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    -

    +

    From Regression to Support Vector Machines @@ -171,7 +173,7 @@ -

    +

    Decision Trees, Ensemble Methods and Boosting @@ -188,7 +190,7 @@ -

    +

    Dimensionality Reduction @@ -199,8 +201,13 @@ 11. Basic ideas of the Principal Component Analysis (PCA) +

  1. + + 12. Clustering and Unsupervised Learning + +
    2. -

    +

    Deep Learning Methods @@ -208,17 +215,27 @@

    @@ -267,7 +284,7 @@ data-placement="left">.ipynb + onclick="printPdf(this)" data-toggle="tooltip" data-placement="left">.pdf @@ -285,7 +302,7 @@ -
    +
    Contents @@ -405,7 +422,130 @@
    - + +
    +

    Linear Regression

    + +
    + +
    +
    +
    @@ -797,13 +937,13 @@ example of the functionality of Scikit-Learn.

    The intercept alpha: 
- [1.99977416]
+ [2.09170751]
 Coefficient beta : 
- [[4.86546962]]
-Mean squared error: 0.31
-Variance score: 0.87
+ [[4.91479093]]
+Mean squared error: 0.21
+Variance score: 0.90
 Mean squared log error: 0.01
-Mean absolute error: 0.44
+Mean absolute error: 0.35
    _images/chapter1_13_1.png @@ -903,7 +1043,7 @@ a linear \(x\)-dependence we s
    _images/chapter1_27_0.png -
    0.004999999999999994
+
    0.004999999999999984
    @@ -1085,6 +1225,34 @@ covert them into the pandas DataFrame structure.

    +
    +
    ---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+<ipython-input-8-30b53504a633> in <module>
+      1 # Read the experimental data with Pandas
+----> 2 Masses = pd.read_fwf(infile, usecols=(2,3,4,6,11),
+      3               names=('N', 'Z', 'A', 'Element', 'Ebinding'),
+      4               widths=(1,3,5,5,5,1,3,4,1,13,11,11,9,1,2,11,9,1,3,1,12,11,1),
+      5               header=39,
+
+~/miniforge3/envs/myenv/lib/python3.9/site-packages/pandas/util/_decorators.py in wrapper(*args, **kwargs)
+    309                     stacklevel=stacklevel,
+    310                 )
+--> 311             return func(*args, **kwargs)
+    312 
+    313         return wrapper
+
+~/miniforge3/envs/myenv/lib/python3.9/site-packages/pandas/io/parsers/readers.py in read_fwf(filepath_or_buffer, colspecs, widths, infer_nrows, **kwds)
+    869                         len_index = len(index_col)
+    870             if len(names) + len_index != len(colspecs):
+--> 871                 raise ValueError("Length of colspecs must match length of names")
+    872 
+    873     kwds["colspecs"] = colspecs
+
+ValueError: Length of colspecs must match length of names
+
    +
    +

    We have now read in the data, grouped them according to the variables we are interested in. We see how easy it is to reorganize the data using pandas. If we @@ -1106,25 +1274,6 @@ the number of nucleons \(A\),

    -
    -
                N    Z    A Element  Ebinding
-A                                        
-4   0       1    3    4      Li  1.153760
-5   2       3    2    5      He  5.512132
-6   7       3    3    6      Li  5.332331
-7   12      4    3    7      Li  5.606439
-8   17      4    4    8      Be  7.062435
-...       ...  ...  ...     ...       ...
-264 3297  156  108  264      Hs  7.298375
-265 3303  157  108  265      Hs  7.296247
-266 3310  158  108  266      Hs  7.298273
-269 3331  159  110  269      Ds  7.250154
-270 3337  160  110  270      Ds  7.253775
-
-[264 rows x 5 columns]
-
    -
    -

    The next step, and we will define this mathematically later, is to set up the so-called design matrix. We will throughout call this matrix \(\boldsymbol{X}\). It has dimensionality \(n\times p\), where \(n\) is the number of data points and \(p\) are the so-called predictors. In our case here they are given by the number of polynomials in \(A\) we wish to include in the fit.

    @@ -1180,14 +1329,6 @@ Now we can print measures of how our fit is doing, the coefficients from the fit -
    -
    Mean squared error: 0.02
-Variance score: 0.95
-Mean absolute error: 0.05
-
    -
    -_images/chapter1_57_1.png -

    As a teaser, let us now see how we can do this with decision trees using Scikit-Learn. Later we will switch to so-called random forests!

    @@ -1224,27 +1365,6 @@ Mean absolute error: 0.05
    -
    -_images/chapter1_59_0.png -
                N    Z    A Element  Ebinding   Eapprox
-A                                                  
-4   0       1    3    4      Li  1.153760  1.153760
-5   2       3    2    5      He  5.512132  5.512132
-6   7       3    3    6      Li  5.332331  5.332331
-7   12      4    3    7      Li  5.606439  5.606439
-8   17      4    4    8      Be  7.062435  7.062435
-...       ...  ...  ...     ...       ...       ...
-264 3297  156  108  264      Hs  7.298375  7.298375
-265 3303  157  108  265      Hs  7.296247  7.296247
-266 3310  158  108  266      Hs  7.298273  7.298273
-269 3331  159  110  269      Ds  7.250154  7.250154
-270 3337  160  110  270      Ds  7.253775  7.253775
-
-[264 rows x 6 columns]
-0.007012403613997257
-
    -
    -

    With a deeper and deeper tree level, we can almost reproduce every single data point by increasing the max depth of the tree. @@ -1291,99 +1411,6 @@ functionality.

    -
    -
    /Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
-  warnings.warn(
-/Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
-  warnings.warn(
-/Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
-  warnings.warn(
-
    -
    -
    /Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
-  warnings.warn(
-/Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
-  warnings.warn(
-/Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
-  warnings.warn(
-
    -
    -
    /Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
-  warnings.warn(
-/Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
-  warnings.warn(
-/Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
-  warnings.warn(
-
    -
    -
    /Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
-  warnings.warn(
-/Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
-  warnings.warn(
-/Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
-  warnings.warn(
-
    -
    -
    /Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
-  warnings.warn(
-/Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
-  warnings.warn(
-/Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
-  warnings.warn(
-
    -
    -
    /Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
-  warnings.warn(
-/Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
-  warnings.warn(
-/Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
-  warnings.warn(
-
    -
    -
    /Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
-  warnings.warn(
-/Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
-  warnings.warn(
-/Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
-  warnings.warn(
-
    -
    -
    /Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
-  warnings.warn(
-/Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
-  warnings.warn(
-/Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
-  warnings.warn(
-
    -
    -
    /Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
-  warnings.warn(
-/Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
-  warnings.warn(
-/Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
-  warnings.warn(
-
    -
    -
    /Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
-  warnings.warn(
-/Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
-  warnings.warn(
-
    -
    -
    /Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
-  warnings.warn(
-/Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
-  warnings.warn(
-
    -
    -
    /Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
-  warnings.warn(
-/Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
-  warnings.warn(
-
    -
    -_images/chapter1_61_12.png -
    @@ -1620,133 +1647,6 @@ our matrix as \(\boldsymbol{X}\in {\m -
    -
    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    1AA^(2/3)A^(-1/3)1/A
    A
    41.04.02.5198420.6299610.250000
    51.05.02.9240180.5848040.200000
    61.06.03.3019270.5503210.166667
    71.07.03.6593060.5227580.142857
    81.08.04.0000000.5000000.125000
    ..................
    2641.0264.041.1531060.1558830.003788
    2651.0265.041.2569620.1556870.003774
    2661.0266.041.3606880.1554910.003759
    2691.0269.041.6710890.1549110.003717
    2701.0270.041.7743000.1547200.003704
    -

    264 rows × 5 columns

    -

    With \(\boldsymbol{\beta}\in {\mathbb{R}}^{p\times 1}\), it means that we will hereafter write our equations for the approximation as

    @@ -1972,9 +1872,6 @@ write

    -
    -_images/chapter1_136_0.png -

    We can easily test our fit by computing the \(R2\) score that we discussed in connection with the functionality of Scikit-Learn in the introductory slides. Since we are not using Scikit-Learn here we can define our own \(R2\) function as

    @@ -1993,11 +1890,6 @@ Since we are not using Scikit-Learn here we can define our own -
    -
    0.9549351910143222
-
    -
    -

    We can easily add our MSE score as

    @@ -2010,11 +1902,6 @@ Since we are not using Scikit-Learn here we can define our own
    -
    -
    0.022022882954618364
-
    -
    -

    and finally the relative error as

    @@ -2025,23 +1912,6 @@ Since we are not using Scikit-Learn here we can define our own
    -
    -
    A        
-4    0       1.093247
-5    2       0.275341
-6    7       0.060080
-7    12      0.019587
-8    17      0.117986
-               ...   
-264  3297    0.000148
-265  3303    0.001263
-266  3310    0.002948
-269  3331    0.000599
-270  3337    0.002526
-Name: Ebinding, Length: 264, dtype: float64
-
    -
    -

    3.4.1. The \(\chi^2\) function

    @@ -2253,15 +2123,6 @@ instead of our own matrix inversion implementation.

    -
    -
    Mean squared error: 12.36
-Variance score: 1.00
-Mean absolute error: 2.83
-[   0.          618.32047562 -861.13519106 1404.91549644] -11.057088709963182
-
    -
    -_images/chapter1_183_1.png -

    The above simple polynomial in density \(\rho\) gives an excellent fit to the data.

    @@ -2327,19 +2188,6 @@ the fit becomes better or worse.

    -
    -
    [1.98036405 0.07345504 4.90054363]
-Training R2
-0.9955282554647219
-Training MSE
-0.009450756365829578
-Test R2
-0.9893149172528393
-Test MSE
-0.014209325470380275
-
    -
    -

    Alternatively, you could write your own test-train splitting function as shown here.

    @@ -2437,18 +2285,6 @@ but now splitting the data into a training set and a test set.

    -
    -
    Training R2
-0.9999858320366368
-Training MSE
-6.690569639355314
-Test R2
-0.9999840939906267
-Test MSE
-5.457770268480242
-
    -
    -
    @@ -2503,49 +2339,6 @@ the house using the features (predictors) listed here.

    -
    -
    /Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/utils/deprecation.py:87: FutureWarning: Function load_boston is deprecated; `load_boston` is deprecated in 1.0 and will be removed in 1.2.
-
-    The Boston housing prices dataset has an ethical problem. You can refer to
-    the documentation of this function for further details.
-
-    The scikit-learn maintainers therefore strongly discourage the use of this
-    dataset unless the purpose of the code is to study and educate about
-    ethical issues in data science and machine learning.
-
-    In this case special case, you can fetch the dataset from the original
-    source::
-
-        import pandas as pd
-        import numpy as np
-
-
-        data_url = "http://lib.stat.cmu.edu/datasets/boston"
-        raw_df = pd.read_csv(data_url, sep="\s+", skiprows=22, header=None)
-        data = np.hstack([raw_df.values[::2, :], raw_df.values[1::2, :2]])
-        target = raw_df.values[1::2, 2]
-
-    Alternative datasets include the California housing dataset (i.e.
-    func:`~sklearn.datasets.fetch_california_housing`) and the Ames housing
-    dataset. You can load the datasets as follows:
-
-        from sklearn.datasets import fetch_california_housing
-        housing = fetch_california_housing()
-
-    for the California housing dataset and:
-
-        from sklearn.datasets import fetch_openml
-        housing = fetch_openml(name="house_prices", as_frame=True)
-
-    for the Ames housing dataset.
-    
-  warnings.warn(msg, category=FutureWarning)
-
    -
    -
    dict_keys(['data', 'target', 'feature_names', 'DESCR', 'filename', 'data_module'])
-
    -
    -

    Then we invoke Pandas

    @@ -2565,25 +2358,6 @@ the house using the features (predictors) listed here.

    -
    -
    CRIM       0
-ZN         0
-INDUS      0
-CHAS       0
-NOX        0
-RM         0
-AGE        0
-DIS        0
-RAD        0
-TAX        0
-PTRATIO    0
-B          0
-LSTAT      0
-MEDV       0
-dtype: int64
-
    -
    -

    We can then visualize the data

    @@ -2597,13 +2371,6 @@ dtype: int64
    -
    -
    /Users/MortenImac/anaconda3/lib/python3.8/site-packages/seaborn/distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
-  warnings.warn(msg, FutureWarning)
-
    -
    -_images/chapter1_199_1.png -

    It is now useful to look at the correlation matrix

    @@ -2616,12 +2383,6 @@ dtype: int64
    -
    -
    <AxesSubplot:>
-
    -
    -_images/chapter1_201_1.png -

    From the above coorelation plot we can see that MEDV is strongly correlated to LSTAT and RM. We see also that RAD and TAX are stronly correlated, but we don’t include this in our features together to avoid multi-colinearity

    @@ -2642,9 +2403,6 @@ dtype: int64
    -
    -_images/chapter1_203_0.png -

    Now we start training our model

    @@ -2670,14 +2428,6 @@ dtype: int64
    -
    -
    (404, 2)
-(102, 2)
-(404,)
-(102,)
-
    -
    -

    Then we use the linear regression functionality from Scikit-Learn

    @@ -2716,20 +2466,6 @@ dtype: int64
    -
    -
    The model performance for training set
---------------------------------------
-RMSE is 5.6371293350711955
-R2 score is 0.6300745149331701
-
-
-The model performance for testing set
---------------------------------------
-RMSE is 5.137400784702911
-R2 score is 0.6628996975186953
-
    -
    -
    @@ -2740,9 +2476,6 @@ R2 score is 0.6628996975186953
    -
    -_images/chapter1_210_0.png -
    @@ -2846,346 +2579,6 @@ represent a specific feature whose mean value is subracted.

    -
    -
    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    01234
    0-1.7497650.3426801.153036-0.2524360.981321
    10.5142190.221180-1.070043-0.1894960.255001
    2-0.4580270.435163-0.5835950.8168470.672721
    3-0.104411-0.5312801.029733-0.438136-1.118318
    41.6189821.541605-0.251879-0.8424360.184519
    50.9370820.7310001.361556-0.3262380.055676
    60.222400-1.443217-0.7563520.8164540.750445
    7-0.4559471.189622-1.690617-1.356399-1.232435
    8-0.544439-0.6681720.007315-0.6129391.299748
    9-1.733096-0.9833100.357508-1.6135791.470714
    -
    0   -0.175300
-1    0.083527
-2   -0.044334
-3   -0.399836
-4    0.331939
-dtype: float64
-0    1.069584
-1    0.965548
-2    1.018232
-3    0.793167
-4    0.918992
-dtype: float64
-
    -
    -
    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    01234
    0-1.5744650.2591531.1973700.1474000.649382
    10.6895190.137652-1.0257090.210340-0.076938
    2-0.2827270.351636-0.5392611.2166830.340782
    30.070889-0.6148081.074067-0.038300-1.450257
    41.7942821.458078-0.207545-0.442600-0.147420
    51.1123830.6474731.4058900.073598-0.276263
    60.397700-1.526744-0.7120181.2162900.418506
    7-0.2806471.106095-1.646283-0.956563-1.564374
    8-0.369139-0.7516990.051649-0.2131030.967809
    9-1.557795-1.0668370.401842-1.2137431.138775
    -
    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    01234
    00.00.00.00.00.0
    10.00.00.00.00.0
    20.00.00.00.00.0
    30.00.00.00.00.0
    40.00.00.00.00.0
    50.00.00.00.00.0
    60.00.00.00.00.0
    70.00.00.00.00.0
    80.00.00.00.00.0
    90.00.00.00.00.0
    -

    Small exercise: perform the standard scaling by including the standard deviation and compare with what Scikit-Learn gives.

    Another commonly used scaling method is min-max scaling. This is very @@ -3247,9 +2640,6 @@ ourmodel (here in terms of the polynomial degree of the model).

    -
    -_images/chapter1_218_0.png -
    @@ -3455,54 +2845,42 @@ your results. For which polynomial degree do you find an optimal MSE
    - - - - -
    - -
    -
    -

    - - By Morten Hjorth-Jensen
    - - © Copyright 2021.
    -

    -
    -
    +

    + + By Morten Hjorth-Jensen
    + + © Copyright 2021.
    +

    + - + - \ No newline at end of file diff --git a/doc/LectureNotes/_build/html/chapter10.html b/doc/LectureNotes/_build/html/chapter10.html index 3bc899723..fc1d0dba7 100644 --- a/doc/LectureNotes/_build/html/chapter10.html +++ b/doc/LectureNotes/_build/html/chapter10.html @@ -7,8 +7,8 @@ 14. Building a Feed Forward Neural Network — Applied Data Analysis and Machine Learning - - + + - + @@ -41,22 +41,24 @@ - - - - - + + + + - + + + + @@ -91,11 +93,11 @@ -

    +

    About the course @@ -117,7 +119,7 @@ -

    +

    Review of Statistics with Resampling Techniques and Linear Algebra @@ -134,7 +136,7 @@ -

    +

    From Regression to Support Vector Machines @@ -171,7 +173,7 @@ -

    +

    Decision Trees, Ensemble Methods and Boosting @@ -188,7 +190,7 @@ -

    +

    Dimensionality Reduction @@ -205,7 +207,7 @@ -

    +

    Deep Learning Methods @@ -282,7 +284,7 @@ data-placement="left">.ipynb + onclick="printPdf(this)" data-toggle="tooltip" data-placement="left">.pdf @@ -300,7 +302,7 @@ -

    +
    Contents @@ -464,7 +466,174 @@
    - + +
    +

    Building a Feed Forward Neural Network

    + +
    + +
    +
    +
    -
    -

    - - By Morten Hjorth-Jensen
    - - © Copyright 2021.
    -

    -
    -
    +

    + + By Morten Hjorth-Jensen
    + + © Copyright 2021.
    +

    +
    - + - \ No newline at end of file diff --git a/doc/LectureNotes/_build/html/chapter11.html b/doc/LectureNotes/_build/html/chapter11.html index 59a43e75a..485855bb4 100644 --- a/doc/LectureNotes/_build/html/chapter11.html +++ b/doc/LectureNotes/_build/html/chapter11.html @@ -7,8 +7,8 @@ 15. Solving Differential Equations with Deep Learning — Applied Data Analysis and Machine Learning - - + + - + @@ -41,22 +41,24 @@ - - - - - + + + + - + + + + @@ -91,11 +93,11 @@ -

    +

    About the course @@ -117,7 +119,7 @@ -

    +

    Review of Statistics with Resampling Techniques and Linear Algebra @@ -134,7 +136,7 @@ -

    +

    From Regression to Support Vector Machines @@ -171,7 +173,7 @@ -

    +

    Decision Trees, Ensemble Methods and Boosting @@ -188,7 +190,7 @@ -

    +

    Dimensionality Reduction @@ -205,7 +207,7 @@ -

    +

    Deep Learning Methods @@ -282,7 +284,7 @@ data-placement="left">.ipynb + onclick="printPdf(this)" data-toggle="tooltip" data-placement="left">.pdf

    @@ -300,7 +302,7 @@ -
    +
    Contents @@ -403,7 +405,113 @@
    - + +
    +

    Solving Differential Equations with Deep Learning

    + +
    + +
    +
    +
    -
    -

    - - By Morten Hjorth-Jensen
    - - © Copyright 2021.
    -

    -
    -
    +

    + + By Morten Hjorth-Jensen
    + + © Copyright 2021.
    +

    +
    - + - \ No newline at end of file diff --git a/doc/LectureNotes/_build/html/chapter12.html b/doc/LectureNotes/_build/html/chapter12.html index c1b605ab8..bba46ff2e 100644 --- a/doc/LectureNotes/_build/html/chapter12.html +++ b/doc/LectureNotes/_build/html/chapter12.html @@ -7,8 +7,8 @@ 16. Convolutional Neural Networks — Applied Data Analysis and Machine Learning - - + + - + @@ -41,22 +41,24 @@ - - - - - + + + + - + + + + @@ -91,11 +93,11 @@ -

    +

    About the course @@ -117,7 +119,7 @@ -

    +

    Review of Statistics with Resampling Techniques and Linear Algebra @@ -134,7 +136,7 @@ -

    +

    From Regression to Support Vector Machines @@ -171,7 +173,7 @@ -

    +

    Decision Trees, Ensemble Methods and Boosting @@ -188,7 +190,7 @@ -

    +

    Dimensionality Reduction @@ -205,7 +207,7 @@ -

    +

    Deep Learning Methods @@ -282,7 +284,7 @@ data-placement="left">.ipynb + onclick="printPdf(this)" data-toggle="tooltip" data-placement="left">.pdf

    @@ -300,7 +302,7 @@ -
    +
    Contents @@ -384,7 +386,94 @@
    - + +
    +

    Convolutional Neural Networks

    + +
    + +
    +
    +
    -
    -

    - - By Morten Hjorth-Jensen
    - - © Copyright 2021.
    -

    -
    -
    +

    + + By Morten Hjorth-Jensen
    + + © Copyright 2021.
    +

    +
    - + - \ No newline at end of file diff --git a/doc/LectureNotes/_build/html/chapter13.html b/doc/LectureNotes/_build/html/chapter13.html index f7f0db19c..99753044f 100644 --- a/doc/LectureNotes/_build/html/chapter13.html +++ b/doc/LectureNotes/_build/html/chapter13.html @@ -7,8 +7,8 @@ 17. Recurrent neural networks: Overarching view — Applied Data Analysis and Machine Learning - - + + - + @@ -41,21 +41,23 @@ - - - - - + + + + - + + + + @@ -90,11 +92,11 @@ -

    +

    About the course @@ -116,7 +118,7 @@ -

    +

    Review of Statistics with Resampling Techniques and Linear Algebra @@ -133,7 +135,7 @@ -

    +

    From Regression to Support Vector Machines @@ -170,7 +172,7 @@ -

    +

    Decision Trees, Ensemble Methods and Boosting @@ -187,7 +189,7 @@ -

    +

    Dimensionality Reduction @@ -204,7 +206,7 @@ -

    +

    Deep Learning Methods @@ -281,7 +283,7 @@ data-placement="left">.ipynb + onclick="printPdf(this)" data-toggle="tooltip" data-placement="left">.pdf

    @@ -299,7 +301,7 @@ -
    +
    Contents @@ -365,7 +367,76 @@
    - + +
    +

    Recurrent neural networks: Overarching view

    + +
    + +
    +
    +
    -
    -

    - - By Morten Hjorth-Jensen
    - - © Copyright 2021.
    -

    -
    -
    +

    + + By Morten Hjorth-Jensen
    + + © Copyright 2021.
    +

    +
    - + - \ No newline at end of file diff --git a/doc/LectureNotes/_build/html/chapter2.html b/doc/LectureNotes/_build/html/chapter2.html index 40fee84d2..cbf86722e 100644 --- a/doc/LectureNotes/_build/html/chapter2.html +++ b/doc/LectureNotes/_build/html/chapter2.html @@ -7,8 +7,8 @@ 4. Ridge and Lasso Regression — Applied Data Analysis and Machine Learning - - + + - + @@ -41,22 +41,24 @@ - - - - - + + + + - + + + + @@ -91,11 +93,11 @@ -

    +

    About the course @@ -117,7 +119,7 @@ -

    +

    Review of Statistics with Resampling Techniques and Linear Algebra @@ -134,7 +136,7 @@ -

    +

    From Regression to Support Vector Machines @@ -171,7 +173,7 @@ -

    +

    Decision Trees, Ensemble Methods and Boosting @@ -188,7 +190,7 @@ -

    +

    Dimensionality Reduction @@ -199,8 +201,13 @@ 11. Basic ideas of the Principal Component Analysis (PCA) +

  2. + + 12. Clustering and Unsupervised Learning + +
    3. -

    +

    Deep Learning Methods @@ -208,17 +215,27 @@

    @@ -267,7 +284,7 @@ data-placement="left">.ipynb + onclick="printPdf(this)" data-toggle="tooltip" data-placement="left">.pdf
    @@ -285,7 +302,7 @@ -
    +
    Contents @@ -370,7 +387,95 @@
    - + +
    +

    Ridge and Lasso Regression

    + +
    + +
    +
    +
    @@ -721,13 +826,13 @@ The simple answer is to use the linear algebra function for the pseudoinverse, t [2 4 5] [3 5 6]] test U -[[ 2.22044605e-16 -1.11362930e-15 -8.52945798e-16] - [-1.11362930e-15 0.00000000e+00 -1.37835429e-16] - [-8.52945798e-16 -1.37835429e-16 -1.11022302e-16]] +[[ 4.44089210e-16 -4.69484813e-16 -6.67314874e-16] + [-4.69484813e-16 -4.44089210e-16 -1.54041041e-16] + [-6.67314874e-16 -1.54041041e-16 1.11022302e-16]] test VT -[[ 1.11022302e-16 -1.84228957e-16 2.68545647e-16] - [-1.84228957e-16 0.00000000e+00 -6.33166055e-17] - [ 2.68545647e-16 -6.33166055e-17 -1.11022302e-16]] +[[ 2.22044605e-16 3.78156479e-17 1.85278920e-16] + [ 3.78156479e-17 0.00000000e+00 -6.33166055e-17] + [ 1.85278920e-16 -6.33166055e-17 -1.11022302e-16]] [[0. 0. 0.] [0. 0. 0.] [0. 0. 0.]] @@ -1109,10 +1214,10 @@ covariance matrix through the np.linalg.eig() function.

    -
    0.0934597075922044
-4.185278747229417
-[[0.84292394 2.47432993]
- [2.47432993 8.32458459]]
+
    -0.13876586436927824
+3.722047011333792
+[[ 1.233528    3.58428804]
+ [ 3.58428804 11.47942814]]
    @@ -1149,10 +1254,10 @@ a more brute force way. Here we scale the mean values for each column of the des
    -
    0.08673755293381497
-1.3925515884752442
-[[1.         0.62364974]
- [0.62364974 1.        ]]
+
    0.08464758160254343
+1.8503720991789538
+[[1.         0.65626043]
+ [0.65626043 1.        ]]
    @@ -1182,30 +1287,30 @@ this matrix we easily see that it is a positive definite matrix.

    -
    [[ 0.77034458  1.03056589]
- [-0.46986815 -1.26822717]
- [ 0.82650876 -0.37655936]
- [ 1.1323603   2.97788031]
- [-0.07989327  0.08630331]
- [-1.8608479  -5.59839245]
- [-0.3528556   0.06021285]
- [ 0.25286618  1.40116777]
- [-1.1224392  -2.14042769]
- [ 0.90382431  3.82747653]]
+
    [[-1.41876267 -4.93248252]
+ [ 1.83687444  5.28097861]
+ [ 0.37429133  0.59766   ]
+ [ 0.59159438  1.71869727]
+ [-0.80315282 -0.89348922]
+ [-0.38748219 -2.12288563]
+ [-2.08917679 -5.64933923]
+ [ 0.27803645  0.89944994]
+ [ 1.23703839  3.2321528 ]
+ [ 0.38073947  1.86925797]]
           0         1
-0  0.770345  1.030566
-1 -0.469868 -1.268227
-2  0.826509 -0.376559
-3  1.132360  2.977880
-4 -0.079893  0.086303
-5 -1.860848 -5.598392
-6 -0.352856  0.060213
-7  0.252866  1.401168
-8 -1.122439 -2.140428
-9  0.903824  3.827477
+0 -1.418763 -4.932483
+1  1.836874  5.280979
+2  0.374291  0.597660
+3  0.591594  1.718697
+4 -0.803153 -0.893489
+5 -0.387482 -2.122886
+6 -2.089177 -5.649339
+7  0.278036  0.899450
+8  1.237038  3.232153
+9  0.380739  1.869258
           0         1
-0  1.000000  0.900449
-1  0.900449  1.000000
+0  1.000000  0.977418
+1  0.977418  1.000000
    @@ -1262,37 +1367,37 @@ this matrix we easily see that it is a positive definite matrix.

         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  0.088611  0.086567  0.090229  0.089425  0.088631  0.082174  0.081773   
-2   0.0  0.086567  0.085416  0.088176  0.087834  0.087501  0.080517  0.080406   
-3   0.0  0.090229  0.088176  0.097360  0.096623  0.095871  0.091891  0.091630   
-4   0.0  0.089425  0.087834  0.096623  0.096173  0.095702  0.091426  0.091363   
-5   0.0  0.088631  0.087501  0.095871  0.095702  0.095510  0.090929  0.091060   
-6   0.0  0.082174  0.080517  0.091891  0.091426  0.090929  0.088853  0.088816   
-7   0.0  0.081773  0.080406  0.091630  0.091363  0.091060  0.088816  0.088926   
-8   0.0  0.081431  0.080347  0.091414  0.091340  0.091224  0.088809  0.089059   
-9   0.0  0.081140  0.080334  0.091236  0.091349  0.091416  0.088825  0.089212   
-10  0.0  0.073695  0.072492  0.084408  0.084224  0.084000  0.083053  0.083220   
-11  0.0  0.073531  0.072530  0.084400  0.084364  0.084282  0.083227  0.083506   
-12  0.0  0.073423  0.072617  0.084444  0.084549  0.084604  0.083441  0.083829   
-13  0.0  0.073368  0.072750  0.084536  0.084777  0.084965  0.083692  0.084184   
-14  0.0  0.073362  0.072928  0.084670  0.085044  0.085361  0.083977  0.084570   
+1   0.0  0.081253  0.083015  0.080297  0.079157  0.078040  0.071112  0.069847   
+2   0.0  0.083015  0.086807  0.084909  0.084904  0.084702  0.076955  0.076338   
+3   0.0  0.080297  0.084909  0.084414  0.084862  0.085018  0.077793  0.077402   
+4   0.0  0.079157  0.084904  0.084862  0.086076  0.086872  0.079281  0.079383   
+5   0.0  0.078040  0.084702  0.085018  0.086872  0.088212  0.080319  0.080847   
+6   0.0  0.071112  0.076955  0.077793  0.079281  0.080319  0.073719  0.074034   
+7   0.0  0.069847  0.076338  0.077402  0.079383  0.080847  0.074034  0.074693   
+8   0.0  0.068735  0.075760  0.077003  0.079405  0.081233  0.074237  0.075195   
+9   0.0  0.067769  0.075241  0.076628  0.079389  0.081533  0.074375  0.075594   
+10  0.0  0.062136  0.068318  0.069888  0.071921  0.073449  0.067622  0.068376   
+11  0.0  0.061149  0.067723  0.069408  0.071767  0.073583  0.067612  0.068608   
+12  0.0  0.060309  0.067213  0.068991  0.071632  0.073699  0.067599  0.068806   
+13  0.0  0.059601  0.066789  0.068642  0.071529  0.073816  0.067597  0.068992   
+14  0.0  0.059013  0.066449  0.068363  0.071467  0.073949  0.067620  0.069181   
 
           8         9         10        11        12        13        14  
 0   0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  
-1   0.081431  0.081140  0.073695  0.073531  0.073423  0.073368  0.073362  
-2   0.080347  0.080334  0.072492  0.072530  0.072617  0.072750  0.072928  
-3   0.091414  0.091236  0.084408  0.084400  0.084444  0.084536  0.084670  
-4   0.091340  0.091349  0.084224  0.084364  0.084549  0.084777  0.085044  
-5   0.091224  0.091416  0.084000  0.084282  0.084604  0.084965  0.085361  
-6   0.088809  0.088825  0.083053  0.083227  0.083441  0.083692  0.083977  
-7   0.089059  0.089212  0.083220  0.083506  0.083829  0.084184  0.084570  
-8   0.089329  0.089614  0.083404  0.083799  0.084226  0.084683  0.085167  
-9   0.089614  0.090028  0.083600  0.084101  0.084629  0.085184  0.085764  
-10  0.083404  0.083600  0.078667  0.078992  0.079347  0.079729  0.080137  
-11  0.083799  0.084101  0.078992  0.079406  0.079847  0.080312  0.080801  
-12  0.084226  0.084629  0.079347  0.079847  0.080370  0.080916  0.081483  
-13  0.084683  0.085184  0.079729  0.080312  0.080916  0.081540  0.082183  
-14  0.085167  0.085764  0.080137  0.080801  0.081483  0.082183  0.082900  
+1   0.068735  0.067769  0.062136  0.061149  0.060309  0.059601  0.059013  
+2   0.075760  0.075241  0.068318  0.067723  0.067213  0.066789  0.066449  
+3   0.077003  0.076628  0.069888  0.069408  0.068991  0.068642  0.068363  
+4   0.079405  0.079389  0.071921  0.071767  0.071632  0.071529  0.071467  
+5   0.081233  0.081533  0.073449  0.073583  0.073699  0.073816  0.073949  
+6   0.074237  0.074375  0.067622  0.067612  0.067599  0.067597  0.067620  
+7   0.075195  0.075594  0.068376  0.068608  0.068806  0.068992  0.069181  
+8   0.075959  0.076589  0.068965  0.069409  0.069796  0.070150  0.070491  
+9   0.076589  0.077425  0.069441  0.070074  0.070630  0.071136  0.071614  
+10  0.068965  0.069441  0.063052  0.063364  0.063631  0.063874  0.064110  
+11  0.069409  0.070074  0.063364  0.063851  0.064274  0.064658  0.065020  
+12  0.069796  0.070630  0.063631  0.064274  0.064838  0.065348  0.065826  
+13  0.070150  0.071136  0.063874  0.064658  0.065348  0.065974  0.066558  
+14  0.070491  0.071614  0.064110  0.065020  0.065826  0.066558  0.067240
    @@ -2149,9 +2254,9 @@ set of \(\lambda\) values.

    [ 2.03099776 -0.17917768  5.18029127]
 Training MSE for OLS
-0.009163470508352211
+0.009163470508352218
 Test MSE OLS
-0.008675369724976501
+0.008675369724975977
    _images/chapter2_249_1.png @@ -2428,7 +2533,7 @@ The following code example solves the simpler problem we discussed above, where 
    ---------------------------------------------------------------------------
 ModuleNotFoundError                       Traceback (most recent call last)
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42449/3530606977.py in <module>
+<ipython-input-12-d670a873ab0c> in <module>
 ----> 1 from cvxopt import matrix, spdiag, mul, div, sqrt, normal, setseed
       2 from cvxopt import blas, lapack, solvers, sparse, spmatrix
       3 import math
@@ -3049,54 +3154,42 @@ decreasing \(\lambda\) and shr
    - - - - -
    - -
    -
    -

    - - By Morten Hjorth-Jensen
    - - © Copyright 2021.
    -

    -
    -
    +

    + + By Morten Hjorth-Jensen
    + + © Copyright 2021.
    +

    +
    - + - \ No newline at end of file diff --git a/doc/LectureNotes/_build/html/chapter3.html b/doc/LectureNotes/_build/html/chapter3.html index 3a92ba03b..0b5490f37 100644 --- a/doc/LectureNotes/_build/html/chapter3.html +++ b/doc/LectureNotes/_build/html/chapter3.html @@ -7,8 +7,8 @@ 5. Resampling Methods — Applied Data Analysis and Machine Learning - - + + - + @@ -41,22 +41,24 @@ - - - - - + + + + - + + + + @@ -91,11 +93,11 @@ -

    +

    About the course @@ -117,7 +119,7 @@ -

    +

    Review of Statistics with Resampling Techniques and Linear Algebra @@ -134,7 +136,7 @@ -

    +

    From Regression to Support Vector Machines @@ -171,7 +173,7 @@ -

    +

    Decision Trees, Ensemble Methods and Boosting @@ -188,7 +190,7 @@ -

    +

    Dimensionality Reduction @@ -199,8 +201,13 @@ 11. Basic ideas of the Principal Component Analysis (PCA) +

  3. + + 12. Clustering and Unsupervised Learning + +
    4. -

    +

    Deep Learning Methods @@ -208,17 +215,27 @@

    @@ -267,7 +284,7 @@ data-placement="left">.ipynb + onclick="printPdf(this)" data-toggle="tooltip" data-placement="left">.pdf
    @@ -285,7 +302,7 @@
    -
    +
    Contents @@ -379,7 +396,104 @@
    - + +
    +

    Resampling Methods

    + +
    + +
    +
    +
    @@ -643,10 +757,10 @@ number \(i\) is left out. Usin
    -
    Runtime: 0.184895 sec
+
    Runtime: 0.0896981 sec
 Jackknife Statistics :
 original           bias      std. error
- 100.109        100.099        0.148768
+ 100.213        100.203        0.148564
    @@ -865,7 +979,7 @@ theorem.

    Bootstrap Statistics :
 original           bias      std. error
- 99.7134  15.0572        99.7151        0.151986
+ 99.8879  15.0782        99.8894        0.149213
    @@ -1001,10 +1115,10 @@ We use a more compact notation in terms of the expectation value

    -
    Error: 0.013121573975499602
-Bias^2: 0.012073649439965807
-Var: 0.0010479245355337968
-0.013121573975499602 >= 0.012073649439965807 + 0.0010479245355337968 = 0.013121573975499604
+
    Error: 0.013121574061370796
+Bias^2: 0.012073649472576395
+Var: 0.0010479245887943952
+0.013121574061370796 >= 0.012073649472576395 + 0.0010479245887943952 = 0.01312157406137079
 
    
 
    
 _images/chapter3_61_1.png
@@ -1063,86 +1177,83 @@ Var: 0.0010479245355337968
 
    Polynomial degree: 0
-Error: 0.3214960170351912
+Error: 0.32149601703519115
 Bias^2: 0.3123314713548606
 Var: 0.009164545680330616
-0.3214960170351912 >= 0.3123314713548606 + 0.009164545680330616 = 0.3214960170351912
+0.32149601703519115 >= 0.3123314713548606 + 0.009164545680330616 = 0.3214960170351912
 Polynomial degree: 1
-Error: 0.08426840630693411
-Bias^2: 0.07968918676726029
-Var: 0.004579219539673836
-0.08426840630693411 >= 0.07968918676726029 + 0.004579219539673836 = 0.08426840630693413
+Error: 0.08426840630693412
+Bias^2: 0.0796891867672603
+Var: 0.004579219539673834
+0.08426840630693412 >= 0.0796891867672603 + 0.004579219539673834 = 0.08426840630693413
 Polynomial degree: 2
-Error: 0.10398646080125035
+Error: 0.10398646080125037
 Bias^2: 0.10077114273548984
-Var: 0.003215318065760509
-0.10398646080125035 >= 0.10077114273548984 + 0.003215318065760509 = 0.10398646080125035
-
    -
    -
    Polynomial degree: 3
-Error: 0.06547790180152357
-Bias^2: 0.06208238634231953
-Var: 0.0033955154592040944
-0.06547790180152357 >= 0.06208238634231953 + 0.0033955154592040944 = 0.06547790180152363
+Var: 0.0032153180657605125
+0.10398646080125037 >= 0.10077114273548984 + 0.0032153180657605125 = 0.10398646080125036
+Polynomial degree: 3
+Error: 0.06547790180152352
+Bias^2: 0.06208238634231944
+Var: 0.003395515459204093
+0.06547790180152352 >= 0.06208238634231944 + 0.003395515459204093 = 0.06547790180152353
 Polynomial degree: 4
-Error: 0.06844519414009438
-Bias^2: 0.06453579006728315
-Var: 0.003909404072811231
-0.06844519414009438 >= 0.06453579006728315 + 0.003909404072811231 = 0.06844519414009438
+Error: 0.06844519414009442
+Bias^2: 0.06453579006728322
+Var: 0.003909404072811217
+0.06844519414009442 >= 0.06453579006728322 + 0.003909404072811217 = 0.06844519414009444
 Polynomial degree: 5
-Error: 0.05227921801205692
-Bias^2: 0.04818727730430296
-Var: 0.0040919407077539514
-0.05227921801205692 >= 0.04818727730430296 + 0.0040919407077539514 = 0.05227921801205691
+Error: 0.052279218012057004
+Bias^2: 0.048187277304303056
+Var: 0.004091940707753948
+0.052279218012057004 >= 0.048187277304303056 + 0.004091940707753948 = 0.052279218012057004
 
    Polynomial degree: 6
-Error: 0.03781367141738885
-Bias^2: 0.033657685071527485
-Var: 0.004155986345861374
-0.03781367141738885 >= 0.033657685071527485 + 0.004155986345861374 = 0.03781367141738886
+Error: 0.037813671417388985
+Bias^2: 0.033657685071527624
+Var: 0.004155986345861364
+0.037813671417388985 >= 0.033657685071527624 + 0.004155986345861364 = 0.03781367141738899
 Polynomial degree: 7
-Error: 0.027609773491022314
-Bias^2: 0.02299949826036602
-Var: 0.004610275230656294
-0.027609773491022314 >= 0.02299949826036602 + 0.004610275230656294 = 0.027609773491022314
+Error: 0.027609773491022407
+Bias^2: 0.0229994982603662
+Var: 0.004610275230656187
+0.027609773491022407 >= 0.0229994982603662 + 0.004610275230656187 = 0.027609773491022387
 Polynomial degree: 8
-Error: 0.017355848195591845
-Bias^2: 0.01033172130665515
-Var: 0.007024126888936694
-0.017355848195591845 >= 0.01033172130665515 + 0.007024126888936694 = 0.01735584819559184
+Error: 0.017355848195593354
+Bias^2: 0.010331721306655144
+Var: 0.0070241268889382116
+0.017355848195593354 >= 0.010331721306655144 + 0.0070241268889382116 = 0.017355848195593354
+Polynomial degree:
    -
    Polynomial degree: 9
-Error: 0.026605727637176654
-Bias^2: 0.010018312644139347
-Var: 0.016587414993037307
-0.026605727637176654 >= 0.010018312644139347 + 0.016587414993037307 = 0.026605727637176654
+
     9
+Error: 0.026605727637184613
+Bias^2: 0.010018312644139205
+Var: 0.016587414993045405
+0.026605727637184613 >= 0.010018312644139205 + 0.016587414993045405 = 0.02660572763718461
 Polynomial degree: 10
-Error: 0.02159270458799264
-Bias^2: 0.010516485576652856
-Var: 0.011076219011339788
-0.02159270458799264 >= 0.010516485576652856 + 0.011076219011339788 = 0.021592704587992645
+Error: 0.021592704588021167
+Bias^2: 0.010516485576646513
+Var: 0.01107621901137465
+0.021592704588021167 >= 0.010516485576646513 + 0.01107621901137465 = 0.021592704588021164
 Polynomial degree: 11
-Error: 0.07160048164248561
-Bias^2: 0.014436800088969727
-Var: 0.05716368155351588
-0.07160048164248561 >= 0.014436800088969727 + 0.05716368155351588 = 0.07160048164248561
-
    
-
    
-
    Polynomial degree: 12
-Error: 0.11547777218940905
-Bias^2: 0.016285782696075054
-Var: 0.099191989493334
-0.11547777218940905 >= 0.016285782696075054 + 0.099191989493334 = 0.11547777218940906
+Error: 0.07160048164232467
+Bias^2: 0.014436800088896274
+Var: 0.057163681553428394
+0.07160048164232467 >= 0.014436800088896274 + 0.057163681553428394 = 0.07160048164232467
+Polynomial degree: 12
+Error: 0.11547777218875695
+Bias^2: 0.016285782696017055
+Var: 0.0991919894927399
+0.11547777218875695 >= 0.016285782696017055 + 0.0991919894927399 = 0.11547777218875696
 Polynomial degree: 13
-Error: 0.22842468702288576
-Bias^2: 0.01975416527179247
-Var: 0.20867052175109335
-0.22842468702288576 >= 0.01975416527179247 + 0.20867052175109335 = 0.22842468702288582
+Error: 0.2284246870217459
+Bias^2: 0.019754165271682844
+Var: 0.20867052175006306
+0.2284246870217459 >= 0.019754165271682844 + 0.20867052175006306 = 0.2284246870217459
 
    
 
    
-_images/chapter3_62_5.png
+_images/chapter3_62_3.png

    The bias-variance tradeoff summarizes the fundamental tension in @@ -1360,17 +1471,13 @@ Mean squared error on test data: 481979.17861098 Degree of polynomial: 2 Mean squared error on training data: 115822.95008046 Mean squared error on test data: 123711.53703498 -

    -
    -
    Degree of polynomial:   3
+Degree of polynomial:   3
 Mean squared error on training data: 9011.85263220
 Mean squared error on test data: 10913.84780262
 Degree of polynomial:   4
 Mean squared error on training data: 303.47610036
 Mean squared error on test data: 426.30787294
-
    -
    -
    Degree of polynomial:   5
+Degree of polynomial:   5
 Mean squared error on training data: 3.80354994
 Mean squared error on test data: 5.98822371
 Degree of polynomial:   6
@@ -1384,19 +1491,15 @@ Mean squared error on test data: 2.00607783
 Degree of polynomial:   8
 Mean squared error on training data: 0.04912436
 Mean squared error on test data: 0.21596432
-
    -
    -
    Degree of polynomial:   9
+Degree of polynomial:   9
 Mean squared error on training data: 0.02522069
 Mean squared error on test data: 0.08576932
 Degree of polynomial:  10
 Mean squared error on training data: 0.02511518
 Mean squared error on test data: 1.20015436
-
    -
    -
    Degree of polynomial:  11
+Degree of polynomial:  11
 Mean squared error on training data: 0.01640891
-Mean squared error on test data: 1.35533774
+Mean squared error on test data: 1.35533773
 Degree of polynomial:  12
 Mean squared error on training data: 0.00813803
 Mean squared error on test data: 0.17446471
@@ -1407,77 +1510,65 @@ Mean squared error on training data: 0.00759119
 Mean squared error on test data: 1.08131003
 Degree of polynomial:  14
 Mean squared error on training data: 0.00472199
-Mean squared error on test data: 0.81333805
-
    -
    -
    Degree of polynomial:  15
+Mean squared error on test data: 0.81333804
+Degree of polynomial:  15
 Mean squared error on training data: 0.00410478
-Mean squared error on test data: 92.09149881
+Mean squared error on test data: 92.09172408
 Degree of polynomial:  16
 Mean squared error on training data: 0.00315593
-Mean squared error on test data: 234.39095416
-
    -
    -
    Degree of polynomial:  17
+Mean squared error on test data: 234.38533184
+Degree of polynomial:  17
 Mean squared error on training data: 0.00242999
-Mean squared error on test data: 1270.94548496
+Mean squared error on test data: 1271.35771842
 Degree of polynomial:  18
 Mean squared error on training data: 0.00228741
-Mean squared error on test data: 108.28590743
+Mean squared error on test data: 108.27092897
 
    Degree of polynomial:  19
-Mean squared error on training data: 0.00156379
-Mean squared error on test data: 1378.43761347
+Mean squared error on training data: 0.00156382
+Mean squared error on test data: 1371.99049330
 Degree of polynomial:  20
-Mean squared error on training data: 0.00137835
-Mean squared error on test data: 1954.37992857
-
    -
    -
    Degree of polynomial:  21
-Mean squared error on training data: 0.00118527
-Mean squared error on test data: 14818.20320502
+Mean squared error on training data: 0.00137823
+Mean squared error on test data: 1887.85953586
+Degree of polynomial:  21
+Mean squared error on training data: 0.00118504
+Mean squared error on test data: 14859.70127680
 Degree of polynomial:  22
-Mean squared error on training data: 0.00092646
-Mean squared error on test data: 871.17339342
-
    -
    -
    Degree of polynomial:  23
-Mean squared error on training data: 0.00085884
-Mean squared error on test data: 5566.16660817
+Mean squared error on training data: 0.00092645
+Mean squared error on test data: 876.51214899
+Degree of polynomial:  23
+Mean squared error on training data: 0.00085883
+Mean squared error on test data: 5594.60685864
 Degree of polynomial:  24
-Mean squared error on training data: 0.00084705
-Mean squared error on test data: 1314.42631342
+Mean squared error on training data: 0.00084711
+Mean squared error on test data: 1277.60619654
 
    Degree of polynomial:  25
-Mean squared error on training data: 0.00079123
-Mean squared error on test data: 127043.53189647
+Mean squared error on training data: 0.00079130
+Mean squared error on test data: 128664.09744272
 Degree of polynomial:  26
-Mean squared error on training data: 0.00076925
-Mean squared error on test data: 18526.05756733
-
    -
    -
    Degree of polynomial:  27
-Mean squared error on training data: 0.00069103
-Mean squared error on test data: 2470.53697476
+Mean squared error on training data: 0.00076919
+Mean squared error on test data: 19003.95079764
+Degree of polynomial:  27
+Mean squared error on training data: 0.00068941
+Mean squared error on test data: 2379.66226149
 Degree of polynomial:  28
-Mean squared error on training data: 0.00062595
-Mean squared error on test data: 4022.12945452
+Mean squared error on training data: 0.00062582
+Mean squared error on test data: 4082.19994371
+Degree of polynomial:  29
+Mean squared error on training data: 0.00060708
+Mean squared error on test data: 3250.24770094
    -
    Degree of polynomial:  29
-Mean squared error on training data: 0.00060705
-Mean squared error on test data: 3384.63675140
-
    -
    -
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42456/626635268.py:73: RuntimeWarning: divide by zero encountered in log10
+
    <ipython-input-7-40a38ad763f1>:73: RuntimeWarning: divide by zero encountered in log10
   plt.plot(polynomial, np.log10(trainingerror), label='Training Error')
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42456/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
+<ipython-input-7-40a38ad763f1>:74: RuntimeWarning: divide by zero encountered in log10
   plt.plot(polynomial, np.log10(testerror), label='Test Error')
 
    
 
    
-_images/chapter3_65_16.png
+_images/chapter3_65_6.png
    @@ -1707,7 +1798,7 @@ cross-validation (LOOCV).

    -
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42456/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10
+
    <ipython-input-9-6e75736fdab1>:63: RuntimeWarning: divide by zero encountered in log10
   plt.plot(polynomial, np.log10(estimated_mse_sklearn), label='Test Error')
 
    
 
    
@@ -1971,17 +2062,17 @@ Note also that we do not split the data into training and test.
    
 Fitted beta: [2.08376632 0.19569961 3.97898392]
 Sklearn fitted beta: [2.08376632 0.19569961 3.97898392]
 MSE with intercept column
-0.0041136346174431284
+0.00411363461744314
 MSE with intercept column from SKL
-0.004113634617443141
-Manual intercept: 2.0837663229239016
+0.004113634617443116
+Manual intercept: 2.083766322923899
 Fitted beta (wiothout intercept): [0.19569961 3.97898392]
-Sklearn intercept: 2.0837663229239025
+Sklearn intercept: 2.0837663229239043
 Sklearn fitted beta (without intercept): [0.19569961 3.97898392]
 MSE with Manual intercept
 0.00411363461744314
 MSE with Sklearn intercept
-0.004113634617443135
+0.004113634617443131
    _images/chapter3_107_1.png @@ -2092,19 +2183,19 @@ intercept.

    Beta values for own Ridge implementation
 [ 1.03032441e+00  6.28336218e-02 -6.24175744e-01  5.21169159e-02
   2.80847477e-01  2.12552073e-01  8.13220608e-02 -1.69634577e-02
- -6.50846112e-02 -7.38962192e-02 -5.94226022e-02 -3.50227564e-02
- -9.80609615e-03  1.08299273e-02  2.41882037e-02  2.93492130e-02
-  2.64742912e-02  1.63249532e-02 -5.01831130e-05 -2.15098090e-02]
+ -6.50846111e-02 -7.38962192e-02 -5.94226022e-02 -3.50227564e-02
+ -9.80609616e-03  1.08299273e-02  2.41882036e-02  2.93492130e-02
+  2.64742912e-02  1.63249532e-02 -5.01831036e-05 -2.15098090e-02]
 Beta values for Scikit-Learn Ridge implementation
 [ 1.03032441e+00  6.28336218e-02 -6.24175744e-01  5.21169159e-02
   2.80847477e-01  2.12552073e-01  8.13220608e-02 -1.69634577e-02
  -6.50846112e-02 -7.38962192e-02 -5.94226022e-02 -3.50227564e-02
  -9.80609615e-03  1.08299273e-02  2.41882037e-02  2.93492130e-02
-  2.64742912e-02  1.63249532e-02 -5.01831200e-05 -2.15098090e-02]
+  2.64742912e-02  1.63249532e-02 -5.01831207e-05 -2.15098090e-02]
 MSE values for own Ridge implementation
-4.3632959170548605e-07
+4.363295924430451e-07
 MSE values for Scikit-Learn Ridge implementation
-4.363295916414895e-07
+4.363295916323784e-07
 Beta values for own Ridge implementation
 [ 1.03630548 -0.01963611 -0.37900111 -0.07062318  0.12182967  0.16343471
   0.13003291  0.07490892  0.02365049 -0.01449782 -0.03814292 -0.04909093
@@ -2116,9 +2207,9 @@ Beta values for Scikit-Learn Ridge implementation
  -0.05009826 -0.04389027 -0.03279636 -0.01866537 -0.00289724  0.01348565
   0.02976145  0.04543942]
 MSE values for own Ridge implementation
-5.194042826653172e-06
+5.19404282648955e-06
 MSE values for Scikit-Learn Ridge implementation
-5.194042826815498e-06
+5.1940428268204826e-06
 Beta values for own Ridge implementation
 [ 1.04220758 -0.10931453 -0.17641709 -0.06020587  0.02208512  0.05789007
   0.06491736  0.05785343  0.04537385  0.03196357  0.01969145  0.00934499
@@ -2130,9 +2221,9 @@ Beta values for Scikit-Learn Ridge implementation
   0.00107405 -0.00526348 -0.00992331 -0.01318643 -0.01531845 -0.01655318
  -0.01708852 -0.01708781]
 MSE values for own Ridge implementation
-2.0940821989673748e-05
+2.094082198966615e-05
 MSE values for Scikit-Learn Ridge implementation
-2.0940821989624095e-05
+2.094082198961999e-05
 Beta values for own Ridge implementation
 [ 1.01219292 -0.06043581 -0.10391807 -0.05651951 -0.01898855  0.00312361
   0.01463049  0.01975848  0.02123176  0.02068067  0.01905883  0.01691985
@@ -2144,9 +2235,9 @@ Beta values for Scikit-Learn Ridge implementation
   0.01458337  0.01223198  0.00996754  0.00784393  0.00588657  0.00410387
   0.00249435  0.00105081]
 MSE values for own Ridge implementation
-0.0003153514830958126
+0.0003153514830958235
 MSE values for Scikit-Learn Ridge implementation
-0.0003153514830958081
+0.00031535148309580783
 Beta values for own Ridge implementation
 [ 8.38916861e-01  1.31276579e-01  8.97497404e-03 -1.72271878e-02
  -2.11744554e-02 -1.91492986e-02 -1.57201944e-02 -1.23002365e-02
@@ -2160,9 +2251,9 @@ Beta values for Scikit-Learn Ridge implementation
  -1.84923989e-03 -8.13661243e-04  7.46984697e-06  6.56636616e-04
   1.16805821e-03  1.56912044e-03  1.88168312e-03  2.12318726e-03]
 MSE values for own Ridge implementation
-0.015072388895177109
+0.015072388895177239
 MSE values for Scikit-Learn Ridge implementation
-0.015072388895177088
+0.0150723888951771
 Beta values for own Ridge implementation
 [0.37396662 0.14174745 0.0764924  0.04892055 0.03447512 0.02586427
  0.02024962 0.01633913 0.01347916 0.0113104  0.0096208  0.00827728
@@ -2174,9 +2265,9 @@ Beta values for Scikit-Learn Ridge implementation
  0.00719176 0.00630331 0.00556826 0.0049544  0.00443743 0.0039987
  0.0036237  0.003301  ]
 MSE values for own Ridge implementation
-0.2640931530791005
+0.26409315307910053
 MSE values for Scikit-Learn Ridge implementation
-0.2640931530791003
+0.26409315307910025
    _images/chapter3_115_1.png @@ -2272,7 +2363,7 @@ Let us see how we can change this code by zero centering.

    Beta values for own Ridge implementation
 [ 3.43579948e-02 -5.43330971e-01 -3.10141413e-03  2.47116868e-01
-  2.18613217e-01  1.02054837e-01 -4.25617657e-04 -5.90475506e-02
+  2.18613217e-01  1.02054837e-01 -4.25617658e-04 -5.90475506e-02
  -7.68534263e-02 -6.68929213e-02 -4.24906604e-02 -1.40927184e-02
   1.11482289e-02  2.88529063e-02  3.67047975e-02  3.38135733e-02
   2.02198702e-02 -3.46383925e-03 -3.63025821e-02]
@@ -2283,13 +2374,13 @@ Beta values for Scikit-Learn Ridge implementation
   1.11482289e-02  2.88529063e-02  3.67047975e-02  3.38135733e-02
   2.02198702e-02 -3.46383925e-03 -3.63025821e-02]
 Intercept from own implementation:
-1.0330308045180234
+1.0330308045190182
 Intercept from Scikit-Learn Ridge implementation
-1.0330308045183163
+1.0330308045183219
 MSE values for own Ridge implementation
-3.1392559581788775e-06
+3.13925595925919e-06
 MSE values for Scikit-Learn Ridge implementation
-3.1392559584983597e-06
+3.1392559585048734e-06
 Beta values for own Ridge implementation
 [-0.05807125 -0.29822833 -0.08551306  0.08156108  0.13679863  0.12333649
   0.08251519  0.03815288  0.00111756 -0.02498832 -0.04010697 -0.04566964
@@ -2301,13 +2392,13 @@ Beta values for Scikit-Learn Ridge implementation
  -0.04355837 -0.03562355 -0.02348765 -0.00848904  0.00831018  0.0260906
   0.04423486]
 Intercept from own implementation:
-1.0411487294305746
+1.041148729430502
 Intercept from Scikit-Learn Ridge implementation
-1.0411487294305246
+1.041148729430523
 MSE values for own Ridge implementation
-1.9601304850213484e-05
+1.9601304850018328e-05
 MSE values for Scikit-Learn Ridge implementation
-1.960130485007934e-05
+1.960130485007504e-05
 Beta values for own Ridge implementation
 [-0.1416398  -0.14021063 -0.05383795  0.01367553  0.04784395  0.05796251
   0.05447415  0.044613    0.03267527  0.02098261  0.01066519  0.00217499
@@ -2319,13 +2410,13 @@ Beta values for Scikit-Learn Ridge implementation
  -0.00440346 -0.00917248 -0.01231917 -0.01405935 -0.0146081  -0.01416528
  -0.01290947]
 Intercept from own implementation:
-1.0495569966278315
+1.0495569966278238
 Intercept from Scikit-Learn Ridge implementation
 1.0495569966278269
 MSE values for own Ridge implementation
-5.495916150938325e-05
+5.4959161509356135e-05
 MSE values for Scikit-Learn Ridge implementation
-5.495916150936654e-05
+5.495916150936645e-05
 Beta values for own Ridge implementation
 [-0.13535942 -0.08593216 -0.03568439 -0.0036367   0.01397146  0.02229529
   0.02503753  0.0245528   0.02228115  0.01908936  0.01549377  0.01179792
@@ -2341,9 +2432,9 @@ Intercept from own implementation:
 Intercept from Scikit-Learn Ridge implementation
 1.0399676689527975
 MSE values for own Ridge implementation
-7.571105947979439e-05
+7.571105947979336e-05
 MSE values for Scikit-Learn Ridge implementation
-7.571105947979395e-05
+7.571105947979394e-05
 Beta values for own Ridge implementation
 [-0.05100875 -0.04063602 -0.02723445 -0.01713366 -0.0100706  -0.00517114
  -0.00174276  0.00068734  0.00243186  0.00369758  0.00462287  0.0053018
@@ -2359,9 +2450,9 @@ Intercept from own implementation:
 Intercept from Scikit-Learn Ridge implementation
 0.999955585168597
 MSE values for own Ridge implementation
-0.0007698473260556339
+0.0007698473260556344
 MSE values for Scikit-Learn Ridge implementation
-0.0007698473260556334
+0.0007698473260556325
 Beta values for own Ridge implementation
 [-0.00834567 -0.00803064 -0.00673407 -0.00554552 -0.00458878 -0.0038335
  -0.00323332 -0.00274989 -0.0023548  -0.00202756 -0.00175331 -0.00152117
@@ -2379,7 +2470,7 @@ Intercept from Scikit-Learn Ridge implementation
 MSE values for own Ridge implementation
 0.0023813163025848865
 MSE values for Scikit-Learn Ridge implementation
-0.002381316302584885
+0.002381316302584886
    _images/chapter3_117_1.png @@ -2596,7 +2687,9 @@ linear system as an equation would reduce this down to
    -
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42456/4162706317.py:7: UserWarning: FixedFormatter should only be used together with FixedLocator
+
    <ipython-input-20-6f7a6bd7d79f>:6: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
+  cb = fig.colorbar(im)
+<ipython-input-20-6f7a6bd7d79f>:7: UserWarning: FixedFormatter should only be used together with FixedLocator
   cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)
 
    
 
    
@@ -2740,7 +2833,9 @@ with the form utilized in linear regression, viz.
    -
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42456/3777801602.py:7: UserWarning: FixedFormatter should only be used together with FixedLocator
+
    <ipython-input-25-5dd54edf2138>:6: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
+  cb = fig.colorbar(im)
+<ipython-input-25-5dd54edf2138>:7: UserWarning: FixedFormatter should only be used together with FixedLocator
   cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)
 
    
 
    
@@ -2788,7 +2883,9 @@ K
    -
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42456/438060758.py:10: UserWarning: FixedFormatter should only be used together with FixedLocator
+
    <ipython-input-26-fe5b9d300cc0>:9: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
+  cb = fig.colorbar(im)
+<ipython-input-26-fe5b9d300cc0>:10: UserWarning: FixedFormatter should only be used together with FixedLocator
   cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)
 
    
 
    
@@ -2823,7 +2920,9 @@ K
    -
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42456/3544313922.py:9: UserWarning: FixedFormatter should only be used together with FixedLocator
+
    <ipython-input-27-25845e8df859>:8: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
+  cb = fig.colorbar(im)
+<ipython-input-27-25845e8df859>:9: UserWarning: FixedFormatter should only be used together with FixedLocator
   cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)
 
    
 
    
@@ -2876,43 +2975,43 @@ constant as opposed to ridge and OLS. We get a sparse solution with
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    /Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/linear_model/_coordinate_descent.py:645: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations, check the scale of the features or consider increasing regularisation. Duality gap: 3.924e+00, tolerance: 1.797e+00
+
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_coordinate_descent.py:647: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations, check the scale of the features or consider increasing regularisation. Duality gap: 3.924e+00, tolerance: 1.797e+00
   model = cd_fast.enet_coordinate_descent(
 
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     50%|███████████████████████████████████████████████████████████████████                                                                   | 5/10 [00:01<00:00,  5.36it/s]
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     60%|████████████████████████████████████████████████████████████████████████████████▍                                                     | 6/10 [00:01<00:00,  6.04it/s]
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     70%|█████████████████████████████████████████████████████████████████████████████████████████████▊                                        | 7/10 [00:01<00:00,  5.69it/s]
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     80%|███████████████████████████████████████████████████████████████████████████████████████████████████████████▏                          | 8/10 [00:01<00:00,  6.18it/s]
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    100%|█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 10/10 [00:01<00:00,  6.75it/s]
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    100%|█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 10/10 [00:01<00:00,  5.15it/s]
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@@ -3059,8 +3158,10 @@ which polynomial fits the data best.
    
 
    
 
    
 
    
-
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42456/3980313467.py:9: 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().
+
    <ipython-input-30-bc298b802fe2>:9: 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')
+<ipython-input-30-bc298b802fe2>:37: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
+  fig.colorbar(surf, shrink=0.5, aspect=5)
 
    
 
    
 _images/chapter3_181_1.png
@@ -3220,7 +3321,7 @@ Python program using
    
 
    
 
    ---------------------------------------------------------------------------
 NameError                                 Traceback (most recent call last)
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42456/1950915150.py in <module>
+<ipython-input-31-d985fb40c43d> in <module>
 ----> 1 scipy.misc.imread
 
 NameError: name 'scipy' is not defined
@@ -3292,54 +3393,42 @@ of data presented here (either the terrain data we propose or other data sets).<
 
               
    
               
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-        
-          By Morten Hjorth-Jensen
    
-        
-            © Copyright 2021.
    
-      
    
-    
    
-  
    
+  
    
+    
+      By Morten Hjorth-Jensen
    
+    
+        © Copyright 2021.
    
+  
    
+
 
 
 
       
    
     
    
   
-  
+  
 
-  
   
 
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diff --git a/doc/LectureNotes/_build/html/chapter4.html b/doc/LectureNotes/_build/html/chapter4.html
index c7c40cc38..22300f549 100644
--- a/doc/LectureNotes/_build/html/chapter4.html
+++ b/doc/LectureNotes/_build/html/chapter4.html
@@ -7,8 +7,8 @@
     
     6. Logistic Regression — Applied Data Analysis and Machine Learning
     
-  
-  
+  
+  
 
     
   
     
     
-  
+  
 
     
     
@@ -41,22 +41,24 @@
     
     
     
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-    
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+    
+    
     
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+    
     
     
     
     
     
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+    
+    
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@@ -91,11 +93,11 @@
         
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+
    
  
   About the course
  
@@ -117,7 +119,7 @@
   
  
 
-
    
+
    
  
   Review of Statistics with Resampling Techniques and Linear Algebra
  
@@ -134,7 +136,7 @@
   
  
 
-
    
+
    
  
   From Regression to Support Vector Machines
  
@@ -171,7 +173,7 @@
   
  
 
-
    
+
    
  
   Decision Trees, Ensemble Methods and Boosting
  
@@ -188,7 +190,7 @@
   
  
 
-
    
+
    
  
   Dimensionality Reduction
  
@@ -199,8 +201,13 @@
    11. Basic ideas of the Principal Component Analysis (PCA)
   
  
+ 
  4. 
+  
+   12. Clustering and Unsupervised Learning
+  
+ 
    5. 
 
-
    
+
    
  
   Deep Learning Methods
  
@@ -208,17 +215,27 @@
 
    
@@ -267,7 +284,7 @@
                 data-placement="left">.ipynb
         
         
+                onclick="printPdf(this)" data-toggle="tooltip" data-placement="left">.pdf
     
    
 
    
 
@@ -285,7 +302,7 @@
         
    
 
         
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+        
    
             
             
    
                  Contents
@@ -325,7 +342,50 @@
 
    
     
    
         
    
-        
+            
+            
    
+                
    Logistic Regression
    
+                
+                
    
+                    
+                
    
+            
    
+            
               
    
                 
   
    
@@ -875,11 +935,11 @@ classification.
    
 
    
 
    (426, 30)
 (143, 30)
-Test set accuracy with Logistic Regression: 0.95
+Test set accuracy with Logistic Regression: 0.94
 Test set accuracy Logistic Regression with scaled data: 0.96
 
    
 
    
-
    /Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):
+
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):
 STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.
 
 Increase the number of iterations (max_iter) or scale the data as shown in:
@@ -1019,14 +1079,14 @@ applications. This will be discussed later this semester (
 
    (426, 30)
 (143, 30)
-Test set accuracy with Logistic Regression: 0.95
+Test set accuracy with Logistic Regression: 0.94
 Test set accuracy Logistic Regression with scaled data: 0.96
 [1.         1.         1.         1.         1.         1.
  1.         1.         0.92857143 0.92857143]
 Test set accuracy with Logistic Regression  and scaled data: 0.96
 
    
 
    
-
    /Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):
+
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):
 STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.
 
 Increase the number of iterations (max_iter) or scale the data as shown in:
@@ -1036,9 +1096,18 @@ Please also refer to the documentation for alternative solver options:
   n_iter_i = _check_optimize_result(
 
    
 
    
-_images/chapter4_57_2.png
-_images/chapter4_57_3.png
-_images/chapter4_57_4.png
+
    ---------------------------------------------------------------------------
+ModuleNotFoundError                       Traceback (most recent call last)
+<ipython-input-8-12adb44b1c20> in <module>
+     34 
+     35 
+---> 36 import scikitplot as skplt
+     37 y_pred = logreg.predict(X_test_scaled)
+     38 skplt.metrics.plot_confusion_matrix(y_test, y_pred, normalize=True)
+
+ModuleNotFoundError: No module named 'scikitplot'
+
    
+
    
 
    
 
    
 
    
@@ -1066,54 +1135,42 @@ Please also refer to the documentation for alternative solver options:
 
               
    
               
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-    
    
-      
    
-        
-          By Morten Hjorth-Jensen
    
-        
-            © Copyright 2021.
    
-      
    
-    
    
-  
    
+  
    
+    
+      By Morten Hjorth-Jensen
    
+    
+        © Copyright 2021.
    
+  
    
+
 
 
 
       
    
     
    
   
-  
+  
 
-  
   
 
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diff --git a/doc/LectureNotes/_build/html/chapter5.html b/doc/LectureNotes/_build/html/chapter5.html
index 391860a81..8717ab250 100644
--- a/doc/LectureNotes/_build/html/chapter5.html
+++ b/doc/LectureNotes/_build/html/chapter5.html
@@ -7,8 +7,8 @@
     
     8. Support Vector Machines, overarching aims — Applied Data Analysis and Machine Learning
     
-  
-  
+  
+  
 
     
   
     
     
-  
+  
 
     
     
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-    
-    
-    
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+    
+    
     
     
     
     
     
-    
+    
+    
+
+    
     
   
   
@@ -91,11 +93,11 @@
         
-
    
+
    
  
   About the course
  
@@ -117,7 +119,7 @@
   
  
 
-
    
+
    
  
   Review of Statistics with Resampling Techniques and Linear Algebra
  
@@ -134,7 +136,7 @@
   
  
 
-
    
+
    
  
   From Regression to Support Vector Machines
  
@@ -171,7 +173,7 @@
   
  
 
-
    
+
    
  
   Decision Trees, Ensemble Methods and Boosting
  
@@ -188,7 +190,7 @@
   
  
 
-
    
+
    
  
   Dimensionality Reduction
  
@@ -199,8 +201,13 @@
    11. Basic ideas of the Principal Component Analysis (PCA)
   
  
+ 
  5. 
+  
+   12. Clustering and Unsupervised Learning
+  
+ 
    6. 
 
-
    
+
    
  
   Deep Learning Methods
  
@@ -208,17 +215,27 @@
 
    
@@ -267,7 +284,7 @@
                 data-placement="left">.ipynb
         
         
+                onclick="printPdf(this)" data-toggle="tooltip" data-placement="left">.pdf
     
    
 
    
 
@@ -285,7 +302,7 @@
         
    
 
         
-        
    
+        
    
             
             
    
                  Contents
@@ -347,7 +364,72 @@
 
    
     
    
         
    
-        
+            
+            
    
+                
    Support Vector Machines, overarching aims
    
+                
+                
    
+                    
+                
    
+            
    
+            
               
    
                 
   
    
@@ -1214,7 +1296,7 @@ in practice.
    
 
    
 
    
 _images/chapter5_129_0.png
-
    /Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/svm/_base.py:1199: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.
+
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/svm/_base.py:1206: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.
   warnings.warn(
 
    
 
    
@@ -1263,7 +1345,7 @@ converge. So, welcome to the promised land of quadratic programming.
    
 
    
 
    ---------------------------------------------------------------------------
 ModuleNotFoundError                       Traceback (most recent call last)
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42530/4034668048.py in <module>
+<ipython-input-4-703716d317a7> in <module>
       1 import numpy
 ----> 2 import cvxopt
 
@@ -1374,54 +1456,42 @@ With  the slack constants this leads to the additional constraint 
-        
-            
-            
    
-                
    previous
    
-                
    7. Optimization, the central part of any Machine Learning algortithm
    
-            
    
-            
+                
+
     
+    
+        
+        
    
+            
    previous
    
+            
    7. Optimization, the central part of any Machine Learning algortithm
    
+        
    
+        
+    
+    
    
+        
    next
    
+        
    9. Decision trees, overarching aims
    
     
    
-         
-
+    
+    
 
    
-        
+            
         
    
     
    
     
    
-    
    
-      
    
-        
-          By Morten Hjorth-Jensen
    
-        
-            © Copyright 2021.
    
-      
    
-    
    
-  
    
+  
    
+    
+      By Morten Hjorth-Jensen
    
+    
+        © Copyright 2021.
    
+  
    
+
 
 
 
       
    
     
    
   
-  
+  
 
-  
   
 
\ No newline at end of file
diff --git a/doc/LectureNotes/_build/html/chapter6.html b/doc/LectureNotes/_build/html/chapter6.html
index 102f13ddb..83296791e 100644
--- a/doc/LectureNotes/_build/html/chapter6.html
+++ b/doc/LectureNotes/_build/html/chapter6.html
@@ -7,8 +7,8 @@
     
     9. Decision trees, overarching aims — Applied Data Analysis and Machine Learning
     
-  
-  
+  
+  
 
     
   
     
     
-  
+  
 
     
     
@@ -41,22 +41,24 @@
     
     
     
-    
-    
-    
-    
-    
+    
+    
     
+    
+    
     
     
     
     
     
-    
+    
+    
+
+    
     
   
   
@@ -91,11 +93,11 @@
         
-
    
+
    
  
   About the course
  
@@ -117,7 +119,7 @@
   
  
 
-
    
+
    
  
   Review of Statistics with Resampling Techniques and Linear Algebra
  
@@ -134,7 +136,7 @@
   
  
 
-
    
+
    
  
   From Regression to Support Vector Machines
  
@@ -171,7 +173,7 @@
   
  
 
-
    
+
    
  
   Decision Trees, Ensemble Methods and Boosting
  
@@ -188,7 +190,7 @@
   
  
 
-
    
+
    
  
   Dimensionality Reduction
  
@@ -199,8 +201,13 @@
    11. Basic ideas of the Principal Component Analysis (PCA)
   
  
+ 
  6. 
+  
+   12. Clustering and Unsupervised Learning
+  
+ 
    7. 
 
-
    
+
    
  
   Deep Learning Methods
  
@@ -208,17 +215,27 @@
 
    
@@ -267,7 +284,7 @@
                 data-placement="left">.ipynb
         
         
+                onclick="printPdf(this)" data-toggle="tooltip" data-placement="left">.pdf
     
    
 
    
 
@@ -285,7 +302,7 @@
         
    
 
         
-        
    
+        
    
             
             
    
                  Contents
@@ -400,7 +417,125 @@
 
    
     
    
         
    
-        
+            
+            
    
+                
    Decision trees, overarching aims
    
+                
+                
    
+                    
+                
    
+            
    
+            
               
    
                 
   
    
@@ -550,9 +685,9 @@ predicting the target features of query instances is as follows:
    
 
    
 
    
 
    2nd degree coefficients:
-zero power:  -5.456418966187335
-first power:  0.07099747918547346
-second power:  -0.00028369228101198006
+zero power:  3.975510299261579
+first power:  -0.12345260617257443
+second power:  -0.0003043256065368937
 
    
 
    
 _images/chapter6_1_1.png
@@ -785,105 +920,16 @@ s = -\sum_{k=1}^K p_{mk}\log{p_{mk}}.
 
    
 
    
 
    
-
         mean radius  mean texture  mean perimeter  mean area  mean smoothness  \
-0          17.99         10.38          122.80     1001.0          0.11840   
-1          20.57         17.77          132.90     1326.0          0.08474   
-2          19.69         21.25          130.00     1203.0          0.10960   
-3          11.42         20.38           77.58      386.1          0.14250   
-4          20.29         14.34          135.10     1297.0          0.10030   
-..           ...           ...             ...        ...              ...   
-564        21.56         22.39          142.00     1479.0          0.11100   
-565        20.13         28.25          131.20     1261.0          0.09780   
-566        16.60         28.08          108.30      858.1          0.08455   
-567        20.60         29.33          140.10     1265.0          0.11780   
-568         7.76         24.54           47.92      181.0          0.05263   
+
    ---------------------------------------------------------------------------
+ModuleNotFoundError                       Traceback (most recent call last)
+<ipython-input-2-7c394b1e8b71> in <module>
+      7 
+      8 from IPython.display import Image
+----> 9 from pydot import graph_from_dot_data
+     10 import pandas as pd
+     11 import numpy as np
 
-     mean compactness  mean concavity  mean concave points  mean symmetry  \
-0             0.27760         0.30010              0.14710         0.2419   
-1             0.07864         0.08690              0.07017         0.1812   
-2             0.15990         0.19740              0.12790         0.2069   
-3             0.28390         0.24140              0.10520         0.2597   
-4             0.13280         0.19800              0.10430         0.1809   
-..                ...             ...                  ...            ...   
-564           0.11590         0.24390              0.13890         0.1726   
-565           0.10340         0.14400              0.09791         0.1752   
-566           0.10230         0.09251              0.05302         0.1590   
-567           0.27700         0.35140              0.15200         0.2397   
-568           0.04362         0.00000              0.00000         0.1587   
-
-     mean fractal dimension  ...  worst radius  worst texture  \
-0                   0.07871  ...        25.380          17.33   
-1                   0.05667  ...        24.990          23.41   
-2                   0.05999  ...        23.570          25.53   
-3                   0.09744  ...        14.910          26.50   
-4                   0.05883  ...        22.540          16.67   
-..                      ...  ...           ...            ...   
-564                 0.05623  ...        25.450          26.40   
-565                 0.05533  ...        23.690          38.25   
-566                 0.05648  ...        18.980          34.12   
-567                 0.07016  ...        25.740          39.42   
-568                 0.05884  ...         9.456          30.37   
-
-     worst perimeter  worst area  worst smoothness  worst compactness  \
-0             184.60      2019.0           0.16220            0.66560   
-1             158.80      1956.0           0.12380            0.18660   
-2             152.50      1709.0           0.14440            0.42450   
-3              98.87       567.7           0.20980            0.86630   
-4             152.20      1575.0           0.13740            0.20500   
-..               ...         ...               ...                ...   
-564           166.10      2027.0           0.14100            0.21130   
-565           155.00      1731.0           0.11660            0.19220   
-566           126.70      1124.0           0.11390            0.30940   
-567           184.60      1821.0           0.16500            0.86810   
-568            59.16       268.6           0.08996            0.06444   
-
-     worst concavity  worst concave points  worst symmetry  \
-0             0.7119                0.2654          0.4601   
-1             0.2416                0.1860          0.2750   
-2             0.4504                0.2430          0.3613   
-3             0.6869                0.2575          0.6638   
-4             0.4000                0.1625          0.2364   
-..               ...                   ...             ...   
-564           0.4107                0.2216          0.2060   
-565           0.3215                0.1628          0.2572   
-566           0.3403                0.1418          0.2218   
-567           0.9387                0.2650          0.4087   
-568           0.0000                0.0000          0.2871   
-
-     worst fractal dimension  
-0                    0.11890  
-1                    0.08902  
-2                    0.08758  
-3                    0.17300  
-4                    0.07678  
-..                       ...  
-564                  0.07115  
-565                  0.06637  
-566                  0.07820  
-567                  0.12400  
-568                  0.07039  
-
-[569 rows x 30 columns]
-     malignant  benign
-0            1       0
-1            1       0
-2            1       0
-3            1       0
-4            1       0
-..         ...     ...
-564          1       0
-565          1       0
-566          1       0
-567          1       0
-568          0       1
-
-[569 rows x 2 columns]
-
    
-
    
-
    sh: dot: command not found
-
    
-
    
-
    32512
+ModuleNotFoundError: No module named 'pydot'
 
    
 
    
 
    
@@ -917,14 +963,6 @@ s = -\sum_{k=1}^K p_{mk}\log{p_{mk}}.
 
    
 
    
 
    
-
    
-
    sh: dot: command not found
-
    
-
    
-
    32512
-
    
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@@ -942,28 +980,6 @@ s = -\sum_{k=1}^K p_{mk}\log{p_{mk}}.
 
    
 
    
 
    
-
    
-
    [Text(167.4, 199.32, 'X[2] <= 2.45\ngini = 0.667\nsamples = 150\nvalue = [50, 50, 50]'),
- Text(141.64615384615385, 163.07999999999998, 'gini = 0.0\nsamples = 50\nvalue = [50, 0, 0]'),
- Text(193.15384615384616, 163.07999999999998, 'X[3] <= 1.75\ngini = 0.5\nsamples = 100\nvalue = [0, 50, 50]'),
- Text(103.01538461538462, 126.83999999999999, 'X[2] <= 4.95\ngini = 0.168\nsamples = 54\nvalue = [0, 49, 5]'),
- Text(51.50769230769231, 90.6, 'X[3] <= 1.65\ngini = 0.041\nsamples = 48\nvalue = [0, 47, 1]'),
- Text(25.753846153846155, 54.359999999999985, 'gini = 0.0\nsamples = 47\nvalue = [0, 47, 0]'),
- Text(77.26153846153846, 54.359999999999985, 'gini = 0.0\nsamples = 1\nvalue = [0, 0, 1]'),
- Text(154.52307692307693, 90.6, 'X[3] <= 1.55\ngini = 0.444\nsamples = 6\nvalue = [0, 2, 4]'),
- Text(128.76923076923077, 54.359999999999985, 'gini = 0.0\nsamples = 3\nvalue = [0, 0, 3]'),
- Text(180.27692307692308, 54.359999999999985, 'X[2] <= 5.45\ngini = 0.444\nsamples = 3\nvalue = [0, 2, 1]'),
- Text(154.52307692307693, 18.119999999999976, 'gini = 0.0\nsamples = 2\nvalue = [0, 2, 0]'),
- Text(206.03076923076924, 18.119999999999976, 'gini = 0.0\nsamples = 1\nvalue = [0, 0, 1]'),
- Text(283.2923076923077, 126.83999999999999, 'X[2] <= 4.85\ngini = 0.043\nsamples = 46\nvalue = [0, 1, 45]'),
- Text(257.53846153846155, 90.6, 'X[1] <= 3.1\ngini = 0.444\nsamples = 3\nvalue = [0, 1, 2]'),
- Text(231.7846153846154, 54.359999999999985, 'gini = 0.0\nsamples = 2\nvalue = [0, 0, 2]'),
- Text(283.2923076923077, 54.359999999999985, 'gini = 0.0\nsamples = 1\nvalue = [0, 1, 0]'),
- Text(309.04615384615386, 90.6, 'gini = 0.0\nsamples = 43\nvalue = [0, 0, 43]')]
-
    
-
    
-_images/chapter6_24_1.png
-
    
 
    
 
    Alternatively, the tree can also be exported in textual format with the function exporttext.
 This method doesn’t require the installation of external libraries and is more compact:
    
@@ -980,17 +996,6 @@ This method doesn’t require the installation of external libraries and is more
 
    
 
    
 
    
-
    
-
    |--- petal width (cm) <= 0.80
-|   |--- class: 0
-|--- petal width (cm) >  0.80
-|   |--- petal width (cm) <= 1.75
-|   |   |--- class: 1
-|   |--- petal width (cm) >  1.75
-|   |   |--- class: 2
-
    
-
    
-
    
 
    
 
    
 
    
@@ -1155,20 +1160,6 @@ humidity and weak and strong for wind.
    
 
    
 
    
 
    
-
    
-
    ---------------------------------------------------------------------------
-FileNotFoundError                         Traceback (most recent call last)
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42541/4192423635.py in <module>
-     35     plt.savefig(image_path(fig_id) + ".png", format='png')
-     36 
----> 37 infile = open(data_path("rideclass.csv"),'r')
-     38 
-     39 # Read the experimental data with Pandas
-
-FileNotFoundError: [Errno 2] No such file or directory: 'DataFiles/rideclass.csv'
-
    
-
    
-
    
 
    
 
    The above functions (gini, entropy and misclassification error) are
 important components of the so-called CART algorithm. We will discuss
@@ -1565,54 +1556,42 @@ trees can be substantially improved.
    
 
               
    
               
-        
             
-
-
-
-
    
-    
-    
     
    
     
    
-    
    
-      
    
-        
-          By Morten Hjorth-Jensen
    
-        
-            © Copyright 2021.
    
-      
    
-    
    
-  
    
+  
    
+    
+      By Morten Hjorth-Jensen
    
+    
+        © Copyright 2021.
    
+  
    
+
    - + - \ No newline at end of file diff --git a/doc/LectureNotes/_build/html/chapter7.html b/doc/LectureNotes/_build/html/chapter7.html index bfcee0e41..297a52172 100644 --- a/doc/LectureNotes/_build/html/chapter7.html +++ b/doc/LectureNotes/_build/html/chapter7.html @@ -7,8 +7,8 @@ 10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods — Applied Data Analysis and Machine Learning - - + + - + @@ -41,22 +41,24 @@ - - - - - + + + + - + + + + @@ -91,11 +93,11 @@ -

    +

    About the course @@ -117,7 +119,7 @@ -

    +

    Review of Statistics with Resampling Techniques and Linear Algebra @@ -134,7 +136,7 @@ -

    +

    From Regression to Support Vector Machines @@ -171,7 +173,7 @@ -

    +

    Decision Trees, Ensemble Methods and Boosting @@ -188,7 +190,7 @@ -

    +

    Dimensionality Reduction @@ -199,8 +201,13 @@ 11. Basic ideas of the Principal Component Analysis (PCA) +

  7. + + 12. Clustering and Unsupervised Learning + +
    8. -

    +

    Deep Learning Methods @@ -208,17 +215,27 @@

    @@ -267,7 +284,7 @@ data-placement="left">.ipynb + onclick="printPdf(this)" data-toggle="tooltip" data-placement="left">.pdf
    @@ -285,7 +302,7 @@
    -
    +
    Contents @@ -381,7 +398,106 @@
    - + +
    +

    Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods

    + +
    + +
    +
    +
    @@ -459,7 +575,7 @@ predictor, averaged over all \(B\) 
    ---------------------------------------------------------------------------
 NameError                                 Traceback (most recent call last)
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42553/2572495066.py in <module>
+<ipython-input-1-eface79dac2c> in <module>
       1 heads_proba = 0.51
 ----> 2 coin_tosses = (np.random.rand(10000, 10) < heads_proba).astype(np.int32)
       3 cumulative_heads_ratio = np.cumsum(coin_tosses, axis=0) / np.arange(1, 10001).reshape(-1, 1)
@@ -1431,54 +1547,42 @@ sketch for efficient proposal calculation. It introduces a novel sparsity-aware
    - - - - -
    - -
    -
    -

    - - By Morten Hjorth-Jensen
    - - © Copyright 2021.
    -

    -
    -
    +

    + + By Morten Hjorth-Jensen
    + + © Copyright 2021.
    +

    +
    - + - \ No newline at end of file diff --git a/doc/LectureNotes/_build/html/chapter8.html b/doc/LectureNotes/_build/html/chapter8.html index e0a88d816..dd6e33067 100644 --- a/doc/LectureNotes/_build/html/chapter8.html +++ b/doc/LectureNotes/_build/html/chapter8.html @@ -7,8 +7,8 @@ 11. Basic ideas of the Principal Component Analysis (PCA) — Applied Data Analysis and Machine Learning - - + + - + @@ -41,22 +41,24 @@ - - - - - + + + + - + - + + + + @@ -91,11 +93,11 @@ -

    +

    About the course @@ -117,7 +119,7 @@ -

    +

    Review of Statistics with Resampling Techniques and Linear Algebra @@ -134,7 +136,7 @@ -

    +

    From Regression to Support Vector Machines @@ -171,7 +173,7 @@ -

    +

    Decision Trees, Ensemble Methods and Boosting @@ -188,7 +190,7 @@ -

    +

    Dimensionality Reduction @@ -199,8 +201,13 @@ 11. Basic ideas of the Principal Component Analysis (PCA) +

  8. + + 12. Clustering and Unsupervised Learning + +
    9. -

    +

    Deep Learning Methods @@ -208,17 +215,27 @@

    @@ -267,7 +284,7 @@ data-placement="left">.ipynb + onclick="printPdf(this)" data-toggle="tooltip" data-placement="left">.pdf
    @@ -285,7 +302,7 @@
    -
    +
    Contents @@ -374,7 +391,99 @@
    - + +
    +

    Basic ideas of the Principal Component Analysis (PCA)

    + +
    + +
    +
    +
    @@ -530,10 +639,10 @@ covariance matrix through the np.linalg.eig() function.

    -
    0.0358909447132981
-4.176880142835407
-[[ 1.09297039  3.38901478]
- [ 3.38901478 11.48089797]]
+
    0.03382304823545749
+4.021250026482402
+[[0.9252772  2.69061276]
+ [2.69061276 8.90540529]]
    @@ -573,10 +682,10 @@ a more brute force way. Here we scale the mean values for each column of the des
    -
    0.10044225464078282
-2.1586300629904382
-[[1.         0.72373129]
- [0.72373129 1.        ]]
+
    0.08328216846752691
+2.094472507965532
+[[1.         0.67697934]
+ [0.67697934 1.        ]]
    @@ -605,30 +714,30 @@ this matrix we easily see that it is a positive definite matrix.

    -
    [[-0.50416731 -0.8962476 ]
- [-1.00198806 -2.48687342]
- [-0.14988578 -0.24485843]
- [ 1.33327369  3.92754397]
- [ 0.47531107  0.66818635]
- [-0.03278964 -1.08041015]
- [-0.32992274  1.59591979]
- [-1.06160438 -3.85324115]
- [ 0.4644244   1.36689784]
- [ 0.80734875  1.0030828 ]]
+
    [[ 2.38295101  5.51289697]
+ [ 0.51803019  2.61399851]
+ [-1.09849763 -1.02255619]
+ [-0.54016188 -0.53794784]
+ [ 0.28634473  1.32721178]
+ [-1.66619972 -6.88017651]
+ [ 1.52811546  4.29512284]
+ [ 0.427017    2.43493232]
+ [-0.80842254 -4.37964744]
+ [-1.02917662 -3.36383443]]
           0         1
-0 -0.504167 -0.896248
-1 -1.001988 -2.486873
-2 -0.149886 -0.244858
-3  1.333274  3.927544
-4  0.475311  0.668186
-5 -0.032790 -1.080410
-6 -0.329923  1.595920
-7 -1.061604 -3.853241
-8  0.464424  1.366898
-9  0.807349  1.003083
+0  2.382951  5.512897
+1  0.518030  2.613999
+2 -1.098498 -1.022556
+3 -0.540162 -0.537948
+4  0.286345  1.327212
+5 -1.666200 -6.880177
+6  1.528115  4.295123
+7  0.427017  2.434932
+8 -0.808423 -4.379647
+9 -1.029177 -3.363834
           0         1
-0  1.000000  0.878297
-1  0.878297  1.000000
+0  1.000000  0.930583
+1  0.930583  1.000000
    @@ -685,37 +794,37 @@ this matrix we easily see that it is a positive definite matrix.

         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  0.068937  0.073016  0.069091  0.070612  0.071705  0.061898  0.062451   
-2   0.0  0.073016  0.079839  0.075573  0.078253  0.080256  0.068659  0.069754   
-3   0.0  0.069091  0.075573  0.074488  0.077022  0.078911  0.069912  0.070911   
-4   0.0  0.070612  0.078253  0.077022  0.080106  0.082451  0.072620  0.073907   
-5   0.0  0.071705  0.080256  0.078911  0.082451  0.085185  0.074666  0.076204   
-6   0.0  0.061898  0.068659  0.069912  0.072620  0.074666  0.067714  0.068809   
-7   0.0  0.062451  0.069754  0.070911  0.073907  0.076204  0.068809  0.070071   
-8   0.0  0.062884  0.070635  0.071698  0.074945  0.077467  0.069672  0.071086   
-9   0.0  0.063250  0.071387  0.072348  0.075820  0.078548  0.070379  0.071935   
-10  0.0  0.054585  0.060841  0.063657  0.066194  0.068120  0.063078  0.064108   
-11  0.0  0.054785  0.061321  0.064052  0.066753  0.068831  0.063513  0.064648   
-12  0.0  0.054963  0.061745  0.064384  0.067236  0.069455  0.063872  0.065106   
-13  0.0  0.055137  0.062142  0.064681  0.067675  0.070028  0.064184  0.065514   
-14  0.0  0.055320  0.062534  0.064964  0.068094  0.070576  0.064469  0.065892   
+1   0.0  0.086074  0.080593  0.088526  0.083276  0.078269  0.081046  0.076604   
+2   0.0  0.080593  0.076130  0.082896  0.078254  0.073810  0.076216  0.072216   
+3   0.0  0.088526  0.082896  0.096472  0.091051  0.085879  0.091696  0.086956   
+4   0.0  0.083276  0.078254  0.091051  0.086112  0.081388  0.086890  0.082536   
+5   0.0  0.078269  0.073810  0.085879  0.081388  0.077083  0.082295  0.078299   
+6   0.0  0.081046  0.076216  0.091696  0.086890  0.082295  0.089501  0.085163   
+7   0.0  0.076604  0.072216  0.086956  0.082536  0.078299  0.085163  0.081144   
+8   0.0  0.072442  0.068461  0.082503  0.078436  0.074530  0.081072  0.077349   
+9   0.0  0.068538  0.064931  0.078314  0.074573  0.070972  0.077211  0.073761   
+10  0.0  0.073062  0.069085  0.084862  0.080738  0.076780  0.084484  0.080647   
+11  0.0  0.069275  0.065641  0.080706  0.076895  0.073230  0.080582  0.077013   
+12  0.0  0.065730  0.062411  0.076804  0.073280  0.069884  0.076905  0.073583   
+13  0.0  0.062409  0.059378  0.073136  0.069877  0.066729  0.073436  0.070343   
+14  0.0  0.059294  0.056528  0.069685  0.066670  0.063752  0.070163  0.067282   
 
           8         9         10        11        12        13        14  
 0   0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  
-1   0.062884  0.063250  0.054585  0.054785  0.054963  0.055137  0.055320  
-2   0.070635  0.071387  0.060841  0.061321  0.061745  0.062142  0.062534  
-3   0.071698  0.072348  0.063657  0.064052  0.064384  0.064681  0.064964  
-4   0.074945  0.075820  0.066194  0.066753  0.067236  0.067675  0.068094  
-5   0.077467  0.078548  0.068120  0.068831  0.069455  0.070028  0.070576  
-6   0.069672  0.070379  0.063078  0.063513  0.063872  0.064184  0.064469  
-7   0.071086  0.071935  0.064108  0.064648  0.065106  0.065514  0.065892  
-8   0.072242  0.073225  0.064918  0.065557  0.066110  0.066609  0.067079  
-9   0.073225  0.074336  0.065575  0.066309  0.066954  0.067544  0.068103  
-10  0.064918  0.065575  0.059783  0.060183  0.060507  0.060781  0.061025  
-11  0.065557  0.066309  0.060183  0.060655  0.061048  0.061390  0.061701  
-12  0.066110  0.066954  0.060507  0.061048  0.061509  0.061917  0.062294  
-13  0.066609  0.067544  0.060781  0.061390  0.061917  0.062391  0.062834  
-14  0.067079  0.068103  0.061025  0.061701  0.062294  0.062834  0.063343  
+1   0.072442  0.068538  0.073062  0.069275  0.065730  0.062409  0.059294  
+2   0.068461  0.064931  0.069085  0.065641  0.062411  0.059378  0.056528  
+3   0.082503  0.078314  0.084862  0.080706  0.076804  0.073136  0.069685  
+4   0.078436  0.074573  0.080738  0.076895  0.073280  0.069877  0.066670  
+5   0.074530  0.070972  0.076780  0.073230  0.069884  0.066729  0.063752  
+6   0.081072  0.077211  0.084484  0.080582  0.076905  0.073436  0.070163  
+7   0.077349  0.073761  0.080647  0.077013  0.073583  0.070343  0.067282  
+8   0.073827  0.070492  0.077015  0.073629  0.070429  0.067402  0.064538  
+9   0.070492  0.067392  0.073575  0.070419  0.067432  0.064604  0.061923  
+10  0.077015  0.073575  0.080984  0.077452  0.074111  0.070950  0.067956  
+11  0.073629  0.070419  0.077452  0.074149  0.071022  0.068059  0.065249  
+12  0.070429  0.067432  0.074111  0.071022  0.068093  0.065314  0.062676  
+13  0.067402  0.064604  0.070950  0.068059  0.065314  0.062706  0.060228  
+14  0.064538  0.061923  0.067956  0.065249  0.062676  0.060228  0.057899
    @@ -904,10 +1013,10 @@ We can write our own code or simply use either the functionaly of numpy< 
              0         1
-0  3.947903  1.993972
-1  1.993972  1.993535
-[[3.94790323 1.99397245]
- [1.99397245 1.99353454]]
+0  4.038506  2.027865
+1  2.027865  2.037559
+[[4.03850557 2.02786488]
+ [2.02786488 2.03755944]]
    @@ -934,8 +1043,8 @@ Our own code here is not very elegant and asks for obvious improvements. It is t 
    Centered covariance using own code
-[[3.94790323 1.99397245]
- [1.99397245 1.99353454]]
+[[4.03850557 2.02786488]
+ [2.02786488 2.03755944]]
    _images/chapter8_65_1.png @@ -995,16 +1104,16 @@ questions.

    Eigenvalues of Covariance matrix
-5.191262820314401
-0.7501749450963715
+5.299267190588216
+0.7767978193240488
 First eigenvector
-[0.84854738 0.52911941]
+[0.84924834 0.52799362]
 Second eigenvector
-[-0.52911941  0.84854738]
+[-0.52799362  0.84924834]
 
    Eigenvector of largest eigenvalue
-[-0.84854738 -0.52911941]
+[0.84924834 0.52799362]
    @@ -1349,7 +1458,7 @@ Train set accuracy scaled data: 0.99 Train set accuracy scaled and PCA data: 0.96
    -
    /Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):
+
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):
 STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.
 
 Increase the number of iterations (max_iter) or scale the data as shown in:
@@ -1461,54 +1570,42 @@ For example, the following code uses Scikit-Learn’s KernelPCA class to perform
 
               
    
               
-        
             
-
-
-
-
    
-    
-    
     
    
     
    
-    
    
-      
    
-        
-          By Morten Hjorth-Jensen
    
-        
-            © Copyright 2021.
    
-      
    
-    
    
-  
    
+  
    
+    
+      By Morten Hjorth-Jensen
    
+    
+        © Copyright 2021.
    
+  
    
+
    - + - \ No newline at end of file diff --git a/doc/LectureNotes/_build/html/chapter9.html b/doc/LectureNotes/_build/html/chapter9.html index aca38d4f7..3bf37a1b5 100644 --- a/doc/LectureNotes/_build/html/chapter9.html +++ b/doc/LectureNotes/_build/html/chapter9.html @@ -7,8 +7,8 @@ 13. Neural networks — Applied Data Analysis and Machine Learning - - + + - + @@ -41,22 +41,24 @@ - - - - - + + + + - + + + + @@ -91,11 +93,11 @@ -

    +

    About the course @@ -117,7 +119,7 @@ -

    +

    Review of Statistics with Resampling Techniques and Linear Algebra @@ -134,7 +136,7 @@ -

    +

    From Regression to Support Vector Machines @@ -171,7 +173,7 @@ -

    +

    Decision Trees, Ensemble Methods and Boosting @@ -188,7 +190,7 @@ -

    +

    Dimensionality Reduction @@ -205,7 +207,7 @@ -

    +

    Deep Learning Methods @@ -282,7 +284,7 @@ data-placement="left">.ipynb + onclick="printPdf(this)" data-toggle="tooltip" data-placement="left">.pdf

    @@ -300,7 +302,7 @@
    -
    +
    Contents @@ -391,7 +393,101 @@
    - + +
    +

    Neural networks

    + +
    + +
    +
    +
    @@ -1141,54 +1237,42 @@ Here it is convenient to use stochastic gradient descent (see the examples below
    - - - - -
    - -
    -
    -

    - - By Morten Hjorth-Jensen
    - - © Copyright 2021.
    -

    -
    -
    +

    + + By Morten Hjorth-Jensen
    + + © Copyright 2021.
    +

    +
    - + - \ No newline at end of file diff --git a/doc/LectureNotes/_build/html/chapteroptimization.html b/doc/LectureNotes/_build/html/chapteroptimization.html index 79431ac4e..8070bf2ab 100644 --- a/doc/LectureNotes/_build/html/chapteroptimization.html +++ b/doc/LectureNotes/_build/html/chapteroptimization.html @@ -7,8 +7,8 @@ 7. Optimization, the central part of any Machine Learning algortithm — Applied Data Analysis and Machine Learning - - + + - + @@ -41,22 +41,24 @@ - - - - - + + + + - + + + + @@ -91,11 +93,11 @@ -

    +

    About the course @@ -117,7 +119,7 @@ -

    +

    Review of Statistics with Resampling Techniques and Linear Algebra @@ -134,7 +136,7 @@ -

    +

    From Regression to Support Vector Machines @@ -171,7 +173,7 @@ -

    +

    Decision Trees, Ensemble Methods and Boosting @@ -188,7 +190,7 @@ -

    +

    Dimensionality Reduction @@ -205,7 +207,7 @@ -

    +

    Deep Learning Methods @@ -282,7 +284,7 @@ data-placement="left">.ipynb + onclick="printPdf(this)" data-toggle="tooltip" data-placement="left">.pdf

    @@ -300,7 +302,7 @@
    -
    +
    Contents @@ -408,7 +410,118 @@
    - + +
    +

    Optimization, the central part of any Machine Learning algortithm

    + +
    + +
    +
    +
    -
    -

    - - By Morten Hjorth-Jensen
    - - © Copyright 2021.
    -

    -
    -
    +

    + + By Morten Hjorth-Jensen
    + + © Copyright 2021.
    +

    +
    - + - \ No newline at end of file diff --git a/doc/LectureNotes/_build/html/clustering.html b/doc/LectureNotes/_build/html/clustering.html index 41cdce5da..95a9e92c4 100644 --- a/doc/LectureNotes/_build/html/clustering.html +++ b/doc/LectureNotes/_build/html/clustering.html @@ -7,8 +7,8 @@ 12. Clustering and Unsupervised Learning — Applied Data Analysis and Machine Learning - - + + - + @@ -41,22 +41,24 @@ - - - - - + + + + - + + + + @@ -91,11 +93,11 @@ -

    +

    About the course @@ -117,7 +119,7 @@ -

    +

    Review of Statistics with Resampling Techniques and Linear Algebra @@ -134,7 +136,7 @@ -

    +

    From Regression to Support Vector Machines @@ -171,7 +173,7 @@ -

    +

    Decision Trees, Ensemble Methods and Boosting @@ -188,7 +190,7 @@ -

    +

    Dimensionality Reduction @@ -205,7 +207,7 @@ -

    +

    Deep Learning Methods @@ -282,7 +284,7 @@ data-placement="left">.ipynb + onclick="printPdf(this)" data-toggle="tooltip" data-placement="left">.pdf

    @@ -300,7 +302,7 @@
    -
    +
    Contents @@ -320,7 +322,30 @@
    - + +
    +

    Clustering and Unsupervised Learning

    + +
    +
    + +
    +

    Contents

    +
    + +
    +
    +
    +
    -
    -

    - - By Morten Hjorth-Jensen
    - - © Copyright 2021.
    -

    -
    -
    +

    + + By Morten Hjorth-Jensen
    + + © Copyright 2021.
    +

    +
    - + - \ No newline at end of file diff --git a/doc/LectureNotes/_build/html/genindex.html b/doc/LectureNotes/_build/html/genindex.html index 9b2d54ecf..1033c472d 100644 --- a/doc/LectureNotes/_build/html/genindex.html +++ b/doc/LectureNotes/_build/html/genindex.html @@ -7,8 +7,8 @@ Index — Applied Data Analysis and Machine Learning - - + + - + @@ -41,11 +41,20 @@ - + + + - + + + + @@ -84,7 +93,7 @@ -

    +

    About the course @@ -106,7 +115,7 @@ -

    +

    Review of Statistics with Resampling Techniques and Linear Algebra @@ -123,7 +132,7 @@ -

    +

    From Regression to Support Vector Machines @@ -160,7 +169,7 @@ -

    +

    Decision Trees, Ensemble Methods and Boosting @@ -177,7 +186,7 @@ -

    +

    Dimensionality Reduction @@ -194,7 +203,7 @@ -

    +

    Deep Learning Methods @@ -272,14 +281,24 @@

    -
    +
    - + +
    +

    + +
    +
    + +
    +
    +
    +
    @@ -292,36 +311,28 @@
    - - - - -
    - - + +
    - +
    -
    -

    - - By Morten Hjorth-Jensen
    - - © Copyright 2021.
    -

    -
    -
    +

    + + By Morten Hjorth-Jensen
    + + © Copyright 2021.
    +

    +
    - + - \ No newline at end of file diff --git a/doc/LectureNotes/_build/html/intro.html b/doc/LectureNotes/_build/html/intro.html index 599331c80..f2c1442b0 100644 --- a/doc/LectureNotes/_build/html/intro.html +++ b/doc/LectureNotes/_build/html/intro.html @@ -7,8 +7,8 @@ Applied Data Analysis and Machine Learning — Applied Data Analysis and Machine Learning - - + + - + @@ -41,19 +41,21 @@ - - - + + - + + + + @@ -92,7 +94,7 @@ -

    +

    About the course @@ -114,7 +116,7 @@ -

    +

    Review of Statistics with Resampling Techniques and Linear Algebra @@ -131,7 +133,7 @@ -

    +

    From Regression to Support Vector Machines @@ -168,7 +170,7 @@ -

    +

    Decision Trees, Ensemble Methods and Boosting @@ -185,7 +187,7 @@ -

    +

    Dimensionality Reduction @@ -202,7 +204,7 @@ -

    +

    Deep Learning Methods @@ -279,7 +281,7 @@ data-placement="left">.md + onclick="printPdf(this)" data-toggle="tooltip" data-placement="left">.pdf

    @@ -297,7 +299,7 @@
    -
    +
    Contents @@ -361,7 +363,74 @@
    - + +
    +

    Applied Data Analysis and Machine Learning

    + +
    + +
    +
    +
    @@ -539,45 +608,35 @@ no setup and runs entirely in the cloud. Try it out!

    - - - - -
    - - - + +
    + +
    +

    next

    +

    Teaching schedule with links to material

    +
    + +
    - +
    -
    -

    - - By Morten Hjorth-Jensen
    - - © Copyright 2021.
    -

    -
    -
    +

    + + By Morten Hjorth-Jensen
    + + © Copyright 2021.
    +

    +
    - + - \ No newline at end of file diff --git a/doc/LectureNotes/_build/html/linalg.html b/doc/LectureNotes/_build/html/linalg.html index 9d1973405..1adf2c77d 100644 --- a/doc/LectureNotes/_build/html/linalg.html +++ b/doc/LectureNotes/_build/html/linalg.html @@ -7,8 +7,8 @@ 2. Linear Algebra, Handling of Arrays and more Python Features — Applied Data Analysis and Machine Learning - - + + - + @@ -41,22 +41,24 @@ - - - - - + + + + - + + + + @@ -91,11 +93,11 @@ -

    +

    About the course @@ -117,7 +119,7 @@ -

    +

    Review of Statistics with Resampling Techniques and Linear Algebra @@ -134,7 +136,7 @@ -

    +

    From Regression to Support Vector Machines @@ -171,7 +173,7 @@ -

    +

    Decision Trees, Ensemble Methods and Boosting @@ -188,7 +190,7 @@ -

    +

    Dimensionality Reduction @@ -199,8 +201,13 @@ 11. Basic ideas of the Principal Component Analysis (PCA) +

  9. + + 12. Clustering and Unsupervised Learning + +
    10. -

    +

    Deep Learning Methods @@ -208,17 +215,27 @@

    @@ -267,7 +284,7 @@ data-placement="left">.ipynb + onclick="printPdf(this)" data-toggle="tooltip" data-placement="left">.pdf
    @@ -285,7 +302,7 @@
    -
    +
    Contents @@ -337,7 +354,62 @@
    - + +
    +

    Linear Algebra, Handling of Arrays and more Python Features

    + +
    + +
    +
    +
    @@ -453,8 +525,8 @@ matrices and vectors.

    -
    [-0.96653373  0.0433816   0.49636583 -1.12196674 -0.69295955  0.01756972
- -0.90268858  0.30535506  0.70769586 -1.05087958]
+
    [ 1.8108619  -0.65136857  0.00577441  0.11499517  0.32179365 -0.70598996
+  0.96992454  1.77865169 -0.40599799  0.04284519]
    @@ -541,7 +613,7 @@ The attentive reader will also notice that the output is -
      File "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42580/2775623201.py", line 3
+
      File "<ipython-input-6-f6d7a289d493>", line 3
     print(x)
     ^
 SyntaxError: invalid syntax
@@ -1179,54 +1251,42 @@ can be written as a vector with unknown entries
    
 
               
    
               
-        
             
-
-
-
-
    
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-        
-          By Morten Hjorth-Jensen
    
-        
-            © Copyright 2021.
    
-      
    
-    
    
-  
    
+  
    
+    
+      By Morten Hjorth-Jensen
    
+    
+        © Copyright 2021.
    
+  
    
+
    - + - \ No newline at end of file diff --git a/doc/LectureNotes/_build/html/schedule.html b/doc/LectureNotes/_build/html/schedule.html index f6e990f52..b260113c4 100644 --- a/doc/LectureNotes/_build/html/schedule.html +++ b/doc/LectureNotes/_build/html/schedule.html @@ -7,8 +7,8 @@ Teaching schedule with links to material — Applied Data Analysis and Machine Learning - - + + - + @@ -41,20 +41,22 @@ - - - + + - + - + + + + @@ -89,11 +91,11 @@ -

    +

    About the course @@ -115,7 +117,7 @@ -

    +

    Review of Statistics with Resampling Techniques and Linear Algebra @@ -132,7 +134,7 @@ -

    +

    From Regression to Support Vector Machines @@ -169,7 +171,7 @@ -

    +

    Decision Trees, Ensemble Methods and Boosting @@ -186,7 +188,7 @@ -

    +

    Dimensionality Reduction @@ -197,8 +199,13 @@ 11. Basic ideas of the Principal Component Analysis (PCA) +

  10. + + 12. Clustering and Unsupervised Learning + +
    11. -

    +

    Deep Learning Methods @@ -206,17 +213,27 @@

    @@ -265,7 +282,7 @@ data-placement="left">.md + onclick="printPdf(this)" data-toggle="tooltip" data-placement="left">.pdf
    @@ -283,7 +300,7 @@
    -
    +
    Contents @@ -296,73 +313,73 @@ @@ -375,7 +392,102 @@
    - + +
    +

    Teaching schedule with links to material

    + +
    + +
    +
    +