updated hw2

doc/Projects/2020/hw2/pdf/hw2.tex

@@ -167,10 +167,10 @@ distribution. The function $y$ is a quadratic polynomial in $x$ with
 added stochastic noise according to the normal distribution $\cal{N}(0,1)$.
 
 The following simple Python instructions define our $x$ and $y$ values (with 100 data points).
-\begin{print}
+\begin{verbatim}
 x = np.random.rand(100)
 y = 2.0+5*x*x+0.1*np.random.randn(100)
-\end{print}
+\end{verbatim}
 
 
 \subex{a)}
@@ -180,7 +180,7 @@ Write your own code for the Ridge method (see chapter 3.4 of Hastie \emph{et al.
 % --- begin solution of exercise ---
 \paragraph{Solution.}
 The code here allows you to perform your own Ridge calculation and perform calculations for various values of the regularization parameter $\lambda$. This program can easily be extended upon.
-\begin{print}
+\begin{verbatim}
 import os
 import numpy as np
 import pandas as pd
@@ -254,7 +254,7 @@ plt.xlabel('log10(lambda)')
 plt.ylabel('MSE')
 plt.legend()
 plt.show()
-\end{print}
+\end{verbatim}
 
 % --- end solution of exercise ---
 
@@ -265,7 +265,7 @@ Repeat the above but using the functionality of \textbf{Scikit-Learn}. Compare y
 % --- begin solution of exercise ---
 \paragraph{Solution.}
 To use \textbf{scikit-learn} with Ridge, we simply need to add the relevant function \textbf{Ridge()}, as done in the code here.
-\begin{print}
+\begin{verbatim}
 import numpy as np
 import pandas as pd
 import matplotlib.pyplot as plt
@@ -345,7 +345,7 @@ plt.xlabel('log10(lambda)')
 plt.ylabel('MSE')
 plt.legend()
 plt.show()
-\end{print}
+\end{verbatim}
 
 % --- end solution of exercise ---
 
@@ -355,7 +355,7 @@ Our next step is to study the variance of the parameters $\beta_1$ and $\beta_2$
 
 % --- begin solution of exercise ---
 \paragraph{Solution.}
-\begin{print}
+\begin{verbatim}
 import numpy as np
 import pandas as pd
 import matplotlib.pyplot as plt
@@ -412,7 +412,7 @@ for i in range(nlambdas):
 
 
 
-\end{print}
+\end{verbatim}
 
 % --- end solution of exercise ---
 
@@ -422,7 +422,7 @@ Repeat the previous step but add now the Lasso method, see equation (3.53) of Ha
 
 % --- begin solution of exercise ---
 \paragraph{Solution.}
-\begin{print}
+\begin{verbatim}
 import numpy as np
 import pandas as pd
 import matplotlib.pyplot as plt
@@ -497,7 +497,7 @@ plt.xlabel('log10(lambda)')
 plt.ylabel('MSE')
 plt.legend()
 plt.show()
-\end{print}
+\end{verbatim}
 
 % --- end solution of exercise ---
 
@@ -574,17 +574,17 @@ techniques.
 
 It also common to split the data in a \textbf{training} set and a \textbf{testing} set. A typical split is to use $80\%$ of the data for training and the rest
 for testing. This can be done as follows with our design matrix $\bm{X}$ and data $\bm{y}$ (remember to import \textbf{scikit-learn})
-\begin{print}
+\begin{verbatim}
 # split in training and test data
 X_train, X_test, y_train, y_test = train_test_split(X,y,test_size=0.2)
-\end{print}
+\end{verbatim}
 Then we can use the standard scaler to scale our data as
-\begin{print}
+\begin{verbatim}
 scaler = StandardScaler()
 scaler.fit(X_train)
 X_train_scaled = scaler.transform(X_train)
 X_test_scaled = scaler.transform(X_test)
-\end{print}
+\end{verbatim}
 
 
 In this exercise we want you to to compute the MSE for the training
@@ -597,14 +597,14 @@ We will also use Ridge and Lasso regression.
 
 
 Our data is defined by $x\in [-3,3]$ with a total of for example $100$ data points.
-\begin{print}
+\begin{verbatim}
 np.random.seed()
 n = 100
 maxdegree = 14
 # Make data set.
 x = np.linspace(-3, 3, n).reshape(-1, 1)
 y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2)+ np.random.normal(0, 0.1, x.shape)
-\end{print}
+\end{verbatim}
 where $y$ is the function we want to fit with a given polynomial.
 
 
@@ -614,7 +614,7 @@ Write a first code which sets up a design matrix $X$ defined by a fifth-order po
 
 % --- begin solution of exercise ---
 \paragraph{Solution.}
-\begin{print}
+\begin{verbatim}
 import matplotlib.pyplot as plt
 import numpy as np
 from sklearn.linear_model import LinearRegression, Ridge, Lasso
@@ -651,7 +651,7 @@ plt.plot(polydegree, TestError, label='Test Error')
 plt.plot(polydegree, TrainError, label='Train Error')
 plt.legend()
 plt.show()
-\end{print}
+\end{verbatim}
 
 % --- end solution of exercise ---
 
@@ -682,7 +682,7 @@ Repeat part (2c) but now using Ridge regressions with various hyperparameters $\
 % --- begin solution of exercise ---
 \paragraph{Solution.}
 Here you need to add for example the same loop over the parameters $\lambda$ as you did in the first exercise, that is add
-\begin{print}
+\begin{verbatim}
 nlambdas = 100
 MSEPredictRidge = np.zeros(nlambdas)
 lambdas = np.logspace(-4, 0, nlambdas)
@@ -691,7 +691,7 @@ for i in range(nlambdas):
     # add ridge
     clf_ridge = skl.Ridge(alpha=lmb).fit(X_train_scaled, y_train)
 
-\end{print}
+\end{verbatim}
 The plotting functionality of the first exercise can be reused here as well.
 
 % --- end solution of exercise ---