd with OLS
+# ## Replace or not
+#
+# In the above code, we have use replacement in setting up the
+# mini-batches. The discussion
+# [here](https://sebastianraschka.com/faq/docs/sgd-methods.html) may be
+# useful.
+
+# ## Using Autograd
#
# We conclude the part on optmization by showing how we can make codes
# for linear regression and logistic regression using **autograd**. The
@@ -1802,13 +1821,118 @@ plt.title(r'Random numbers ')
plt.show()
-# ### Including Stochastic Gradient Descent with Autograd
-#
-# In this code we include the stochastic gradient descent approach discussed above. Note here that we specify which argument we are taking the derivative with respect to when using **autograd**.
+# ## Same code but now with momentum gradient descent
# In[27]:
+# Using Autograd to calculate gradients for OLS
+from random import random, seed
+import numpy as np
+import autograd.numpy as np
+import matplotlib.pyplot as plt
+from autograd import grad
+
+def CostOLS(beta):
+ return (1.0/n)*np.sum((y-X @ beta)**2)
+
+n = 100
+x = 2*np.random.rand(n,1)
+y = 4+3*x#+np.random.randn(n,1)
+
+X = np.c_[np.ones((n,1)), x]
+XT_X = X.T @ X
+theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)
+print("Own inversion")
+print(theta_linreg)
+# Hessian matrix
+H = (2.0/n)* XT_X
+EigValues, EigVectors = np.linalg.eig(H)
+print(f"Eigenvalues of Hessian Matrix:{EigValues}")
+
+theta = np.random.randn(2,1)
+eta = 1.0/np.max(EigValues)
+Niterations = 30
+
+# define the gradient
+training_gradient = grad(CostOLS)
+
+for iter in range(Niterations):
+ gradients = training_gradient(theta)
+ theta -= eta*gradients
+ print(iter,gradients[0],gradients[1])
+print("theta from own gd")
+print(theta)
+
+# Now improve with momentum gradient descent
+change = 0.0
+delta_momentum = 0.3
+for iter in range(Niterations):
+ # calculate gradient
+ gradients = training_gradient(theta)
+ # calculate update
+ new_change = eta*gradients+delta_momentum*change
+ # take a step
+ theta -= new_change
+ # save the change
+ change = new_change
+ print(iter,gradients[0],gradients[1])
+print("theta from own gd wth momentum")
+print(theta)
+
+
+# We note indeed a considerable increase in efficiency here, we less iterations needed.
+# However, if we can invert the Hessian matrix, this is the preferred approach, as shown in the example here.
+
+# In[28]:
+
+
+# Using Newton's method
+from random import random, seed
+import numpy as np
+import autograd.numpy as np
+import matplotlib.pyplot as plt
+from autograd import grad
+
+def CostOLS(beta):
+ return (1.0/n)*np.sum((y-X @ beta)**2)
+
+n = 100
+x = 2*np.random.rand(n,1)
+y = 4+3*x+np.random.randn(n,1)
+
+X = np.c_[np.ones((n,1)), x]
+XT_X = X.T @ X
+beta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)
+print("Own inversion")
+print(beta_linreg)
+# Hessian matrix
+H = (2.0/n)* XT_X
+# Note that here the Hessian does not depend on the parameters beta
+invH = np.linalg.pinv(H)
+EigValues, EigVectors = np.linalg.eig(H)
+print(f"Eigenvalues of Hessian Matrix:{EigValues}")
+
+beta = np.random.randn(2,1)
+Niterations = 5
+
+# define the gradient
+training_gradient = grad(CostOLS)
+
+for iter in range(Niterations):
+ gradients = training_gradient(beta)
+ beta -= invH @ gradients
+ print(iter,gradients[0],gradients[1])
+print("beta from own Newton code")
+print(beta)
+
+
+# ## Including Stochastic Gradient Descent with Autograd
+# In this code we include the stochastic gradient descent approach discussed above. Note here that we specify which argument we are taking the derivative with respect to when using **autograd**.
+
+# In[29]:
+
+
# Using Autograd to calculate gradients using SGD
# OLS example
from random import random, seed
@@ -1884,42 +2008,227 @@ print("theta from own sdg")
print(theta)
-# ### And Logistic Regression
+# Here we include momentum in the standard gradient descent approach.
-# In[28]:
+# In[30]:
+# Using Autograd to calculate gradients using SGD
+# OLS example
+from random import random, seed
+import numpy as np
import autograd.numpy as np
+import matplotlib.pyplot as plt
from autograd import grad
-def sigmoid(x):
- return 0.5 * (np.tanh(x / 2.) + 1)
+# Note change from previous example
+def CostOLS(y,X,theta):
+ return np.sum((y-X @ theta)**2)
-def logistic_predictions(weights, inputs):
- # Outputs probability of a label being true according to logistic model.
- return sigmoid(np.dot(inputs, weights))
+n = 100
+x = 2*np.random.rand(n,1)
+y = 4+3*x+np.random.randn(n,1)
-def training_loss(weights):
- # Training loss is the negative log-likelihood of the training labels.
- preds = logistic_predictions(weights, inputs)
- label_probabilities = preds * targets + (1 - preds) * (1 - targets)
- return -np.sum(np.log(label_probabilities))
+X = np.c_[np.ones((n,1)), x]
+XT_X = X.T @ X
+theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)
+print("Own inversion")
+print(theta_linreg)
+# Hessian matrix
+H = (2.0/n)* XT_X
+EigValues, EigVectors = np.linalg.eig(H)
+print(f"Eigenvalues of Hessian Matrix:{EigValues}")
-# Build a toy dataset.
-inputs = np.array([[0.52, 1.12, 0.77],
- [0.88, -1.08, 0.15],
- [0.52, 0.06, -1.30],
- [0.74, -2.49, 1.39]])
-targets = np.array([True, True, False, True])
+theta = np.random.randn(2,1)
+eta = 1.0/np.max(EigValues)
+Niterations = 100
-# Define a function that returns gradients of training loss using Autograd.
-training_gradient_fun = grad(training_loss)
+# Note that we request the derivative wrt third argument (theta, 2 here)
+training_gradient = grad(CostOLS,2)
-# Optimize weights using gradient descent.
-weights = np.array([0.0, 0.0, 0.0])
-print("Initial loss:", training_loss(weights))
-for i in range(100):
- weights -= training_gradient_fun(weights) * 0.01
+for iter in range(Niterations):
+ gradients = (1.0/n)*training_gradient(y, X, theta)
+ theta -= eta*gradients
+print("theta from own gd")
+print(theta)
-print("Trained loss:", training_loss(weights))
+
+n_epochs = 50
+M = 5 #size of each minibatch
+m = int(n/M) #number of minibatches
+t0, t1 = 5, 50
+def learning_schedule(t):
+ return t0/(t+t1)
+
+theta = np.random.randn(2,1)
+
+change = 0.0
+delta_momentum = 0.3
+
+for epoch in range(n_epochs):
+ for i in range(m):
+ random_index = M*np.random.randint(m)
+ xi = X[random_index:random_index+M]
+ yi = y[random_index:random_index+M]
+ gradients = (1.0/M)*training_gradient(yi, xi, theta)
+ eta = learning_schedule(epoch*m+i)
+ # calculate update
+ new_change = eta*gradients+delta_momentum*change
+ # take a step
+ theta -= new_change
+ # save the change
+ change = new_change
+print("theta from own sdg with momentum")
+print(theta)
+
+
+# ### Similar (second order function now) problem but now with AdaGrad
+
+# In[31]:
+
+
+# Using Autograd to calculate gradients using AdaGrad and Stochastic Gradient descent
+# OLS example
+from random import random, seed
+import numpy as np
+import autograd.numpy as np
+import matplotlib.pyplot as plt
+from autograd import grad
+
+# Note change from previous example
+def CostOLS(y,X,theta):
+ return np.sum((y-X @ theta)**2)
+
+n = 10000
+x = np.random.rand(n,1)
+y = 2.0+3*x +4*x*x# +np.random.randn(n,1)
+
+X = np.c_[np.ones((n,1)), x, x*x]
+XT_X = X.T @ X
+theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)
+print("Own inversion")
+print(theta_linreg)
+
+
+# Note that we request the derivative wrt third argument (theta, 2 here)
+training_gradient = grad(CostOLS,2)
+# Define parameters for Stochastic Gradient Descent
+n_epochs = 50
+M = 5 #size of each minibatch
+m = int(n/M) #number of minibatches
+# Guess for unknown parameters theta
+theta = np.random.randn(3,1)
+
+# Value for learning rate
+eta = 0.01
+# Including AdaGrad parameter to avoid possible division by zero
+delta = 1e-8
+for epoch in range(n_epochs):
+ # The outer product is calculated from scratch for each epoch
+ Giter = np.zeros(shape=(3,3))
+ for i in range(m):
+ random_index = M*np.random.randint(m)
+ xi = X[random_index:random_index+M]
+ yi = y[random_index:random_index+M]
+ gradients = (1.0/M)*training_gradient(yi, xi, theta)
+ # Calculate the outer product of the gradients
+ Giter +=gradients @ gradients.T
+ # Simpler algorithm with only diagonal elements
+ Ginverse = np.c_[eta/(delta+np.sqrt(np.diagonal(Giter)))]
+ # compute update
+ update = np.multiply(Ginverse,gradients)
+ theta -= update
+print("theta from own AdaGrad")
+print(theta)
+
+
+# Running this code we note an almost perfect agreement with the results from matrix inversion.
+#
+# Similarly, here is our implementation of RMSprop.
+
+# In[32]:
+
+
+# Using Autograd to calculate gradients using RMSprop and Stochastic Gradient descent
+# OLS example
+from random import random, seed
+import numpy as np
+import autograd.numpy as np
+import matplotlib.pyplot as plt
+from autograd import grad
+
+# Note change from previous example
+def CostOLS(y,X,theta):
+ return np.sum((y-X @ theta)**2)
+
+n = 10000
+x = np.random.rand(n,1)
+y = 2.0+3*x +4*x*x# +np.random.randn(n,1)
+
+X = np.c_[np.ones((n,1)), x, x*x]
+XT_X = X.T @ X
+theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)
+print("Own inversion")
+print(theta_linreg)
+
+
+# Note that we request the derivative wrt third argument (theta, 2 here)
+training_gradient = grad(CostOLS,2)
+# Define parameters for Stochastic Gradient Descent
+n_epochs = 50
+M = 5 #size of each minibatch
+m = int(n/M) #number of minibatches
+# Guess for unknown parameters theta
+theta = np.random.randn(3,1)
+
+# Value for learning rate
+eta = 0.01
+# Value for parameter rho
+rho = 0.99
+# Including AdaGrad parameter to avoid possible division by zero
+delta = 1e-8
+for epoch in range(n_epochs):
+ Giter = np.zeros(shape=(3,3))
+ for i in range(m):
+ random_index = M*np.random.randint(m)
+ xi = X[random_index:random_index+M]
+ yi = y[random_index:random_index+M]
+ gradients = (1.0/M)*training_gradient(yi, xi, theta)
+ # Previous value for the outer product of gradients
+ Previous = Giter
+ # Accumulated gradient
+ Giter +=gradients @ gradients.T
+ # Scaling with rho the new and the previous results
+ Gnew = (rho*Previous+(1-rho)*Giter)
+ # Taking the diagonal only and inverting
+ Ginverse = np.c_[eta/(delta+np.sqrt(np.diagonal(Gnew)))]
+ # Hadamard product
+ update = np.multiply(Ginverse,gradients)
+ theta -= update
+print("theta from own RMSprop")
+print(theta)
+
+
+# ## Introducing [JAX](https://jax.readthedocs.io/en/latest/)
+#
+# Presently, instead of using **autograd**, we recommend using [JAX](https://jax.readthedocs.io/en/latest/)
+#
+# **JAX** is Autograd and [XLA (Accelerated Linear Algebra))](https://www.tensorflow.org/xla),
+# brought together for high-performance numerical computing and machine learning research.
+# It provides composable transformations of Python+NumPy programs: differentiate, vectorize, parallelize, Just-In-Time compile to GPU/TPU, and more.
+#
+# Here's a simple example on how you can use **JAX** to compute the derivate of the logistic function.
+
+# In[33]:
+
+
+import jax.numpy as jnp
+from jax import grad, jit, vmap
+
+def sum_logistic(x):
+ return jnp.sum(1.0 / (1.0 + jnp.exp(-x)))
+
+x_small = jnp.arange(3.)
+derivative_fn = grad(sum_logistic)
+print(derivative_fn(x_small))
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7.11.2. And Logistic Regression¶
+Here we include momentum in the standard gradient descent approach.
-
+
+import autograd.numpy as np
+# Using Autograd to calculate gradients using SGD
+# OLS example
+from random import random, seed
+import numpy as np
+import autograd.numpy as np
+import matplotlib.pyplot as plt
from autograd import grad
-def sigmoid(x):
- return 0.5 * (np.tanh(x / 2.) + 1)
+# Note change from previous example
+def CostOLS(y,X,theta):
+ return np.sum((y-X @ theta)**2)
-def logistic_predictions(weights, inputs):
- # Outputs probability of a label being true according to logistic model.
- return sigmoid(np.dot(inputs, weights))
+n = 100
+x = 2*np.random.rand(n,1)
+y = 4+3*x+np.random.randn(n,1)
-def training_loss(weights):
- # Training loss is the negative log-likelihood of the training labels.
- preds = logistic_predictions(weights, inputs)
- label_probabilities = preds * targets + (1 - preds) * (1 - targets)
- return -np.sum(np.log(label_probabilities))
+X = np.c_[np.ones((n,1)), x]
+XT_X = X.T @ X
+theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)
+print("Own inversion")
+print(theta_linreg)
+# Hessian matrix
+H = (2.0/n)* XT_X
+EigValues, EigVectors = np.linalg.eig(H)
+print(f"Eigenvalues of Hessian Matrix:{EigValues}")
-# Build a toy dataset.
-inputs = np.array([[0.52, 1.12, 0.77],
- [0.88, -1.08, 0.15],
- [0.52, 0.06, -1.30],
- [0.74, -2.49, 1.39]])
-targets = np.array([True, True, False, True])
+theta = np.random.randn(2,1)
+eta = 1.0/np.max(EigValues)
+Niterations = 100
-# Define a function that returns gradients of training loss using Autograd.
-training_gradient_fun = grad(training_loss)
+# Note that we request the derivative wrt third argument (theta, 2 here)
+training_gradient = grad(CostOLS,2)
-# Optimize weights using gradient descent.
-weights = np.array([0.0, 0.0, 0.0])
-print("Initial loss:", training_loss(weights))
-for i in range(100):
- weights -= training_gradient_fun(weights) * 0.01
+for iter in range(Niterations):
+ gradients = (1.0/n)*training_gradient(y, X, theta)
+ theta -= eta*gradients
+print("theta from own gd")
+print(theta)
-print("Trained loss:", training_loss(weights))
+
+n_epochs = 50
+M = 5 #size of each minibatch
+m = int(n/M) #number of minibatches
+t0, t1 = 5, 50
+def learning_schedule(t):
+ return t0/(t+t1)
+
+theta = np.random.randn(2,1)
+
+change = 0.0
+delta_momentum = 0.3
+
+for epoch in range(n_epochs):
+ for i in range(m):
+ random_index = M*np.random.randint(m)
+ xi = X[random_index:random_index+M]
+ yi = y[random_index:random_index+M]
+ gradients = (1.0/M)*training_gradient(yi, xi, theta)
+ eta = learning_schedule(epoch*m+i)
+ # calculate update
+ new_change = eta*gradients+delta_momentum*change
+ # take a step
+ theta -= new_change
+ # save the change
+ change = new_change
+print("theta from own sdg with momentum")
+print(theta)
+
+7.14.1. Similar (second order function now) problem but now with AdaGrad¶
+
+
+
+
+
+
+# Using Autograd to calculate gradients using AdaGrad and Stochastic Gradient descent
+# OLS example
+from random import random, seed
+import numpy as np
+import autograd.numpy as np
+import matplotlib.pyplot as plt
+from autograd import grad
+
+# Note change from previous example
+def CostOLS(y,X,theta):
+ return np.sum((y-X @ theta)**2)
+
+n = 10000
+x = np.random.rand(n,1)
+y = 2.0+3*x +4*x*x# +np.random.randn(n,1)
+
+X = np.c_[np.ones((n,1)), x, x*x]
+XT_X = X.T @ X
+theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)
+print("Own inversion")
+print(theta_linreg)
+
+
+# Note that we request the derivative wrt third argument (theta, 2 here)
+training_gradient = grad(CostOLS,2)
+# Define parameters for Stochastic Gradient Descent
+n_epochs = 50
+M = 5 #size of each minibatch
+m = int(n/M) #number of minibatches
+# Guess for unknown parameters theta
+theta = np.random.randn(3,1)
+
+# Value for learning rate
+eta = 0.01
+# Including AdaGrad parameter to avoid possible division by zero
+delta = 1e-8
+for epoch in range(n_epochs):
+ # The outer product is calculated from scratch for each epoch
+ Giter = np.zeros(shape=(3,3))
+ for i in range(m):
+ random_index = M*np.random.randint(m)
+ xi = X[random_index:random_index+M]
+ yi = y[random_index:random_index+M]
+ gradients = (1.0/M)*training_gradient(yi, xi, theta)
+ # Calculate the outer product of the gradients
+ Giter +=gradients @ gradients.T
+ # Simpler algorithm with only diagonal elements
+ Ginverse = np.c_[eta/(delta+np.sqrt(np.diagonal(Giter)))]
+ # compute update
+ update = np.multiply(Ginverse,gradients)
+ theta -= update
+print("theta from own AdaGrad")
+print(theta)
+Running this code we note an almost perfect agreement with the results from matrix inversion.
+Similarly, here is our implementation of RMSprop.
+
+
+
+
+
+
+# Using Autograd to calculate gradients using RMSprop and Stochastic Gradient descent
+# OLS example
+from random import random, seed
+import numpy as np
+import autograd.numpy as np
+import matplotlib.pyplot as plt
+from autograd import grad
+
+# Note change from previous example
+def CostOLS(y,X,theta):
+ return np.sum((y-X @ theta)**2)
+
+n = 10000
+x = np.random.rand(n,1)
+y = 2.0+3*x +4*x*x# +np.random.randn(n,1)
+
+X = np.c_[np.ones((n,1)), x, x*x]
+XT_X = X.T @ X
+theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)
+print("Own inversion")
+print(theta_linreg)
+
+
+# Note that we request the derivative wrt third argument (theta, 2 here)
+training_gradient = grad(CostOLS,2)
+# Define parameters for Stochastic Gradient Descent
+n_epochs = 50
+M = 5 #size of each minibatch
+m = int(n/M) #number of minibatches
+# Guess for unknown parameters theta
+theta = np.random.randn(3,1)
+
+# Value for learning rate
+eta = 0.01
+# Value for parameter rho
+rho = 0.99
+# Including AdaGrad parameter to avoid possible division by zero
+delta = 1e-8
+for epoch in range(n_epochs):
+ Giter = np.zeros(shape=(3,3))
+ for i in range(m):
+ random_index = M*np.random.randint(m)
+ xi = X[random_index:random_index+M]
+ yi = y[random_index:random_index+M]
+ gradients = (1.0/M)*training_gradient(yi, xi, theta)
+ # Previous value for the outer product of gradients
+ Previous = Giter
+ # Accumulated gradient
+ Giter +=gradients @ gradients.T
+ # Scaling with rho the new and the previous results
+ Gnew = (rho*Previous+(1-rho)*Giter)
+ # Taking the diagonal only and inverting
+ Ginverse = np.c_[eta/(delta+np.sqrt(np.diagonal(Gnew)))]
+ # Hadamard product
+ update = np.multiply(Ginverse,gradients)
+ theta -= update
+print("theta from own RMSprop")
+print(theta)
+
+
7.15. Introducing JAX¶
+Presently, instead of using autograd, we recommend using JAX
+JAX is Autograd and XLA (Accelerated Linear Algebra)), +brought together for high-performance numerical computing and machine learning research. +It provides composable transformations of Python+NumPy programs: differentiate, vectorize, parallelize, Just-In-Time compile to GPU/TPU, and more.
+Here’s a simple example on how you can use JAX to compute the derivate of the logistic function.
+
+
+
+
+
import jax.numpy as jnp
+from jax import grad, jit, vmap
+
+def sum_logistic(x):
+ return jnp.sum(1.0 / (1.0 + jnp.exp(-x)))
+
+x_small = jnp.arange(3.)
+derivative_fn = grad(sum_logistic)
+print(derivative_fn(x_small))
+