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mhjensen 8f4b87d5bd More cleaning up of equations
2018-10-11 11:27:08 +02:00

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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-bs020.html#___sec19" style="font-size: 80%;">Exploring the logistic regression</a></li>
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<h2 id="___sec20" class="anchor">Accuracy of a classification model </h2>
<p>
To determine how well a classification model is performing we count
the number of correctly labeled classes and divide by the number of
classes in total. The accuracy is thus given by
$$
\begin{align}
a(y, \hat{y}) = \frac{1}{n}\sum_{i = 1}^{n} I(y_i = \hat{y}_i),
\tag{7}
\end{align}
$$
<p>
where \( I(y_i = \hat{y}_i) \) is the indicator function given by
$$
\begin{align}
I(x = y) = \begin{array}{cc}
1 & x = y, \\
0 & x \neq y.
\end{array}
\tag{8}
\end{align}$$
<p>
This is the accuracy provided by Scikit-learn when using <b>sklearn.metrics.accuracyscore</b>.
<p>
Below we compute the accuracy of the best fit model on the training data (which should give a good accuracy), the test data (which has not been shown to the model) and the critical data (completely new data that needs to be extrapolated).
<p>
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>train_accuracy <span style="color: #666666">=</span> skm<span style="color: #666666">.</span>accuracy_score(y_train, clf<span style="color: #666666">.</span>predict(X_train))
test_accuracy <span style="color: #666666">=</span> skm<span style="color: #666666">.</span>accuracy_score(y_test, clf<span style="color: #666666">.</span>predict(X_test))
critical_accuracy <span style="color: #666666">=</span> skm<span style="color: #666666">.</span>accuracy_score(labels[critical], clf<span style="color: #666666">.</span>predict(data[critical]))
<span style="color: #008000; font-weight: bold">print</span> (<span style="color: #BA2121">&quot;Accuracy on train data: {0}&quot;</span><span style="color: #666666">.</span>format(train_accuracy))
<span style="color: #008000; font-weight: bold">print</span> (<span style="color: #BA2121">&quot;Accuracy on test data: {0}&quot;</span><span style="color: #666666">.</span>format(test_accuracy))
<span style="color: #008000; font-weight: bold">print</span> (<span style="color: #BA2121">&quot;Accuracy on critical data: {0}&quot;</span><span style="color: #666666">.</span>format(critical_accuracy))
</pre></div>
<p>
We can see that we get quite good accuracy on the training data, but gradually worsening accuracy on the test and critical data.
<p>
<p>
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