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381 lines
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{'highest level': 2,
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'sections': [('Logistic Regression', 2, None, '___sec0'),
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('Optimization and Deep learning', 2, None, '___sec1'),
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('Basics', 2, None, '___sec2'),
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('Linear classifier', 2, None, '___sec3'),
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('Some selected properties', 2, None, '___sec4'),
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('The logistic function', 2, None, '___sec5'),
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('Examples of likelihood functions used in logistic regression '
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('Extending to more predictors', 2, None, '___sec12'),
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('Including more classes', 2, None, '___sec13'),
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('More classes', 2, None, '___sec14'),
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('A simple classification problem', 2, None, '___sec15'),
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('The Credit Card example', 2, None, '___sec16')]}
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<!-- navigation toc: --> <li><a href="._LogReg-bs001.html#___sec0" style="font-size: 80%;">Logistic Regression</a></li>
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<!-- navigation toc: --> <li><a href="._LogReg-bs013.html#___sec12" style="font-size: 80%;">Extending to more predictors</a></li>
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<!-- navigation toc: --> <li><a href="#___sec16" style="font-size: 80%;">The Credit Card example</a></li>
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<h2 id="___sec16" class="anchor">The Credit Card example </h2>
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Here we use the the <a href="https://archive.ics.uci.edu/ml/datasets/default+of+credit+card+clients" target="_self">credit card data</a>. More text to come.
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<p>
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<!-- code=python (!bc pycod) typeset with pygments style "default" -->
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<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">pandas</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">pd</span>
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<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">os</span>
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<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>
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<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
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<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> OneHotEncoder
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<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.compose</span> <span style="color: #008000; font-weight: bold">import</span> ColumnTransformer
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<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, OneHotEncoder
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<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.metrics</span> <span style="color: #008000; font-weight: bold">import</span> confusion_matrix, accuracy_score, roc_auc_score
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<span style="color: #408080; font-style: italic"># Trying to set the seed</span>
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np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>seed(<span style="color: #666666">0</span>)
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<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">random</span>
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random<span style="color: #666666">.</span>seed(<span style="color: #666666">0</span>)
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<span style="color: #408080; font-style: italic"># Reading file into data frame</span>
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cwd <span style="color: #666666">=</span> os<span style="color: #666666">.</span>getcwd()
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filename <span style="color: #666666">=</span> cwd <span style="color: #666666">+</span> <span style="color: #BA2121">'/default of credit card clients.xls'</span>
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nanDict <span style="color: #666666">=</span> {}
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df <span style="color: #666666">=</span> pd<span style="color: #666666">.</span>read_excel(filename, header<span style="color: #666666">=1</span>, skiprows<span style="color: #666666">=0</span>, index_col<span style="color: #666666">=0</span>, na_values<span style="color: #666666">=</span>nanDict)
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df<span style="color: #666666">.</span>rename(index<span style="color: #666666">=</span><span style="color: #008000">str</span>, columns<span style="color: #666666">=</span>{<span style="color: #BA2121">"default payment next month"</span>: <span style="color: #BA2121">"defaultPaymentNextMonth"</span>}, inplace<span style="color: #666666">=</span><span style="color: #008000">True</span>)
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<span style="color: #408080; font-style: italic"># Features and targets </span>
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X <span style="color: #666666">=</span> df<span style="color: #666666">.</span>loc[:, df<span style="color: #666666">.</span>columns <span style="color: #666666">!=</span> <span style="color: #BA2121">'defaultPaymentNextMonth'</span>]<span style="color: #666666">.</span>values
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y <span style="color: #666666">=</span> df<span style="color: #666666">.</span>loc[:, df<span style="color: #666666">.</span>columns <span style="color: #666666">==</span> <span style="color: #BA2121">'defaultPaymentNextMonth'</span>]<span style="color: #666666">.</span>values
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<span style="color: #408080; font-style: italic"># Categorical variables to one-hot's</span>
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onehotencoder <span style="color: #666666">=</span> OneHotEncoder(categories<span style="color: #666666">=</span><span style="color: #BA2121">"auto"</span>)
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X <span style="color: #666666">=</span> ColumnTransformer(
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[(<span style="color: #BA2121">""</span>, onehotencoder, [<span style="color: #666666">3</span>]),],
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remainder<span style="color: #666666">=</span><span style="color: #BA2121">"passthrough"</span>
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)<span style="color: #666666">.</span>fit_transform(X)
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y<span style="color: #666666">.</span>shape
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<span style="color: #408080; font-style: italic"># Train-test split</span>
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trainingShare <span style="color: #666666">=</span> <span style="color: #666666">0.5</span>
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seed <span style="color: #666666">=</span> <span style="color: #666666">1</span>
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XTrain, XTest, yTrain, yTest<span style="color: #666666">=</span>train_test_split(X, y, train_size<span style="color: #666666">=</span>trainingShare, \
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test_size <span style="color: #666666">=</span> <span style="color: #666666">1-</span>trainingShare,
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random_state<span style="color: #666666">=</span>seed)
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<span style="color: #408080; font-style: italic"># Input Scaling</span>
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sc <span style="color: #666666">=</span> StandardScaler()
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XTrain <span style="color: #666666">=</span> sc<span style="color: #666666">.</span>fit_transform(XTrain)
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XTest <span style="color: #666666">=</span> sc<span style="color: #666666">.</span>transform(XTest)
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<span style="color: #408080; font-style: italic"># One-hot's of the target vector</span>
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Y_train_onehot, Y_test_onehot <span style="color: #666666">=</span> onehotencoder<span style="color: #666666">.</span>fit_transform(yTrain), onehotencoder<span style="color: #666666">.</span>fit_transform(yTest)
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<span style="color: #408080; font-style: italic"># Remove instances with zeros only for past bill statements or paid amounts</span>
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<span style="color: #BA2121; font-style: italic">'''</span>
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<span style="color: #BA2121; font-style: italic">df = df.drop(df[(df.BILL_AMT1 == 0) &</span>
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<span style="color: #BA2121; font-style: italic"> (df.BILL_AMT2 == 0) &</span>
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<span style="color: #BA2121; font-style: italic"> (df.BILL_AMT3 == 0) &</span>
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<span style="color: #BA2121; font-style: italic"> (df.BILL_AMT4 == 0) &</span>
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<span style="color: #BA2121; font-style: italic"> (df.BILL_AMT5 == 0) &</span>
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<span style="color: #BA2121; font-style: italic"> (df.BILL_AMT6 == 0) &</span>
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<span style="color: #BA2121; font-style: italic"> (df.PAY_AMT1 == 0) &</span>
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<span style="color: #BA2121; font-style: italic"> (df.PAY_AMT2 == 0) &</span>
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<span style="color: #BA2121; font-style: italic"> (df.PAY_AMT3 == 0) &</span>
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<span style="color: #BA2121; font-style: italic"> (df.PAY_AMT4 == 0) &</span>
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<span style="color: #BA2121; font-style: italic"> (df.PAY_AMT5 == 0) &</span>
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<span style="color: #BA2121; font-style: italic"> (df.PAY_AMT6 == 0)].index)</span>
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<span style="color: #BA2121; font-style: italic">'''</span>
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df <span style="color: #666666">=</span> df<span style="color: #666666">.</span>drop(df[(df<span style="color: #666666">.</span>BILL_AMT1 <span style="color: #666666">==</span> <span style="color: #666666">0</span>) <span style="color: #666666">&</span>
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(df<span style="color: #666666">.</span>BILL_AMT2 <span style="color: #666666">==</span> <span style="color: #666666">0</span>) <span style="color: #666666">&</span>
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(df<span style="color: #666666">.</span>BILL_AMT3 <span style="color: #666666">==</span> <span style="color: #666666">0</span>) <span style="color: #666666">&</span>
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(df<span style="color: #666666">.</span>BILL_AMT4 <span style="color: #666666">==</span> <span style="color: #666666">0</span>) <span style="color: #666666">&</span>
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(df<span style="color: #666666">.</span>BILL_AMT5 <span style="color: #666666">==</span> <span style="color: #666666">0</span>) <span style="color: #666666">&</span>
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(df<span style="color: #666666">.</span>BILL_AMT6 <span style="color: #666666">==</span> <span style="color: #666666">0</span>)]<span style="color: #666666">.</span>index)
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df <span style="color: #666666">=</span> df<span style="color: #666666">.</span>drop(df[(df<span style="color: #666666">.</span>PAY_AMT1 <span style="color: #666666">==</span> <span style="color: #666666">0</span>) <span style="color: #666666">&</span>
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(df<span style="color: #666666">.</span>PAY_AMT2 <span style="color: #666666">==</span> <span style="color: #666666">0</span>) <span style="color: #666666">&</span>
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(df<span style="color: #666666">.</span>PAY_AMT3 <span style="color: #666666">==</span> <span style="color: #666666">0</span>) <span style="color: #666666">&</span>
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(df<span style="color: #666666">.</span>PAY_AMT4 <span style="color: #666666">==</span> <span style="color: #666666">0</span>) <span style="color: #666666">&</span>
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(df<span style="color: #666666">.</span>PAY_AMT5 <span style="color: #666666">==</span> <span style="color: #666666">0</span>) <span style="color: #666666">&</span>
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(df<span style="color: #666666">.</span>PAY_AMT6 <span style="color: #666666">==</span> <span style="color: #666666">0</span>)]<span style="color: #666666">.</span>index)
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<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
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<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> GridSearchCV
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lambdas<span style="color: #666666">=</span>np<span style="color: #666666">.</span>logspace(<span style="color: #666666">-5</span>,<span style="color: #666666">7</span>,<span style="color: #666666">13</span>)
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parameters <span style="color: #666666">=</span> [{<span style="color: #BA2121">'C'</span>: <span style="color: #666666">1./</span>lambdas, <span style="color: #BA2121">"solver"</span>:[<span style="color: #BA2121">"lbfgs"</span>]}]<span style="color: #408080; font-style: italic">#*len(parameters)}]</span>
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scoring <span style="color: #666666">=</span> [<span style="color: #BA2121">'accuracy'</span>, <span style="color: #BA2121">'roc_auc'</span>]
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logReg <span style="color: #666666">=</span> LogisticRegression()
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gridSearch <span style="color: #666666">=</span> GridSearchCV(logReg, parameters, cv<span style="color: #666666">=5</span>, scoring<span style="color: #666666">=</span>scoring, refit<span style="color: #666666">=</span><span style="color: #BA2121">'roc_auc'</span>)
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</pre></div>
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<p>
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<!-- code=python (!bc pycod) typeset with pygments style "default" -->
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<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #408080; font-style: italic"># "refit" gives the metric used deciding best model. </span>
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<span style="color: #408080; font-style: italic"># See more http://scikit-learn.org/stable/auto_examples/model_selection/plot_multi_metric_evaluation.html</span>
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gridSearch<span style="color: #666666">.</span>fit(XTrain, yTrain<span style="color: #666666">.</span>ravel())
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<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">gridSearchSummary</span>(method, scoring):
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<span style="color: #BA2121; font-style: italic">"""Prints best parameters from Grid search</span>
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<span style="color: #BA2121; font-style: italic"> and AUC with standard deviation for all </span>
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<span style="color: #BA2121; font-style: italic"> parameter combos """</span>
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method <span style="color: #666666">=</span> <span style="color: #008000">eval</span>(method)
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<span style="color: #008000; font-weight: bold">if</span> scoring <span style="color: #666666">==</span> <span style="color: #BA2121">'accuracy'</span>:
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mean <span style="color: #666666">=</span> <span style="color: #BA2121">'mean_test_score'</span>
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sd <span style="color: #666666">=</span> <span style="color: #BA2121">'std_test_score'</span>
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<span style="color: #008000; font-weight: bold">elif</span> scoring <span style="color: #666666">==</span> <span style="color: #BA2121">'auc'</span>:
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mean <span style="color: #666666">=</span> <span style="color: #BA2121">'mean_test_roc_auc'</span>
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sd <span style="color: #666666">=</span> <span style="color: #BA2121">'std_test_roc_auc'</span>
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<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"Best: </span><span style="color: #BB6688; font-weight: bold">%f</span><span style="color: #BA2121"> using </span><span style="color: #BB6688; font-weight: bold">%s</span><span style="color: #BA2121">"</span> <span style="color: #666666">%</span> (method<span style="color: #666666">.</span>best_score_, method<span style="color: #666666">.</span>best_params_))
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means <span style="color: #666666">=</span> method<span style="color: #666666">.</span>cv_results_[mean]
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stds <span style="color: #666666">=</span> method<span style="color: #666666">.</span>cv_results_[sd]
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params <span style="color: #666666">=</span> method<span style="color: #666666">.</span>cv_results_[<span style="color: #BA2121">'params'</span>]
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<span style="color: #008000; font-weight: bold">for</span> mean, stdev, param <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">zip</span>(means, stds, params):
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<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"</span><span style="color: #BB6688; font-weight: bold">%f</span><span style="color: #BA2121"> (</span><span style="color: #BB6688; font-weight: bold">%f</span><span style="color: #BA2121">) with: </span><span style="color: #BB6688; font-weight: bold">%r</span><span style="color: #BA2121">"</span> <span style="color: #666666">%</span> (mean, stdev, param))
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<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">createConfusionMatrix</span>(method, printOut<span style="color: #666666">=</span><span style="color: #008000">True</span>):
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<span style="color: #BA2121; font-style: italic">"""</span>
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<span style="color: #BA2121; font-style: italic"> Computes and prints confusion matrices, accuracy scores,</span>
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<span style="color: #BA2121; font-style: italic"> and AUC for test and training sets </span>
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<span style="color: #BA2121; font-style: italic"> """</span>
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confusionArray <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(<span style="color: #666666">6</span>, dtype<span style="color: #666666">=</span><span style="color: #008000">object</span>)
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method <span style="color: #666666">=</span> <span style="color: #008000">eval</span>(method)
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<span style="color: #408080; font-style: italic"># Train</span>
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yPredTrain <span style="color: #666666">=</span> method<span style="color: #666666">.</span>predict(XTrain)
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yPredTrain <span style="color: #666666">=</span> (yPredTrain <span style="color: #666666">></span> <span style="color: #666666">0.5</span>)
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cm <span style="color: #666666">=</span> confusion_matrix(
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yTrain, yPredTrain)
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cm <span style="color: #666666">=</span> np<span style="color: #666666">.</span>around(cm<span style="color: #666666">/</span>cm<span style="color: #666666">.</span>sum(axis<span style="color: #666666">=1</span>)[:,<span style="color: #008000">None</span>], <span style="color: #666666">2</span>)
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confusionArray[<span style="color: #666666">0</span>] <span style="color: #666666">=</span> cm
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accScore <span style="color: #666666">=</span> accuracy_score(yTrain, yPredTrain)
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confusionArray[<span style="color: #666666">1</span>] <span style="color: #666666">=</span> accScore
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AUC <span style="color: #666666">=</span> roc_auc_score(yTrain, yPredTrain)
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confusionArray[<span style="color: #666666">2</span>] <span style="color: #666666">=</span> AUC
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<span style="color: #008000; font-weight: bold">if</span> printOut:
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<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">'</span><span style="color: #BB6622; font-weight: bold">\n</span><span style="color: #BA2121">################### Training ###############'</span>)
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<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">'</span><span style="color: #BB6622; font-weight: bold">\n</span><span style="color: #BA2121">Training Confusion matrix: </span><span style="color: #BB6622; font-weight: bold">\n</span><span style="color: #BA2121">'</span>, cm)
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<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">'</span><span style="color: #BB6622; font-weight: bold">\n</span><span style="color: #BA2121">Training Accuracy score: </span><span style="color: #BB6622; font-weight: bold">\n</span><span style="color: #BA2121">'</span>, accScore)
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<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">'</span><span style="color: #BB6622; font-weight: bold">\n</span><span style="color: #BA2121">Train AUC: </span><span style="color: #BB6622; font-weight: bold">\n</span><span style="color: #BA2121">'</span>, AUC)
|
|
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<span style="color: #408080; font-style: italic"># Test</span>
|
|
yPred <span style="color: #666666">=</span> method<span style="color: #666666">.</span>predict(XTest)
|
|
yPred <span style="color: #666666">=</span> (yPred <span style="color: #666666">></span> <span style="color: #666666">0.5</span>)
|
|
cm <span style="color: #666666">=</span> confusion_matrix(
|
|
yTest, yPred)
|
|
cm <span style="color: #666666">=</span> np<span style="color: #666666">.</span>around(cm<span style="color: #666666">/</span>cm<span style="color: #666666">.</span>sum(axis<span style="color: #666666">=1</span>)[:,<span style="color: #008000">None</span>], <span style="color: #666666">2</span>)
|
|
confusionArray[<span style="color: #666666">3</span>] <span style="color: #666666">=</span> cm
|
|
|
|
accScore <span style="color: #666666">=</span> accuracy_score(yTest, yPred)
|
|
confusionArray[<span style="color: #666666">4</span>] <span style="color: #666666">=</span> accScore
|
|
|
|
AUC <span style="color: #666666">=</span> roc_auc_score(yTest, yPred)
|
|
confusionArray[<span style="color: #666666">5</span>] <span style="color: #666666">=</span> AUC
|
|
|
|
<span style="color: #008000; font-weight: bold">if</span> printOut:
|
|
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">'</span><span style="color: #BB6622; font-weight: bold">\n</span><span style="color: #BA2121">################### Testing ###############'</span>)
|
|
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">'</span><span style="color: #BB6622; font-weight: bold">\n</span><span style="color: #BA2121">Test Confusion matrix: </span><span style="color: #BB6622; font-weight: bold">\n</span><span style="color: #BA2121">'</span>, cm)
|
|
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">'</span><span style="color: #BB6622; font-weight: bold">\n</span><span style="color: #BA2121">Test Accuracy score: </span><span style="color: #BB6622; font-weight: bold">\n</span><span style="color: #BA2121">'</span>, accScore)
|
|
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">'</span><span style="color: #BB6622; font-weight: bold">\n</span><span style="color: #BA2121">TestAUC: </span><span style="color: #BB6622; font-weight: bold">\n</span><span style="color: #BA2121">'</span>, AUC)
|
|
|
|
<span style="color: #008000; font-weight: bold">return</span> confusionArray
|
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|
|
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<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">seaborn</span>
|
|
<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>
|
|
|
|
seaborn<span style="color: #666666">.</span>set(style<span style="color: #666666">=</span><span style="color: #BA2121">"white"</span>, context<span style="color: #666666">=</span><span style="color: #BA2121">"notebook"</span>, font_scale<span style="color: #666666">=1.5</span>,
|
|
rc<span style="color: #666666">=</span>{<span style="color: #BA2121">"axes.grid"</span>: <span style="color: #008000">True</span>, <span style="color: #BA2121">"legend.frameon"</span>: <span style="color: #008000">False</span>,
|
|
<span style="color: #BA2121">"lines.markeredgewidth"</span>: <span style="color: #666666">1.4</span>, <span style="color: #BA2121">"lines.markersize"</span>: <span style="color: #666666">10</span>})
|
|
seaborn<span style="color: #666666">.</span>set_context(<span style="color: #BA2121">"notebook"</span>, font_scale<span style="color: #666666">=1.5</span>, rc<span style="color: #666666">=</span>{<span style="color: #BA2121">"lines.linewidth"</span>: <span style="color: #666666">4.5</span>})
|
|
|
|
yPred <span style="color: #666666">=</span> gridSearch<span style="color: #666666">.</span>predict_proba(XTest)
|
|
<span style="color: #008000; font-weight: bold">print</span>(yTest<span style="color: #666666">.</span>ravel()<span style="color: #666666">.</span>shape, yPred<span style="color: #666666">.</span>shape)
|
|
|
|
<span style="color: #408080; font-style: italic">#skplt.metrics.plot_cumulative_gain(yTest.ravel(), yPred_onehot)</span>
|
|
skplt<span style="color: #666666">.</span>metrics<span style="color: #666666">.</span>plot_cumulative_gain(yTest<span style="color: #666666">.</span>ravel(), yPred)
|
|
|
|
defaults <span style="color: #666666">=</span> <span style="color: #008000">sum</span>(yTest <span style="color: #666666">==</span> <span style="color: #666666">1</span>)
|
|
total <span style="color: #666666">=</span> <span style="color: #008000">len</span>(yTest)
|
|
defaultRate <span style="color: #666666">=</span> defaults<span style="color: #666666">/</span>total
|
|
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">bestCurve</span>(defaults, total, defaultRate):
|
|
x <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linspace(<span style="color: #666666">0</span>, <span style="color: #666666">1</span>, total)
|
|
|
|
y1 <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linspace(<span style="color: #666666">0</span>, <span style="color: #666666">1</span>, defaults)
|
|
y2 <span style="color: #666666">=</span> np<span style="color: #666666">.</span>ones(total<span style="color: #666666">-</span>defaults)
|
|
y3 <span style="color: #666666">=</span> np<span style="color: #666666">.</span>concatenate([y1,y2])
|
|
<span style="color: #008000; font-weight: bold">return</span> x, y3
|
|
|
|
x, best <span style="color: #666666">=</span> bestCurve(defaults<span style="color: #666666">=</span>defaults, total<span style="color: #666666">=</span>total, defaultRate<span style="color: #666666">=</span>defaultRate)
|
|
plt<span style="color: #666666">.</span>plot(x, best)
|
|
|
|
|
|
plt<span style="color: #666666">.</span>show()
|
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</pre></div>
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<p>
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