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cleaning up ex2

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mhjensen
2020-09-08 23:05:38 +02:00
parent 9bd71f8050
commit fd91b20596
9 changed files with 182 additions and 175 deletions
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doc/Projects/2020/hw2/html/._hw2-bs000.html
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@@ -118,7 +118,7 @@ MathJax.Hub.Config({
<center><b>Department of Physics, University of Oslo, Norway</b></center>
<br>
<p>
<center><h4>Sep 1, 2020</h4></center> <!-- date -->
<center><h4>Sep 8, 2020</h4></center> <!-- date -->
<br>
<p>
<!-- --- begin exercise --- -->
@@ -206,19 +206,19 @@ X_train_scaled <span style="color: #666666">=</span> scaler<span style="color: #
X_test_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(X_test)
<span style="color: #408080; font-style: italic"># matrix inversion to find beta</span>
OLSbeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> X_train) <span style="color: #666666">@</span> X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> y_train
<span style="color: #008000">print</span>(OLSbeta)
OLSbeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T @ X_train) @ X_train<span style="color: #666666">.</span>T @ y_train
<span style="color: #008000; font-weight: bold">print</span>(OLSbeta)
<span style="color: #408080; font-style: italic"># and then make the prediction</span>
ytildeOLS <span style="color: #666666">=</span> X_train <span style="color: #666666">@</span> OLSbeta
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Training R2 for OLS&quot;</span>)
<span style="color: #008000">print</span>(R2(y_train,ytildeOLS))
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Training MSE for OLS&quot;</span>)
<span style="color: #008000">print</span>(MSE(y_train,ytildeOLS))
ypredictOLS <span style="color: #666666">=</span> X_test <span style="color: #666666">@</span> OLSbeta
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Test R2 for OLS&quot;</span>)
<span style="color: #008000">print</span>(R2(y_test,ypredictOLS))
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Test MSE OLS&quot;</span>)
<span style="color: #008000">print</span>(MSE(y_test,ypredictOLS))
ytildeOLS <span style="color: #666666">=</span> X_train @ OLSbeta
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Training R2 for OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(R2(y_train,ytildeOLS))
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Training MSE for OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(MSE(y_train,ytildeOLS))
ypredictOLS <span style="color: #666666">=</span> X_test @ OLSbeta
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Test R2 for OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(R2(y_test,ypredictOLS))
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Test MSE OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(MSE(y_test,ypredictOLS))
<span style="color: #408080; font-style: italic"># Repeat now for Ridge regression and various values of the regularization parameter</span>
I <span style="color: #666666">=</span> np<span style="color: #666666">.</span>eye(p,p)
@@ -229,13 +229,13 @@ MSETrain <span style="color: #666666">=</span> np<span style="color: #666666">.<
lambdas <span style="color: #666666">=</span> np<span style="color: #666666">.</span>logspace(<span style="color: #666666">-4</span>, <span style="color: #666666">1</span>, nlambdas)
<span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(nlambdas):
lmb <span style="color: #666666">=</span> lambdas[i]
Ridgebeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> X_train<span style="color: #666666">+</span>lmb<span style="color: #666666">*</span>I) <span style="color: #666666">@</span> X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> y_train
Ridgebeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T @ X_train<span style="color: #666666">+</span>lmb<span style="color: #666666">*</span>I) @ X_train<span style="color: #666666">.</span>T @ y_train
<span style="color: #408080; font-style: italic"># and then make the prediction</span>
ytildeRidge <span style="color: #666666">=</span> X_train <span style="color: #666666">@</span> Ridgebeta
ypredictRidge <span style="color: #666666">=</span> X_test <span style="color: #666666">@</span> Ridgebeta
ytildeRidge <span style="color: #666666">=</span> X_train @ Ridgebeta
ypredictRidge <span style="color: #666666">=</span> X_test @ Ridgebeta
MSEPredict[i] <span style="color: #666666">=</span> MSE(y_test,ypredictRidge)
MSETrain[i] <span style="color: #666666">=</span> MSE(y_train,ytildeRidge)
<span style="color: #408080; font-style: italic"># Now plot the resulys</span>
<span style="color: #408080; font-style: italic"># Now plot the results</span>
plt<span style="color: #666666">.</span>figure()
plt<span style="color: #666666">.</span>plot(np<span style="color: #666666">.</span>log10(lambdas), MSETrain, label <span style="color: #666666">=</span> <span style="color: #BA2121">&#39;MSE Ridge train&#39;</span>)
plt<span style="color: #666666">.</span>plot(np<span style="color: #666666">.</span>log10(lambdas), MSEPredict, <span style="color: #BA2121">&#39;r--&#39;</span>, label <span style="color: #666666">=</span> <span style="color: #BA2121">&#39;MSE Ridge Test&#39;</span>)
@@ -309,19 +309,19 @@ X_train_scaled <span style="color: #666666">=</span> scaler<span style="color: #
X_test_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(X_test)
<span style="color: #408080; font-style: italic"># matrix inversion to find beta</span>
OLSbeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> X_train) <span style="color: #666666">@</span> X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> y_train
<span style="color: #008000">print</span>(OLSbeta)
OLSbeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T @ X_train) @ X_train<span style="color: #666666">.</span>T @ y_train
<span style="color: #008000; font-weight: bold">print</span>(OLSbeta)
<span style="color: #408080; font-style: italic"># and then make the prediction</span>
ytildeOLS <span style="color: #666666">=</span> X_train <span style="color: #666666">@</span> OLSbeta
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Training R2 for OLS&quot;</span>)
<span style="color: #008000">print</span>(R2(y_train,ytildeOLS))
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Training MSE for OLS&quot;</span>)
<span style="color: #008000">print</span>(MSE(y_train,ytildeOLS))
ypredictOLS <span style="color: #666666">=</span> X_test <span style="color: #666666">@</span> OLSbeta
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Test R2 for OLS&quot;</span>)
<span style="color: #008000">print</span>(R2(y_test,ypredictOLS))
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Test MSE OLS&quot;</span>)
<span style="color: #008000">print</span>(MSE(y_test,ypredictOLS))
ytildeOLS <span style="color: #666666">=</span> X_train @ OLSbeta
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Training R2 for OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(R2(y_train,ytildeOLS))
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Training MSE for OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(MSE(y_train,ytildeOLS))
ypredictOLS <span style="color: #666666">=</span> X_test @ OLSbeta
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Test R2 for OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(R2(y_test,ypredictOLS))
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Test MSE OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(MSE(y_test,ypredictOLS))
<span style="color: #408080; font-style: italic"># Repeat now for Ridge regression and various values of the regularization parameter</span>
I <span style="color: #666666">=</span> np<span style="color: #666666">.</span>eye(p,p)
@@ -336,10 +336,10 @@ lambdas <span style="color: #666666">=</span> np<span style="color: #666666">.</
<span style="color: #408080; font-style: italic"># add ridge</span>
clf_ridge <span style="color: #666666">=</span> skl<span style="color: #666666">.</span>Ridge(alpha<span style="color: #666666">=</span>lmb)<span style="color: #666666">.</span>fit(X_train, y_train)
yridge <span style="color: #666666">=</span> clf_ridge<span style="color: #666666">.</span>predict(X_test)
Ridgebeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> X_train<span style="color: #666666">+</span>lmb<span style="color: #666666">*</span>I) <span style="color: #666666">@</span> X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> y_train
Ridgebeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T @ X_train<span style="color: #666666">+</span>lmb<span style="color: #666666">*</span>I) @ X_train<span style="color: #666666">.</span>T @ y_train
<span style="color: #408080; font-style: italic"># and then make the prediction</span>
ytildeRidge <span style="color: #666666">=</span> X_train <span style="color: #666666">@</span> Ridgebeta
ypredictRidge <span style="color: #666666">=</span> X_test <span style="color: #666666">@</span> Ridgebeta
ytildeRidge <span style="color: #666666">=</span> X_train @ Ridgebeta
ypredictRidge <span style="color: #666666">=</span> X_test @ Ridgebeta
MSEPredict[i] <span style="color: #666666">=</span> MSE(y_test,ypredictRidge)
MSEPredictSKL[i] <span style="color: #666666">=</span> MSE(y_test,yridge)
MSETrain[i] <span style="color: #666666">=</span> MSE(y_train,ytildeRidge)
@@ -416,10 +416,10 @@ X_train_scaled <span style="color: #666666">=</span> scaler<span style="color: #
X_test_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(X_test)
<span style="color: #408080; font-style: italic"># matrix inversion to find beta</span>
OLSbeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> X_train) <span style="color: #666666">@</span> X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> y_train
<span style="color: #008000">print</span>(OLSbeta)
OLSbeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T @ X_train) @ X_train<span style="color: #666666">.</span>T @ y_train
<span style="color: #008000; font-weight: bold">print</span>(OLSbeta)
<span style="color: #408080; font-style: italic"># The variance is given by the inverse of the matrix X^TX</span>
<span style="color: #008000">print</span>(np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> X_train))
<span style="color: #008000; font-weight: bold">print</span>(np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T @ X_train))
<span style="color: #408080; font-style: italic"># Repeat now for Ridge regression and various values of the regularization parameter</span>
I <span style="color: #666666">=</span> np<span style="color: #666666">.</span>eye(p,p)
@@ -431,8 +431,8 @@ MSETrain <span style="color: #666666">=</span> np<span style="color: #666666">.<
lambdas <span style="color: #666666">=</span> np<span style="color: #666666">.</span>logspace(<span style="color: #666666">-4</span>, <span style="color: #666666">0</span>, nlambdas)
<span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(nlambdas):
lmb <span style="color: #666666">=</span> lambdas[i]
Ridgebeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> X_train<span style="color: #666666">+</span>lmb<span style="color: #666666">*</span>I) <span style="color: #666666">@</span> X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> y_train
<span style="color: #008000">print</span>(np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> X_train<span style="color: #666666">+</span>lmb<span style="color: #666666">*</span>I))
Ridgebeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T @ X_train<span style="color: #666666">+</span>lmb<span style="color: #666666">*</span>I) @ X_train<span style="color: #666666">.</span>T @ y_train
<span style="color: #008000; font-weight: bold">print</span>(np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T @ X_train<span style="color: #666666">+</span>lmb<span style="color: #666666">*</span>I))
</pre></div>
<p>
</div></p>
@@ -497,19 +497,19 @@ X_train_scaled <span style="color: #666666">=</span> scaler<span style="color: #
X_test_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(X_test)
<span style="color: #408080; font-style: italic"># matrix inversion to find beta</span>
OLSbeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> X_train) <span style="color: #666666">@</span> X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> y_train
<span style="color: #008000">print</span>(OLSbeta)
OLSbeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T @ X_train) @ X_train<span style="color: #666666">.</span>T @ y_train
<span style="color: #008000; font-weight: bold">print</span>(OLSbeta)
<span style="color: #408080; font-style: italic"># and then make the prediction</span>
ytildeOLS <span style="color: #666666">=</span> X_train <span style="color: #666666">@</span> OLSbeta
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Training R2 for OLS&quot;</span>)
<span style="color: #008000">print</span>(R2(y_train,ytildeOLS))
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Training MSE for OLS&quot;</span>)
<span style="color: #008000">print</span>(MSE(y_train,ytildeOLS))
ypredictOLS <span style="color: #666666">=</span> X_test <span style="color: #666666">@</span> OLSbeta
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Test R2 for OLS&quot;</span>)
<span style="color: #008000">print</span>(R2(y_test,ypredictOLS))
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Test MSE OLS&quot;</span>)
<span style="color: #008000">print</span>(MSE(y_test,ypredictOLS))
ytildeOLS <span style="color: #666666">=</span> X_train @ OLSbeta
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Training R2 for OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(R2(y_train,ytildeOLS))
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Training MSE for OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(MSE(y_train,ytildeOLS))
ypredictOLS <span style="color: #666666">=</span> X_test @ OLSbeta
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Test R2 for OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(R2(y_test,ypredictOLS))
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Test MSE OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(MSE(y_test,ypredictOLS))
<span style="color: #408080; font-style: italic"># Repeat now for Ridge regression and various values of the regularization parameter</span>
I <span style="color: #666666">=</span> np<span style="color: #666666">.</span>eye(p,p)
@@ -718,7 +718,7 @@ x_train_scaled <span style="color: #666666">=</span> scaler<span style="color: #
x_test_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(x_test)
<span style="color: #008000; font-weight: bold">for</span> degree <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(maxdegree):
model <span style="color: #666666">=</span> make_pipeline(PolynomialFeatures(degree<span style="color: #666666">=</span>degree), LinearRegression(fit_intercept<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">False</span>))
model <span style="color: #666666">=</span> make_pipeline(PolynomialFeatures(degree<span style="color: #666666">=</span>degree), LinearRegression(fit_intercept<span style="color: #666666">=</span><span style="color: #008000">False</span>))
clf <span style="color: #666666">=</span> model<span style="color: #666666">.</span>fit(x_train_scale,y_train)
y_fit <span style="color: #666666">=</span> clf<span style="color: #666666">.</span>predict(x_train_scaled)
y_pred <span style="color: #666666">=</span> clf<span style="color: #666666">.</span>predict(x_test_scaled)
doc/Projects/2020/hw2/html/hw2-bs.html
+50 -50
View File
@@ -118,7 +118,7 @@ MathJax.Hub.Config({
<center><b>Department of Physics, University of Oslo, Norway</b></center>
<br>
<p>
<center><h4>Sep 1, 2020</h4></center> <!-- date -->
<center><h4>Sep 8, 2020</h4></center> <!-- date -->
<br>
<p>
<!-- --- begin exercise --- -->
@@ -206,19 +206,19 @@ X_train_scaled <span style="color: #666666">=</span> scaler<span style="color: #
X_test_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(X_test)
<span style="color: #408080; font-style: italic"># matrix inversion to find beta</span>
OLSbeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> X_train) <span style="color: #666666">@</span> X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> y_train
<span style="color: #008000">print</span>(OLSbeta)
OLSbeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T @ X_train) @ X_train<span style="color: #666666">.</span>T @ y_train
<span style="color: #008000; font-weight: bold">print</span>(OLSbeta)
<span style="color: #408080; font-style: italic"># and then make the prediction</span>
ytildeOLS <span style="color: #666666">=</span> X_train <span style="color: #666666">@</span> OLSbeta
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Training R2 for OLS&quot;</span>)
<span style="color: #008000">print</span>(R2(y_train,ytildeOLS))
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Training MSE for OLS&quot;</span>)
<span style="color: #008000">print</span>(MSE(y_train,ytildeOLS))
ypredictOLS <span style="color: #666666">=</span> X_test <span style="color: #666666">@</span> OLSbeta
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Test R2 for OLS&quot;</span>)
<span style="color: #008000">print</span>(R2(y_test,ypredictOLS))
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Test MSE OLS&quot;</span>)
<span style="color: #008000">print</span>(MSE(y_test,ypredictOLS))
ytildeOLS <span style="color: #666666">=</span> X_train @ OLSbeta
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Training R2 for OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(R2(y_train,ytildeOLS))
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Training MSE for OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(MSE(y_train,ytildeOLS))
ypredictOLS <span style="color: #666666">=</span> X_test @ OLSbeta
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Test R2 for OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(R2(y_test,ypredictOLS))
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Test MSE OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(MSE(y_test,ypredictOLS))
<span style="color: #408080; font-style: italic"># Repeat now for Ridge regression and various values of the regularization parameter</span>
I <span style="color: #666666">=</span> np<span style="color: #666666">.</span>eye(p,p)
@@ -229,13 +229,13 @@ MSETrain <span style="color: #666666">=</span> np<span style="color: #666666">.<
lambdas <span style="color: #666666">=</span> np<span style="color: #666666">.</span>logspace(<span style="color: #666666">-4</span>, <span style="color: #666666">1</span>, nlambdas)
<span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(nlambdas):
lmb <span style="color: #666666">=</span> lambdas[i]
Ridgebeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> X_train<span style="color: #666666">+</span>lmb<span style="color: #666666">*</span>I) <span style="color: #666666">@</span> X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> y_train
Ridgebeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T @ X_train<span style="color: #666666">+</span>lmb<span style="color: #666666">*</span>I) @ X_train<span style="color: #666666">.</span>T @ y_train
<span style="color: #408080; font-style: italic"># and then make the prediction</span>
ytildeRidge <span style="color: #666666">=</span> X_train <span style="color: #666666">@</span> Ridgebeta
ypredictRidge <span style="color: #666666">=</span> X_test <span style="color: #666666">@</span> Ridgebeta
ytildeRidge <span style="color: #666666">=</span> X_train @ Ridgebeta
ypredictRidge <span style="color: #666666">=</span> X_test @ Ridgebeta
MSEPredict[i] <span style="color: #666666">=</span> MSE(y_test,ypredictRidge)
MSETrain[i] <span style="color: #666666">=</span> MSE(y_train,ytildeRidge)
<span style="color: #408080; font-style: italic"># Now plot the resulys</span>
<span style="color: #408080; font-style: italic"># Now plot the results</span>
plt<span style="color: #666666">.</span>figure()
plt<span style="color: #666666">.</span>plot(np<span style="color: #666666">.</span>log10(lambdas), MSETrain, label <span style="color: #666666">=</span> <span style="color: #BA2121">&#39;MSE Ridge train&#39;</span>)
plt<span style="color: #666666">.</span>plot(np<span style="color: #666666">.</span>log10(lambdas), MSEPredict, <span style="color: #BA2121">&#39;r--&#39;</span>, label <span style="color: #666666">=</span> <span style="color: #BA2121">&#39;MSE Ridge Test&#39;</span>)
@@ -309,19 +309,19 @@ X_train_scaled <span style="color: #666666">=</span> scaler<span style="color: #
X_test_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(X_test)
<span style="color: #408080; font-style: italic"># matrix inversion to find beta</span>
OLSbeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> X_train) <span style="color: #666666">@</span> X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> y_train
<span style="color: #008000">print</span>(OLSbeta)
OLSbeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T @ X_train) @ X_train<span style="color: #666666">.</span>T @ y_train
<span style="color: #008000; font-weight: bold">print</span>(OLSbeta)
<span style="color: #408080; font-style: italic"># and then make the prediction</span>
ytildeOLS <span style="color: #666666">=</span> X_train <span style="color: #666666">@</span> OLSbeta
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Training R2 for OLS&quot;</span>)
<span style="color: #008000">print</span>(R2(y_train,ytildeOLS))
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Training MSE for OLS&quot;</span>)
<span style="color: #008000">print</span>(MSE(y_train,ytildeOLS))
ypredictOLS <span style="color: #666666">=</span> X_test <span style="color: #666666">@</span> OLSbeta
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Test R2 for OLS&quot;</span>)
<span style="color: #008000">print</span>(R2(y_test,ypredictOLS))
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Test MSE OLS&quot;</span>)
<span style="color: #008000">print</span>(MSE(y_test,ypredictOLS))
ytildeOLS <span style="color: #666666">=</span> X_train @ OLSbeta
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Training R2 for OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(R2(y_train,ytildeOLS))
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Training MSE for OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(MSE(y_train,ytildeOLS))
ypredictOLS <span style="color: #666666">=</span> X_test @ OLSbeta
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Test R2 for OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(R2(y_test,ypredictOLS))
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Test MSE OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(MSE(y_test,ypredictOLS))
<span style="color: #408080; font-style: italic"># Repeat now for Ridge regression and various values of the regularization parameter</span>
I <span style="color: #666666">=</span> np<span style="color: #666666">.</span>eye(p,p)
@@ -336,10 +336,10 @@ lambdas <span style="color: #666666">=</span> np<span style="color: #666666">.</
<span style="color: #408080; font-style: italic"># add ridge</span>
clf_ridge <span style="color: #666666">=</span> skl<span style="color: #666666">.</span>Ridge(alpha<span style="color: #666666">=</span>lmb)<span style="color: #666666">.</span>fit(X_train, y_train)
yridge <span style="color: #666666">=</span> clf_ridge<span style="color: #666666">.</span>predict(X_test)
Ridgebeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> X_train<span style="color: #666666">+</span>lmb<span style="color: #666666">*</span>I) <span style="color: #666666">@</span> X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> y_train
Ridgebeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T @ X_train<span style="color: #666666">+</span>lmb<span style="color: #666666">*</span>I) @ X_train<span style="color: #666666">.</span>T @ y_train
<span style="color: #408080; font-style: italic"># and then make the prediction</span>
ytildeRidge <span style="color: #666666">=</span> X_train <span style="color: #666666">@</span> Ridgebeta
ypredictRidge <span style="color: #666666">=</span> X_test <span style="color: #666666">@</span> Ridgebeta
ytildeRidge <span style="color: #666666">=</span> X_train @ Ridgebeta
ypredictRidge <span style="color: #666666">=</span> X_test @ Ridgebeta
MSEPredict[i] <span style="color: #666666">=</span> MSE(y_test,ypredictRidge)
MSEPredictSKL[i] <span style="color: #666666">=</span> MSE(y_test,yridge)
MSETrain[i] <span style="color: #666666">=</span> MSE(y_train,ytildeRidge)
@@ -416,10 +416,10 @@ X_train_scaled <span style="color: #666666">=</span> scaler<span style="color: #
X_test_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(X_test)
<span style="color: #408080; font-style: italic"># matrix inversion to find beta</span>
OLSbeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> X_train) <span style="color: #666666">@</span> X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> y_train
<span style="color: #008000">print</span>(OLSbeta)
OLSbeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T @ X_train) @ X_train<span style="color: #666666">.</span>T @ y_train
<span style="color: #008000; font-weight: bold">print</span>(OLSbeta)
<span style="color: #408080; font-style: italic"># The variance is given by the inverse of the matrix X^TX</span>
<span style="color: #008000">print</span>(np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> X_train))
<span style="color: #008000; font-weight: bold">print</span>(np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T @ X_train))
<span style="color: #408080; font-style: italic"># Repeat now for Ridge regression and various values of the regularization parameter</span>
I <span style="color: #666666">=</span> np<span style="color: #666666">.</span>eye(p,p)
@@ -431,8 +431,8 @@ MSETrain <span style="color: #666666">=</span> np<span style="color: #666666">.<
lambdas <span style="color: #666666">=</span> np<span style="color: #666666">.</span>logspace(<span style="color: #666666">-4</span>, <span style="color: #666666">0</span>, nlambdas)
<span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(nlambdas):
lmb <span style="color: #666666">=</span> lambdas[i]
Ridgebeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> X_train<span style="color: #666666">+</span>lmb<span style="color: #666666">*</span>I) <span style="color: #666666">@</span> X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> y_train
<span style="color: #008000">print</span>(np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> X_train<span style="color: #666666">+</span>lmb<span style="color: #666666">*</span>I))
Ridgebeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T @ X_train<span style="color: #666666">+</span>lmb<span style="color: #666666">*</span>I) @ X_train<span style="color: #666666">.</span>T @ y_train
<span style="color: #008000; font-weight: bold">print</span>(np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T @ X_train<span style="color: #666666">+</span>lmb<span style="color: #666666">*</span>I))
</pre></div>
<p>
</div></p>
@@ -497,19 +497,19 @@ X_train_scaled <span style="color: #666666">=</span> scaler<span style="color: #
X_test_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(X_test)
<span style="color: #408080; font-style: italic"># matrix inversion to find beta</span>
OLSbeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> X_train) <span style="color: #666666">@</span> X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> y_train
<span style="color: #008000">print</span>(OLSbeta)
OLSbeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T @ X_train) @ X_train<span style="color: #666666">.</span>T @ y_train
<span style="color: #008000; font-weight: bold">print</span>(OLSbeta)
<span style="color: #408080; font-style: italic"># and then make the prediction</span>
ytildeOLS <span style="color: #666666">=</span> X_train <span style="color: #666666">@</span> OLSbeta
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Training R2 for OLS&quot;</span>)
<span style="color: #008000">print</span>(R2(y_train,ytildeOLS))
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Training MSE for OLS&quot;</span>)
<span style="color: #008000">print</span>(MSE(y_train,ytildeOLS))
ypredictOLS <span style="color: #666666">=</span> X_test <span style="color: #666666">@</span> OLSbeta
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Test R2 for OLS&quot;</span>)
<span style="color: #008000">print</span>(R2(y_test,ypredictOLS))
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Test MSE OLS&quot;</span>)
<span style="color: #008000">print</span>(MSE(y_test,ypredictOLS))
ytildeOLS <span style="color: #666666">=</span> X_train @ OLSbeta
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Training R2 for OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(R2(y_train,ytildeOLS))
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Training MSE for OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(MSE(y_train,ytildeOLS))
ypredictOLS <span style="color: #666666">=</span> X_test @ OLSbeta
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Test R2 for OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(R2(y_test,ypredictOLS))
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Test MSE OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(MSE(y_test,ypredictOLS))
<span style="color: #408080; font-style: italic"># Repeat now for Ridge regression and various values of the regularization parameter</span>
I <span style="color: #666666">=</span> np<span style="color: #666666">.</span>eye(p,p)
@@ -718,7 +718,7 @@ x_train_scaled <span style="color: #666666">=</span> scaler<span style="color: #
x_test_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(x_test)
<span style="color: #008000; font-weight: bold">for</span> degree <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(maxdegree):
model <span style="color: #666666">=</span> make_pipeline(PolynomialFeatures(degree<span style="color: #666666">=</span>degree), LinearRegression(fit_intercept<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">False</span>))
model <span style="color: #666666">=</span> make_pipeline(PolynomialFeatures(degree<span style="color: #666666">=</span>degree), LinearRegression(fit_intercept<span style="color: #666666">=</span><span style="color: #008000">False</span>))
clf <span style="color: #666666">=</span> model<span style="color: #666666">.</span>fit(x_train_scale,y_train)
y_fit <span style="color: #666666">=</span> clf<span style="color: #666666">.</span>predict(x_train_scaled)
y_pred <span style="color: #666666">=</span> clf<span style="color: #666666">.</span>predict(x_test_scaled)
doc/Projects/2020/hw2/html/hw2.html
+50 -50
View File
@@ -85,7 +85,7 @@ MathJax.Hub.Config({
<center><b>Department of Physics, University of Oslo, Norway</b></center>
<br>
<p>
<center><h4>Sep 1, 2020</h4></center> <!-- date -->
<center><h4>Sep 8, 2020</h4></center> <!-- date -->
<br>
<p>
<!-- --- begin exercise --- -->
@@ -160,19 +160,19 @@ X_train_scaled <span style="color: #666666">=</span> scaler<span style="color: #
X_test_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(X_test)
<span style="color: #408080; font-style: italic"># matrix inversion to find beta</span>
OLSbeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> X_train) <span style="color: #666666">@</span> X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> y_train
<span style="color: #008000">print</span>(OLSbeta)
OLSbeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T @ X_train) @ X_train<span style="color: #666666">.</span>T @ y_train
<span style="color: #008000; font-weight: bold">print</span>(OLSbeta)
<span style="color: #408080; font-style: italic"># and then make the prediction</span>
ytildeOLS <span style="color: #666666">=</span> X_train <span style="color: #666666">@</span> OLSbeta
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Training R2 for OLS&quot;</span>)
<span style="color: #008000">print</span>(R2(y_train,ytildeOLS))
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Training MSE for OLS&quot;</span>)
<span style="color: #008000">print</span>(MSE(y_train,ytildeOLS))
ypredictOLS <span style="color: #666666">=</span> X_test <span style="color: #666666">@</span> OLSbeta
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Test R2 for OLS&quot;</span>)
<span style="color: #008000">print</span>(R2(y_test,ypredictOLS))
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Test MSE OLS&quot;</span>)
<span style="color: #008000">print</span>(MSE(y_test,ypredictOLS))
ytildeOLS <span style="color: #666666">=</span> X_train @ OLSbeta
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Training R2 for OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(R2(y_train,ytildeOLS))
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Training MSE for OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(MSE(y_train,ytildeOLS))
ypredictOLS <span style="color: #666666">=</span> X_test @ OLSbeta
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Test R2 for OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(R2(y_test,ypredictOLS))
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Test MSE OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(MSE(y_test,ypredictOLS))
<span style="color: #408080; font-style: italic"># Repeat now for Ridge regression and various values of the regularization parameter</span>
I <span style="color: #666666">=</span> np<span style="color: #666666">.</span>eye(p,p)
@@ -183,13 +183,13 @@ MSETrain <span style="color: #666666">=</span> np<span style="color: #666666">.<
lambdas <span style="color: #666666">=</span> np<span style="color: #666666">.</span>logspace(<span style="color: #666666">-4</span>, <span style="color: #666666">1</span>, nlambdas)
<span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(nlambdas):
lmb <span style="color: #666666">=</span> lambdas[i]
Ridgebeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> X_train<span style="color: #666666">+</span>lmb<span style="color: #666666">*</span>I) <span style="color: #666666">@</span> X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> y_train
Ridgebeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T @ X_train<span style="color: #666666">+</span>lmb<span style="color: #666666">*</span>I) @ X_train<span style="color: #666666">.</span>T @ y_train
<span style="color: #408080; font-style: italic"># and then make the prediction</span>
ytildeRidge <span style="color: #666666">=</span> X_train <span style="color: #666666">@</span> Ridgebeta
ypredictRidge <span style="color: #666666">=</span> X_test <span style="color: #666666">@</span> Ridgebeta
ytildeRidge <span style="color: #666666">=</span> X_train @ Ridgebeta
ypredictRidge <span style="color: #666666">=</span> X_test @ Ridgebeta
MSEPredict[i] <span style="color: #666666">=</span> MSE(y_test,ypredictRidge)
MSETrain[i] <span style="color: #666666">=</span> MSE(y_train,ytildeRidge)
<span style="color: #408080; font-style: italic"># Now plot the resulys</span>
<span style="color: #408080; font-style: italic"># Now plot the results</span>
plt<span style="color: #666666">.</span>figure()
plt<span style="color: #666666">.</span>plot(np<span style="color: #666666">.</span>log10(lambdas), MSETrain, label <span style="color: #666666">=</span> <span style="color: #BA2121">&#39;MSE Ridge train&#39;</span>)
plt<span style="color: #666666">.</span>plot(np<span style="color: #666666">.</span>log10(lambdas), MSEPredict, <span style="color: #BA2121">&#39;r--&#39;</span>, label <span style="color: #666666">=</span> <span style="color: #BA2121">&#39;MSE Ridge Test&#39;</span>)
@@ -248,19 +248,19 @@ X_train_scaled <span style="color: #666666">=</span> scaler<span style="color: #
X_test_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(X_test)
<span style="color: #408080; font-style: italic"># matrix inversion to find beta</span>
OLSbeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> X_train) <span style="color: #666666">@</span> X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> y_train
<span style="color: #008000">print</span>(OLSbeta)
OLSbeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T @ X_train) @ X_train<span style="color: #666666">.</span>T @ y_train
<span style="color: #008000; font-weight: bold">print</span>(OLSbeta)
<span style="color: #408080; font-style: italic"># and then make the prediction</span>
ytildeOLS <span style="color: #666666">=</span> X_train <span style="color: #666666">@</span> OLSbeta
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Training R2 for OLS&quot;</span>)
<span style="color: #008000">print</span>(R2(y_train,ytildeOLS))
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Training MSE for OLS&quot;</span>)
<span style="color: #008000">print</span>(MSE(y_train,ytildeOLS))
ypredictOLS <span style="color: #666666">=</span> X_test <span style="color: #666666">@</span> OLSbeta
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Test R2 for OLS&quot;</span>)
<span style="color: #008000">print</span>(R2(y_test,ypredictOLS))
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Test MSE OLS&quot;</span>)
<span style="color: #008000">print</span>(MSE(y_test,ypredictOLS))
ytildeOLS <span style="color: #666666">=</span> X_train @ OLSbeta
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Training R2 for OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(R2(y_train,ytildeOLS))
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Training MSE for OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(MSE(y_train,ytildeOLS))
ypredictOLS <span style="color: #666666">=</span> X_test @ OLSbeta
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Test R2 for OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(R2(y_test,ypredictOLS))
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Test MSE OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(MSE(y_test,ypredictOLS))
<span style="color: #408080; font-style: italic"># Repeat now for Ridge regression and various values of the regularization parameter</span>
I <span style="color: #666666">=</span> np<span style="color: #666666">.</span>eye(p,p)
@@ -275,10 +275,10 @@ lambdas <span style="color: #666666">=</span> np<span style="color: #666666">.</
<span style="color: #408080; font-style: italic"># add ridge</span>
clf_ridge <span style="color: #666666">=</span> skl<span style="color: #666666">.</span>Ridge(alpha<span style="color: #666666">=</span>lmb)<span style="color: #666666">.</span>fit(X_train, y_train)
yridge <span style="color: #666666">=</span> clf_ridge<span style="color: #666666">.</span>predict(X_test)
Ridgebeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> X_train<span style="color: #666666">+</span>lmb<span style="color: #666666">*</span>I) <span style="color: #666666">@</span> X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> y_train
Ridgebeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T @ X_train<span style="color: #666666">+</span>lmb<span style="color: #666666">*</span>I) @ X_train<span style="color: #666666">.</span>T @ y_train
<span style="color: #408080; font-style: italic"># and then make the prediction</span>
ytildeRidge <span style="color: #666666">=</span> X_train <span style="color: #666666">@</span> Ridgebeta
ypredictRidge <span style="color: #666666">=</span> X_test <span style="color: #666666">@</span> Ridgebeta
ytildeRidge <span style="color: #666666">=</span> X_train @ Ridgebeta
ypredictRidge <span style="color: #666666">=</span> X_test @ Ridgebeta
MSEPredict[i] <span style="color: #666666">=</span> MSE(y_test,ypredictRidge)
MSEPredictSKL[i] <span style="color: #666666">=</span> MSE(y_test,yridge)
MSETrain[i] <span style="color: #666666">=</span> MSE(y_train,ytildeRidge)
@@ -341,10 +341,10 @@ X_train_scaled <span style="color: #666666">=</span> scaler<span style="color: #
X_test_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(X_test)
<span style="color: #408080; font-style: italic"># matrix inversion to find beta</span>
OLSbeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> X_train) <span style="color: #666666">@</span> X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> y_train
<span style="color: #008000">print</span>(OLSbeta)
OLSbeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T @ X_train) @ X_train<span style="color: #666666">.</span>T @ y_train
<span style="color: #008000; font-weight: bold">print</span>(OLSbeta)
<span style="color: #408080; font-style: italic"># The variance is given by the inverse of the matrix X^TX</span>
<span style="color: #008000">print</span>(np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> X_train))
<span style="color: #008000; font-weight: bold">print</span>(np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T @ X_train))
<span style="color: #408080; font-style: italic"># Repeat now for Ridge regression and various values of the regularization parameter</span>
I <span style="color: #666666">=</span> np<span style="color: #666666">.</span>eye(p,p)
@@ -356,8 +356,8 @@ MSETrain <span style="color: #666666">=</span> np<span style="color: #666666">.<
lambdas <span style="color: #666666">=</span> np<span style="color: #666666">.</span>logspace(<span style="color: #666666">-4</span>, <span style="color: #666666">0</span>, nlambdas)
<span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(nlambdas):
lmb <span style="color: #666666">=</span> lambdas[i]
Ridgebeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> X_train<span style="color: #666666">+</span>lmb<span style="color: #666666">*</span>I) <span style="color: #666666">@</span> X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> y_train
<span style="color: #008000">print</span>(np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> X_train<span style="color: #666666">+</span>lmb<span style="color: #666666">*</span>I))
Ridgebeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T @ X_train<span style="color: #666666">+</span>lmb<span style="color: #666666">*</span>I) @ X_train<span style="color: #666666">.</span>T @ y_train
<span style="color: #008000; font-weight: bold">print</span>(np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T @ X_train<span style="color: #666666">+</span>lmb<span style="color: #666666">*</span>I))
</pre></div>
<p>
<!-- --- end solution of exercise --- -->
@@ -408,19 +408,19 @@ X_train_scaled <span style="color: #666666">=</span> scaler<span style="color: #
X_test_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(X_test)
<span style="color: #408080; font-style: italic"># matrix inversion to find beta</span>
OLSbeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> X_train) <span style="color: #666666">@</span> X_train<span style="color: #666666">.</span>T <span style="color: #666666">@</span> y_train
<span style="color: #008000">print</span>(OLSbeta)
OLSbeta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X_train<span style="color: #666666">.</span>T @ X_train) @ X_train<span style="color: #666666">.</span>T @ y_train
<span style="color: #008000; font-weight: bold">print</span>(OLSbeta)
<span style="color: #408080; font-style: italic"># and then make the prediction</span>
ytildeOLS <span style="color: #666666">=</span> X_train <span style="color: #666666">@</span> OLSbeta
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Training R2 for OLS&quot;</span>)
<span style="color: #008000">print</span>(R2(y_train,ytildeOLS))
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Training MSE for OLS&quot;</span>)
<span style="color: #008000">print</span>(MSE(y_train,ytildeOLS))
ypredictOLS <span style="color: #666666">=</span> X_test <span style="color: #666666">@</span> OLSbeta
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Test R2 for OLS&quot;</span>)
<span style="color: #008000">print</span>(R2(y_test,ypredictOLS))
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Test MSE OLS&quot;</span>)
<span style="color: #008000">print</span>(MSE(y_test,ypredictOLS))
ytildeOLS <span style="color: #666666">=</span> X_train @ OLSbeta
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Training R2 for OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(R2(y_train,ytildeOLS))
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Training MSE for OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(MSE(y_train,ytildeOLS))
ypredictOLS <span style="color: #666666">=</span> X_test @ OLSbeta
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Test R2 for OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(R2(y_test,ypredictOLS))
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Test MSE OLS&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span>(MSE(y_test,ypredictOLS))
<span style="color: #408080; font-style: italic"># Repeat now for Ridge regression and various values of the regularization parameter</span>
I <span style="color: #666666">=</span> np<span style="color: #666666">.</span>eye(p,p)
@@ -600,7 +600,7 @@ x_train_scaled <span style="color: #666666">=</span> scaler<span style="color: #
x_test_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(x_test)
<span style="color: #008000; font-weight: bold">for</span> degree <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(maxdegree):
model <span style="color: #666666">=</span> make_pipeline(PolynomialFeatures(degree<span style="color: #666666">=</span>degree), LinearRegression(fit_intercept<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">False</span>))
model <span style="color: #666666">=</span> make_pipeline(PolynomialFeatures(degree<span style="color: #666666">=</span>degree), LinearRegression(fit_intercept<span style="color: #666666">=</span><span style="color: #008000">False</span>))
clf <span style="color: #666666">=</span> model<span style="color: #666666">.</span>fit(x_train_scale,y_train)
y_fit <span style="color: #666666">=</span> clf<span style="color: #666666">.</span>predict(x_train_scaled)
y_pred <span style="color: #666666">=</span> clf<span style="color: #666666">.</span>predict(x_test_scaled)
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+2 -2
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@@ -171,7 +171,7 @@ Homework 2, weeks 36 and 37
% --- begin date ---
\begin{center}
Sep 1, 2020
Sep 8, 2020
\end{center}
% --- end date ---
@@ -276,7 +276,7 @@ for i in range(nlambdas):
ypredictRidge = X_test @ Ridgebeta
MSEPredict[i] = MSE(y_test,ypredictRidge)
MSETrain[i] = MSE(y_train,ytildeRidge)
# Now plot the resulys
# Now plot the results
plt.figure()
plt.plot(np.log10(lambdas), MSETrain, label = 'MSE Ridge train')
plt.plot(np.log10(lambdas), MSEPredict, 'r--', label = 'MSE Ridge Test')
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doc/Projects/2020/hw2/pdf/hw2.tex
+22 -22
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@@ -141,7 +141,7 @@ Homework 2, weeks 36 and 37
% --- begin date ---
\begin{center}
Sep 1, 2020
Sep 8, 2020
\end{center}
% --- end date ---
@@ -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{verbatim}
\begin{print}
x = np.random.rand(100)
y = 2.0+5*x*x+0.1*np.random.randn(100)
\end{verbatim}
\end{print}
\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{verbatim}
\begin{print}
import os
import numpy as np
import pandas as pd
@@ -246,7 +246,7 @@ for i in range(nlambdas):
ypredictRidge = X_test @ Ridgebeta
MSEPredict[i] = MSE(y_test,ypredictRidge)
MSETrain[i] = MSE(y_train,ytildeRidge)
# Now plot the resulys
# Now plot the results
plt.figure()
plt.plot(np.log10(lambdas), MSETrain, label = 'MSE Ridge train')
plt.plot(np.log10(lambdas), MSEPredict, 'r--', label = 'MSE Ridge Test')
@@ -254,7 +254,7 @@ plt.xlabel('log10(lambda)')
plt.ylabel('MSE')
plt.legend()
plt.show()
\end{verbatim}
\end{print}
% --- 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{verbatim}
\begin{print}
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{verbatim}
\end{print}
% --- 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{verbatim}
\begin{print}
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
@@ -412,7 +412,7 @@ for i in range(nlambdas):
\end{verbatim}
\end{print}
% --- 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{verbatim}
\begin{print}
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{verbatim}
\end{print}
% --- 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{verbatim}
\begin{print}
# split in training and test data
X_train, X_test, y_train, y_test = train_test_split(X,y,test_size=0.2)
\end{verbatim}
\end{print}
Then we can use the standard scaler to scale our data as
\begin{verbatim}
\begin{print}
scaler = StandardScaler()
scaler.fit(X_train)
X_train_scaled = scaler.transform(X_train)
X_test_scaled = scaler.transform(X_test)
\end{verbatim}
\end{print}
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{verbatim}
\begin{print}
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{verbatim}
\end{print}
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{verbatim}
\begin{print}
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{verbatim}
\end{print}
% --- 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{verbatim}
\begin{print}
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{verbatim}
\end{print}
The plotting functionality of the first exercise can be reused here as well.
% --- end solution of exercise ---
doc/src/Projects/2020/Exercises/hw2.do.txt
+1 -1
View File
@@ -94,7 +94,7 @@ for i in range(nlambdas):
ypredictRidge = X_test @ Ridgebeta
MSEPredict[i] = MSE(y_test,ypredictRidge)
MSETrain[i] = MSE(y_train,ytildeRidge)
# Now plot the resulys
# Now plot the results
plt.figure()
plt.plot(np.log10(lambdas), MSETrain, label = 'MSE Ridge train')
plt.plot(np.log10(lambdas), MSEPredict, 'r--', label = 'MSE Ridge Test')
doc/src/Projects/2020/Exercises/make.sh
+7
View File
@@ -35,6 +35,9 @@ html=${name}-bs
system doconce format html $name --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=$html $opt
system doconce split_html $html.html --method=split --pagination --nav_button=bottom
# IPython notebook
system doconce format ipynb $name $opt
# Ordinary plain LaTeX document
system doconce format pdflatex $name --print_latex_style=trac --latex_admon=paragraph $opt
@@ -77,3 +80,7 @@ EOF
tar czf ${ipynb_tarfile} README.txt
fi
cp ${ipynb_tarfile} $dest/$name/ipynb