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<!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
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<!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
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<!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">Bias-Variance tradeoff with Bootstrap</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Cross-validation with Ridge</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">The Ising model</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Linear regression</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Singular Value decomposition</a></li>
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<!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">LASSO regression</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Performance as function of the regularization parameter</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Friday September 18: Intro to Logistic Regression</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">Logistic Regression</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Classification problems</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Optimization and Deep learning</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Basics</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Linear classifier</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Some selected properties</a></li>
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<!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">The logistic function</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Two parameters</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">Maximum likelihood</a></li>
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<!-- navigation toc: --> <li><a href="._week38-bs039.html#___sec38" style="font-size: 80%;">Wisconsin Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs040.html#___sec39" style="font-size: 80%;">Using the correlation matrix</a></li>
<!-- navigation toc: --> <li><a href="#___sec40" style="font-size: 80%;">Discussing the correlation data</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs042.html#___sec41" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
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<h2 id="___sec40" class="anchor">Discussing the correlation data </h2>
<p>
In the above example we note two things. In the first plot we display
the overlap of benign and malignant tumors as functions of the various
features in the Wisconsing breast cancer data set. We see that for
some of the features we can distinguish clearly the benign and
malignant cases while for other features we cannot. This can point to
us which features may be of greater interest when we wish to classify
a benign or not benign tumour.
<p>
In the second figure we have computed the so-called correlation
matrix, which in our case with thirty features becomes a \( 30\times 30 \)
matrix.
<p>
We constructed this matrix using <b>pandas</b> via the statements
<p>
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>cancerpd <span style="color: #666666">=</span> pd<span style="color: #666666">.</span>DataFrame(cancer<span style="color: #666666">.</span>data, columns<span style="color: #666666">=</span>cancer<span style="color: #666666">.</span>feature_names)
</pre></div>
<p>
and then
<p>
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>correlation_matrix <span style="color: #666666">=</span> cancerpd<span style="color: #666666">.</span>corr()<span style="color: #666666">.</span>round(<span style="color: #666666">1</span>)
</pre></div>
<p>
Diagonalizing this matrix we can in turn say something about which
features are of relevance and which are not. This leads us to
the classical Principal Component Analysis (PCA) theorem with
applications. This will be discussed later this semester (<a href="https://compphysics.github.io/MachineLearning/doc/pub/week43/html/week43-bs.html" target="_self">week 43</a>).
<p>
<p>
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<!-- navigation toc: --> <li><a href="._week38-bs001.html#___sec0" style="font-size: 80%;">Plans for week 38</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs002.html#___sec1" style="font-size: 80%;">Thursday September 17</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs003.html#___sec2" style="font-size: 80%;">Ridge and LASSO Regression, reminder</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs004.html#___sec3" style="font-size: 80%;">Various steps in cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs005.html#___sec4" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs006.html#___sec5" style="font-size: 80%;">Cross-validation in brief</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs007.html#___sec6" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs008.html#___sec7" style="font-size: 80%;">Bias-Variance tradeoff with Bootstrap</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs009.html#___sec8" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs010.html#___sec9" style="font-size: 80%;">Cross-validation with Ridge</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs011.html#___sec10" style="font-size: 80%;">The Ising model</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs012.html#___sec11" style="font-size: 80%;">Reformulating the problem to suit regression</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs013.html#___sec12" style="font-size: 80%;">Linear regression</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs014.html#___sec13" style="font-size: 80%;">Singular Value decomposition</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs015.html#___sec14" style="font-size: 80%;">The one-dimensional Ising model</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs016.html#___sec15" style="font-size: 80%;">Ridge regression</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs017.html#___sec16" style="font-size: 80%;">LASSO regression</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs018.html#___sec17" style="font-size: 80%;">Performance as function of the regularization parameter</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs019.html#___sec18" style="font-size: 80%;">Finding the optimal value of \( \lambda \)</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs020.html#___sec19" style="font-size: 80%;">Friday September 18: Intro to Logistic Regression</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs021.html#___sec20" style="font-size: 80%;">Logistic Regression</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs022.html#___sec21" style="font-size: 80%;">Classification problems</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs023.html#___sec22" style="font-size: 80%;">Optimization and Deep learning</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs024.html#___sec23" style="font-size: 80%;">Basics</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs025.html#___sec24" style="font-size: 80%;">Linear classifier</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs026.html#___sec25" style="font-size: 80%;">Some selected properties</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs027.html#___sec26" style="font-size: 80%;">Simple example</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs028.html#___sec27" style="font-size: 80%;">Plotting the mean value for each group</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs029.html#___sec28" style="font-size: 80%;">The logistic function</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs030.html#___sec29" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs031.html#___sec30" style="font-size: 80%;">Two parameters</a></li>
<!-- navigation toc: --> <li><a href="._week38-bs032.html#___sec31" style="font-size: 80%;">Maximum likelihood</a></li>
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<!-- navigation toc: --> <li><a href="._week38-bs036.html#___sec35" style="font-size: 80%;">Extending to more predictors</a></li>
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<!-- navigation toc: --> <li><a href="#___sec41" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
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<h2 id="___sec41" class="anchor">Other measures in classification studies: Cancer Data again </h2>
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<!-- code=python (!bc pycod) typeset with pygments style "default" -->
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span> train_test_split
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.datasets</span> <span style="color: #008000; font-weight: bold">import</span> load_breast_cancer
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.linear_model</span> <span style="color: #008000; font-weight: bold">import</span> LogisticRegression
<span style="color: #408080; font-style: italic"># Load the data</span>
cancer <span style="color: #666666">=</span> load_breast_cancer()
X_train, X_test, y_train, y_test <span style="color: #666666">=</span> train_test_split(cancer<span style="color: #666666">.</span>data,cancer<span style="color: #666666">.</span>target,random_state<span style="color: #666666">=0</span>)
<span style="color: #008000; font-weight: bold">print</span>(X_train<span style="color: #666666">.</span>shape)
<span style="color: #008000; font-weight: bold">print</span>(X_test<span style="color: #666666">.</span>shape)
<span style="color: #408080; font-style: italic"># Logistic Regression</span>
logreg <span style="color: #666666">=</span> LogisticRegression(solver<span style="color: #666666">=</span><span style="color: #BA2121">&#39;lbfgs&#39;</span>)
logreg<span style="color: #666666">.</span>fit(X_train, y_train)
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Test set accuracy with Logistic Regression: {:.2f}&quot;</span><span style="color: #666666">.</span>format(logreg<span style="color: #666666">.</span>score(X_test,y_test)))
<span style="color: #408080; font-style: italic">#now scale the data</span>
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.preprocessing</span> <span style="color: #008000; font-weight: bold">import</span> StandardScaler
scaler <span style="color: #666666">=</span> StandardScaler()
scaler<span style="color: #666666">.</span>fit(X_train)
X_train_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(X_train)
X_test_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(X_test)
<span style="color: #408080; font-style: italic"># Logistic Regression</span>
logreg<span style="color: #666666">.</span>fit(X_train_scaled, y_train)
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Test set accuracy Logistic Regression with scaled data: {:.2f}&quot;</span><span style="color: #666666">.</span>format(logreg<span style="color: #666666">.</span>score(X_test_scaled,y_test)))
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.preprocessing</span> <span style="color: #008000; font-weight: bold">import</span> LabelEncoder
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span> cross_validate
<span style="color: #408080; font-style: italic">#Cross validation</span>
accuracy <span style="color: #666666">=</span> cross_validate(logreg,X_test_scaled,y_test,cv<span style="color: #666666">=10</span>)[<span style="color: #BA2121">&#39;test_score&#39;</span>]
<span style="color: #008000; font-weight: bold">print</span>(accuracy)
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Test set accuracy with Logistic Regression and scaled data: {:.2f}&quot;</span><span style="color: #666666">.</span>format(logreg<span style="color: #666666">.</span>score(X_test_scaled,y_test)))
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">scikitplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">skplt</span>
y_pred <span style="color: #666666">=</span> logreg<span style="color: #666666">.</span>predict(X_test_scaled)
skplt<span style="color: #666666">.</span>metrics<span style="color: #666666">.</span>plot_confusion_matrix(y_test, y_pred, normalize<span style="color: #666666">=</span><span style="color: #008000">True</span>)
plt<span style="color: #666666">.</span>show()
y_probas <span style="color: #666666">=</span> logreg<span style="color: #666666">.</span>predict_proba(X_test_scaled)
skplt<span style="color: #666666">.</span>metrics<span style="color: #666666">.</span>plot_roc(y_test, y_probas)
plt<span style="color: #666666">.</span>show()
skplt<span style="color: #666666">.</span>metrics<span style="color: #666666">.</span>plot_cumulative_gain(y_test, y_probas)
plt<span style="color: #666666">.</span>show()
</pre></div>
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