mhjensen
235 lines
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HTML
235 lines
13 KiB
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'sections': [('Logistic Regression', 2, None, '___sec0'),
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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-bs002.html#___sec1" style="font-size: 80%;">Optimization and Deep learning</a></li>
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<!-- navigation toc: --> <li><a href="._LogReg-bs003.html#___sec2" style="font-size: 80%;">Basics</a></li>
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<!-- navigation toc: --> <li><a href="._LogReg-bs005.html#___sec4" style="font-size: 80%;">Some selected properties</a></li>
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<!-- navigation toc: --> <li><a href="._LogReg-bs006.html#___sec5" style="font-size: 80%;">The logistic function</a></li>
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<!-- navigation toc: --> <li><a href="._LogReg-bs007.html#___sec6" style="font-size: 80%;">Two parameters</a></li>
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<!-- navigation toc: --> <li><a href="._LogReg-bs008.html#___sec7" style="font-size: 80%;">Maximum likelihood</a></li>
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<!-- navigation toc: --> <li><a href="._LogReg-bs009.html#___sec8" style="font-size: 80%;">The cost function rewritten</a></li>
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<!-- navigation toc: --> <li><a href="._LogReg-bs010.html#___sec9" style="font-size: 80%;">Minimizing the cross entropy</a></li>
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<!-- navigation toc: --> <li><a href="._LogReg-bs011.html#___sec10" style="font-size: 80%;">A more compact expression</a></li>
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<!-- navigation toc: --> <li><a href="._LogReg-bs012.html#___sec11" style="font-size: 80%;">Extending to more predictors</a></li>
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<!-- navigation toc: --> <li><a href="._LogReg-bs013.html#___sec12" style="font-size: 80%;">Including more classes</a></li>
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<!-- navigation toc: --> <li><a href="._LogReg-bs014.html#___sec13" style="font-size: 80%;">The Softmax function</a></li>
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<!-- navigation toc: --> <li><a href="._LogReg-bs015.html#___sec14" style="font-size: 80%;">A <b>scikit-learn</b> example</a></li>
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<!-- navigation toc: --> <li><a href="._LogReg-bs016.html#___sec15" style="font-size: 80%;">A simple classification problem</a></li>
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<!-- navigation toc: --> <li><a href="._LogReg-bs017.html#___sec16" style="font-size: 80%;">The two-dimensional Ising model, Predicting phase transition of the two-dimensional Ising model</a></li>
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<!-- navigation toc: --> <li><a href="#___sec17" style="font-size: 80%;">Reading in the data</a></li>
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<!-- navigation toc: --> <li><a href="._LogReg-bs019.html#___sec18" 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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<!-- navigation toc: --> <li><a href="._LogReg-bs021.html#___sec20" style="font-size: 80%;">Accuracy of a classification model</a></li>
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<!-- navigation toc: --> <li><a href="._LogReg-bs022.html#___sec21" style="font-size: 80%;">Analyzing the results</a></li>
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<!-- !split -->
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<h2 id="___sec17" class="anchor">Reading in the data </h2>
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<p>
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Using the data from <a href="https://physics.bu.edu/~pankajm/ML-Review-Datasets/isingMC/" target="_self">Mehta et al.</a> (specifically the two datasets named <code>Ising2DFM_reSample_L40_T=All.pkl</code> and <code>Ising2DFM_reSample_L40_T=All_labels.pkl</code>) we have to unpack the data into numpy arrays.
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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>filenames <span style="color: #666666">=</span> glob<span style="color: #666666">.</span>glob(os<span style="color: #666666">.</span>path<span style="color: #666666">.</span>join(<span style="color: #BA2121">".."</span>, <span style="color: #BA2121">"dat"</span>, <span style="color: #BA2121">"*"</span>))
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label_filename <span style="color: #666666">=</span> <span style="color: #008000">list</span>(<span style="color: #008000">filter</span>(<span style="color: #008000; font-weight: bold">lambda</span> x: <span style="color: #BA2121">"label"</span> <span style="color: #AA22FF; font-weight: bold">in</span> x, filenames))[<span style="color: #666666">0</span>]
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dat_filename <span style="color: #666666">=</span> <span style="color: #008000">list</span>(<span style="color: #008000">filter</span>(<span style="color: #008000; font-weight: bold">lambda</span> x: <span style="color: #BA2121">"label"</span> <span style="color: #AA22FF; font-weight: bold">not</span> <span style="color: #AA22FF; font-weight: bold">in</span> x, filenames))[<span style="color: #666666">0</span>]
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<span style="color: #408080; font-style: italic"># Read in the labels</span>
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<span style="color: #008000; font-weight: bold">with</span> <span style="color: #008000">open</span>(label_filename, <span style="color: #BA2121">"rb"</span>) <span style="color: #008000; font-weight: bold">as</span> f:
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labels <span style="color: #666666">=</span> pickle<span style="color: #666666">.</span>load(f)
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<span style="color: #408080; font-style: italic"># Read in the corresponding configurations</span>
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<span style="color: #008000; font-weight: bold">with</span> <span style="color: #008000">open</span>(dat_filename, <span style="color: #BA2121">"rb"</span>) <span style="color: #008000; font-weight: bold">as</span> f:
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data <span style="color: #666666">=</span> np<span style="color: #666666">.</span>unpackbits(pickle<span style="color: #666666">.</span>load(f))<span style="color: #666666">.</span>reshape(<span style="color: #666666">-1</span>, <span style="color: #666666">1600</span>)<span style="color: #666666">.</span>astype(<span style="color: #BA2121">"int"</span>)
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<span style="color: #408080; font-style: italic"># Set spin-down to -1</span>
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data[data <span style="color: #666666">==</span> <span style="color: #666666">0</span>] <span style="color: #666666">=</span> <span style="color: #666666">-1</span>
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</pre></div>
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<p>
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This dataset consists of \( 10000 \) samples, i.e., \( 10000 \) spin
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configurations with \( 40 \times 40 \) spins each, for \( 16 \) temperatures
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between \( 0.25 \) to \( 4.0 \). Next we create a train/test-split and keep
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the data in the critical phase as a separate dataset for
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extrapolation-testing.
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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"># Set up slices of the dataset</span>
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ordered <span style="color: #666666">=</span> <span style="color: #008000">slice</span>(<span style="color: #666666">0</span>, <span style="color: #666666">70000</span>)
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critical <span style="color: #666666">=</span> <span style="color: #008000">slice</span>(<span style="color: #666666">70000</span>, <span style="color: #666666">100000</span>)
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disordered <span style="color: #666666">=</span> <span style="color: #008000">slice</span>(<span style="color: #666666">100000</span>, <span style="color: #666666">160000</span>)
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X_train, X_test, y_train, y_test <span style="color: #666666">=</span> skms<span style="color: #666666">.</span>train_test_split(
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np<span style="color: #666666">.</span>concatenate((data[ordered], data[disordered])),
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np<span style="color: #666666">.</span>concatenate((labels[ordered], labels[disordered])),
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test_size<span style="color: #666666">=0.95</span>
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)
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</pre></div>
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<p>
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Using a small training set yields a better accuracy. This will be discussed in the end.
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