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<div class="reveal">
<div class="slides">
<section id="title-slide" data-background-image="images/main.jpg" class="quarto-title-block center">
<h1 class="title">Machine Learning in Economics</h1>
<div class="quarto-title-authors">
<div class="quarto-title-author">
<div class="quarto-title-author-name">
Wooyong Park
</div>
</div>
</div>
</section>
<section id="agenda" class="slide level2">
<h2>Agenda</h2>
<div class="cell">
<style type="text/css">
.my_class1 {
height: 200px;
}
</style>
</div>
<ul>
<li><p style="font-size: 30px;">
Penalized Regressions
</p>
<ul>
<li><p style="font-size: 30px;">
Ridge Regression and LASSO
</p></li>
</ul></li>
</ul>
<p><br></p>
<ul>
<li><p style="font-size: 30px;">
Tree-based Models
</p>
<ul>
<li><p style="font-size: 30px;">
Decision Trees and Forests
</p></li>
<li><p style="font-size: 30px;">
Causal Trees
</p></li>
</ul></li>
</ul>
</section>
<section id="disclaimer" class="slide level2">
<h2>Disclaimer</h2>
<p>I brought quite an extensive combination of useful materials. You can find tons of materials to learn, understand, and practice ML. That also means that there are tons of algorithms and processes that we can’t cover in these slides.</p>
<p>Indeed, important areas of ML such as deep learning, cross validation, theoretical aspects of bias-variance tradeoffs are dropped out here.</p>
<p>Also, in these slides, we only focus on supervised ML, where there are correct answers and we want the model to find them.</p>
</section>
<section>
<section id="what-is-our-primary-interest" class="title-slide slide level1 center">
<h1>What is our primary interest?</h1>
</section>
<section id="machine-learning-and-econometrics" class="slide level2">
<h2>Machine Learning and Econometrics</h2>
<p><br></p>
<div class="columns">
<div class="column" style="width:50%;">
<h3 id="prediction">Prediction</h3>
<p>In ML and recent applied statistics, people want a better prediction of the future or a specific value from a new data, which often does not require statistical properties or CIs.</p>
<h3 id="estimation">Estimation</h3>
<p>In econometrics, people want to understand the DGP, obtain causal parameters and their statistical properties or CIs.</p>
</div><div class="column" style="width:50%;">
<div class="cell">
<div class="cell-output-display">
<div>
<figure>
<p><img data-src="MLCI_files/figure-revealjs/unnamed-chunk-2-1.png" width="768"></p>
</figure>
</div>
</div>
</div>
</div></div>
</section>
<section id="machine-learning-and-econometrics-1" class="slide level2">
<h2>Machine Learning and Econometrics</h2>
<p><br></p>
<div class="columns">
<div class="column" style="width:50%;">
<h3 id="prediction-1">Prediction</h3>
<p>We find <span class="math inline">\(f\)</span> such that <span class="math display">\[ f(X_i) \approx y_i\]</span></p>
<h3 id="estimation-1">Estimation</h3>
<p>We find <span class="math inline">\(g\)</span> such that</p>
<p><span class="math inline">\(g(X_i) \approx y_i\)</span> and <span class="math inline">\(\nabla g(X_i)\)</span> captures the causal effect.</p>
<p>e.g. Hotel fees and reservation rates</p>
</div><div class="column" style="width:50%;">
<div class="cell">
<div class="cell-output-display">
<div>
<figure>
<p><img data-src="MLCI_files/figure-revealjs/unnamed-chunk-3-3.png" width="768"></p>
</figure>
</div>
</div>
</div>
</div></div>
</section>
<section id="machine-learning-and-econometrics-2" class="slide level2">
<h2>Machine Learning and Econometrics</h2>
<p>In most cases, we need both prediction and estimation.</p>
<p>Rather than relying on one strategy, why don’t we allocate the tasks to whoever is good at them?</p>
<p><strong>Example 1)</strong> Imputation with ML, and causal inference with IVs</p>
<p><strong>Example 2)</strong> Select out covariates with LASSO to reduce the dimension, and do the rest with DiD</p>
<p><strong>Example 3)</strong> Minimize the MSE on the suggested causal parameters rather than on outcomes.</p>
</section></section>
<section>
<section id="penalized-regressions" class="title-slide slide level1 center">
<h1>Penalized Regressions</h1>
</section>
<section id="background" class="slide level2">
<h2>Background</h2>
<p>Penalized regressions, or regularized regressions, are regressions with loss functions modified to reduce the possibility of overfitting. Usually, large coefficients lead to overfitting. Thus, penalized regressions such as ridge regressions and LASSO(Least Absolute Shrinkage and Selection Operator) penalizes large sized coefficients, by including the size of coefficients into the loss function.</p>
<h3 id="loss-function-of-ols">Loss Function of OLS</h3>
<p><span class="math display">\[
MSE = \sum_{i=1}^n(y_i-X_i'\beta)^2
\]</span></p>
<h3 id="loss-function-of-ridgelasso">Loss Function of Ridge/LASSO</h3>
<p><span class="math display">\[
Loss(\beta;\alpha) = MSE + \alpha\cdot\sum_{k=1}^K||\beta_k||
\]</span></p>
</section>
<section id="the-problem-with-overfitting" class="slide level2">
<h2>The Problem with overfitting</h2>
<p><img data-src="figures/Overfitting.png" style="height:5in"></p>
</section>
<section id="ridge-regressions-and-lasso" class="slide level2">
<h2>Ridge Regressions and LASSO</h2>
<p>Details are in my <a href="https://wyeconomics.github.io/ML_intro/ML_Python.html#penalized-regressions">web document</a>.</p>
<div class="columns">
<div class="column" style="width:50%;">
<h3 id="ridge">Ridge</h3>
<p><span class="math display">\[
Loss(\beta; \alpha) = MSE + \alpha\cdot\sum_{k=1}^K\beta_k^2
\]</span></p>
<h3 id="lasso">LASSO</h3>
<p><span class="math display">\[
Loss(\beta; \alpha) = MSE + \alpha\cdot\sum_{k=1}^K|\beta_k|
\]</span></p>
</div><div class="column" style="width:50%;">
<div class="quarto-figure quarto-figure-center">
<figure>
<p><img data-src="figures/lasso_ridge.png"></p>
<figcaption>(Figure from Datacamp)</figcaption>
</figure>
</div>
</div></div>
<div class="fragment">
<ul>
<li>Here, <span class="math inline">\(\alpha\)</span> is called a <em>hyperparameter</em>, a parameter that we choose to optimize the prediction.</li>
<li>In the case of <span class="math inline">\(\alpha = 0\)</span>, LASSO would be equivalent to OLS.</li>
<li>LASSO shrinks the coefficients of less important features to zero</li>
</ul>
</div>
</section></section>
<section>
<section id="practice-with-python" class="title-slide slide level1 center">
<h1>Practice with Python</h1>
</section>
<section id="loading-data" class="slide level2">
<h2>Loading Data</h2>
<div class="cell">
<details class="code-fold">
<summary>Code</summary>
<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode numberSource python code-overflow-scroll number-lines code-with-copy"><code class="sourceCode python"><span id="cb1-1"><a href=""></a><span class="co">#libraries</span></span>
<span id="cb1-2"><a href=""></a><span class="im">import</span> pandas <span class="im">as</span> pd</span>
<span id="cb1-3"><a href=""></a><span class="im">import</span> numpy <span class="im">as</span> np</span>
<span id="cb1-4"><a href=""></a><span class="im">import</span> seaborn <span class="im">as</span> sns</span>
<span id="cb1-5"><a href=""></a><span class="im">import</span> matplotlib.pyplot <span class="im">as</span> plt</span>
<span id="cb1-6"><a href=""></a><span class="im">from</span> sklearn.model_selection <span class="im">import</span> train_test_split</span>
<span id="cb1-7"><a href=""></a><span class="im">from</span> sklearn.linear_model <span class="im">import</span> LinearRegression</span>
<span id="cb1-8"><a href=""></a><span class="im">from</span> sklearn.linear_model <span class="im">import</span> Lasso</span>
<span id="cb1-9"><a href=""></a><span class="im">from</span> sklearn.preprocessing <span class="im">import</span> StandardScaler</span>
<span id="cb1-10"><a href=""></a><span class="im">from</span> sklearn.datasets <span class="im">import</span> fetch_california_housing</span>
<span id="cb1-11"><a href=""></a></span>
<span id="cb1-12"><a href=""></a><span class="co">#data</span></span>
<span id="cb1-13"><a href=""></a>housing <span class="op">=</span> fetch_california_housing()</span>
<span id="cb1-14"><a href=""></a></span>
<span id="cb1-15"><a href=""></a>X <span class="op">=</span> fetch_california_housing(as_frame <span class="op">=</span> <span class="va">True</span>)[<span class="st">'data'</span>]</span>
<span id="cb1-16"><a href=""></a>y <span class="op">=</span> fetch_california_housing(as_frame <span class="op">=</span> <span class="va">True</span>)[<span class="st">'target'</span>]</span>
<span id="cb1-17"><a href=""></a></span>
<span id="cb1-18"><a href=""></a>data <span class="op">=</span> pd.concat([X, y], axis <span class="op">=</span> <span class="dv">1</span>)</span>
<span id="cb1-19"><a href=""></a></span>
<span id="cb1-20"><a href=""></a><span class="co">#Exploration</span></span>
<span id="cb1-21"><a href=""></a>plt.figure(figsize <span class="op">=</span> (<span class="dv">10</span>, <span class="dv">10</span>))</span>
<span id="cb1-22"><a href=""></a>sns.heatmap(data.corr(), annot <span class="op">=</span> <span class="va">True</span>)</span>
<span id="cb1-23"><a href=""></a><span class="bu">print</span>(<span class="st">'features: '</span>, X.columns)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</details>
<div class="cell-output cell-output-stdout">
<pre><code>features: Index(['MedInc', 'HouseAge', 'AveRooms', 'AveBedrms', 'Population', 'AveOccup',
'Latitude', 'Longitude'],
dtype='object')</code></pre>
</div>
<details class="code-fold">
<summary>Code</summary>
<div class="sourceCode cell-code" id="cb3"><pre class="sourceCode numberSource python code-overflow-scroll number-lines code-with-copy"><code class="sourceCode python"><span id="cb3-1"><a href=""></a><span class="bu">print</span>(<span class="st">'target: '</span>, y.name)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</details>
<div class="cell-output cell-output-stdout">
<pre><code>target: MedHouseVal</code></pre>
</div>
</div>
<img data-src="MLCI_files/figure-revealjs/unnamed-chunk-4-5.png" width="960" class="r-stretch"></section>
<section id="data-splitting-and-normalization" class="slide level2">
<h2>Data Splitting and Normalization</h2>
<div class="cell">
<div class="sourceCode cell-code" id="cb5"><pre class="sourceCode numberSource python code-overflow-scroll number-lines code-with-copy"><code class="sourceCode python"><span id="cb5-1"><a href=""></a>features <span class="op">=</span> data.columns[<span class="dv">0</span>:<span class="dv">8</span>]</span>
<span id="cb5-2"><a href=""></a>target <span class="op">=</span> data.columns[<span class="op">-</span><span class="dv">1</span>]</span>
<span id="cb5-3"><a href=""></a></span>
<span id="cb5-4"><a href=""></a><span class="co">#X and y values</span></span>
<span id="cb5-5"><a href=""></a>X <span class="op">=</span> data[features].values</span>
<span id="cb5-6"><a href=""></a>y <span class="op">=</span> data[target].values</span>
<span id="cb5-7"><a href=""></a></span>
<span id="cb5-8"><a href=""></a><span class="co">#split</span></span>
<span id="cb5-9"><a href=""></a>X_train, X_test, y_train, y_test <span class="op">=</span> train_test_split(X, y, test_size<span class="op">=</span><span class="fl">0.3</span>, random_state<span class="op">=</span><span class="dv">17</span>)</span>
<span id="cb5-10"><a href=""></a></span>
<span id="cb5-11"><a href=""></a><span class="co"># Normalization</span></span>
<span id="cb5-12"><a href=""></a>scaler <span class="op">=</span> StandardScaler()</span>
<span id="cb5-13"><a href=""></a>X_train <span class="op">=</span> scaler.fit_transform(X_train)</span>
<span id="cb5-14"><a href=""></a>X_test <span class="op">=</span> scaler.transform(X_test)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
<section id="lassoalpha3" class="slide level2">
<h2>LASSO(<span class="math inline">\(\alpha=3\)</span>)</h2>
<div class="cell">
<div class="sourceCode cell-code" id="cb6"><pre class="sourceCode numberSource python code-overflow-scroll number-lines code-with-copy"><code class="sourceCode python"><span id="cb6-1"><a href=""></a><span class="co">#Lasso regression model</span></span>
<span id="cb6-2"><a href=""></a></span>
<span id="cb6-3"><a href=""></a>lasso <span class="op">=</span> Lasso(alpha <span class="op">=</span> <span class="dv">3</span>)</span>
<span id="cb6-4"><a href=""></a>lasso.fit(X_train,y_train)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output-display">
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#sk-container-id-1 a.estimator_doc_link:hover {
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color: var(--sklearn-color-background);
text-decoration: none;
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}
</style><div id="sk-container-id-1" class="sk-top-container"><div class="sk-text-repr-fallback"><pre>Lasso(alpha=3)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br>On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class="sk-container" hidden=""><div class="sk-item"><div class="sk-estimator fitted sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-1" type="checkbox" checked=""><label for="sk-estimator-id-1" class="sk-toggleable__label fitted sk-toggleable__label-arrow"><div><div>Lasso</div></div><div><a class="sk-estimator-doc-link fitted" rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.6/modules/generated/sklearn.linear_model.Lasso.html">?<span>Documentation for Lasso</span></a><span class="sk-estimator-doc-link fitted">i<span>Fitted</span></span></div></label><div class="sk-toggleable__content fitted"><pre>Lasso(alpha=3)</pre></div> </div></div></div></div>
</div>
<div class="sourceCode cell-code" id="cb7"><pre class="sourceCode numberSource python code-overflow-scroll number-lines code-with-copy"><code class="sourceCode python"><span id="cb7-1"><a href=""></a></span>
<span id="cb7-2"><a href=""></a>pd.Series(lasso.coef_, features).sort_values(ascending <span class="op">=</span> <span class="va">True</span>).plot(kind <span class="op">=</span> <span class="st">"bar"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<img data-src="MLCI_files/figure-revealjs/unnamed-chunk-6-7.png" width="960" class="r-stretch"></section>
<section id="lassoalpha0.1" class="slide level2">
<h2>LASSO(<span class="math inline">\(\alpha=0.1\)</span>)</h2>
<div class="cell">
<div class="sourceCode cell-code" id="cb8"><pre class="sourceCode numberSource python code-overflow-scroll number-lines code-with-copy"><code class="sourceCode python"><span id="cb8-1"><a href=""></a><span class="co">#Lasso regression model</span></span>
<span id="cb8-2"><a href=""></a></span>
<span id="cb8-3"><a href=""></a>lasso <span class="op">=</span> Lasso(alpha <span class="op">=</span> <span class="fl">0.1</span>)</span>
<span id="cb8-4"><a href=""></a>lasso.fit(X_train,y_train)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output-display">
<style>#sk-container-id-2 {
/* Definition of color scheme common for light and dark mode */
--sklearn-color-text: #000;
--sklearn-color-text-muted: #666;
--sklearn-color-line: gray;
/* Definition of color scheme for unfitted estimators */
--sklearn-color-unfitted-level-0: #fff5e6;
--sklearn-color-unfitted-level-1: #f6e4d2;
--sklearn-color-unfitted-level-2: #ffe0b3;
--sklearn-color-unfitted-level-3: chocolate;
/* Definition of color scheme for fitted estimators */
--sklearn-color-fitted-level-0: #f0f8ff;
--sklearn-color-fitted-level-1: #d4ebff;
--sklearn-color-fitted-level-2: #b3dbfd;
--sklearn-color-fitted-level-3: cornflowerblue;
/* Specific color for light theme */
--sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));
--sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));
--sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));
--sklearn-color-icon: #696969;
@media (prefers-color-scheme: dark) {
/* Redefinition of color scheme for dark theme */
--sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));
--sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));
--sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));
--sklearn-color-icon: #878787;
}
}
#sk-container-id-2 {
color: var(--sklearn-color-text);
}
#sk-container-id-2 pre {
padding: 0;
}
#sk-container-id-2 input.sk-hidden--visually {
border: 0;
clip: rect(1px 1px 1px 1px);
clip: rect(1px, 1px, 1px, 1px);
height: 1px;
margin: -1px;
overflow: hidden;
padding: 0;
position: absolute;
width: 1px;
}
#sk-container-id-2 div.sk-dashed-wrapped {
border: 1px dashed var(--sklearn-color-line);
margin: 0 0.4em 0.5em 0.4em;
box-sizing: border-box;
padding-bottom: 0.4em;
background-color: var(--sklearn-color-background);
}
#sk-container-id-2 div.sk-container {
/* jupyter's `normalize.less` sets `[hidden] { display: none; }`
but bootstrap.min.css set `[hidden] { display: none !important; }`
so we also need the `!important` here to be able to override the
default hidden behavior on the sphinx rendered scikit-learn.org.
See: https://github.com/scikit-learn/scikit-learn/issues/21755 */
display: inline-block !important;
position: relative;
}
#sk-container-id-2 div.sk-text-repr-fallback {
display: none;
}
div.sk-parallel-item,
div.sk-serial,
div.sk-item {
/* draw centered vertical line to link estimators */
background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));
background-size: 2px 100%;
background-repeat: no-repeat;
background-position: center center;
}
/* Parallel-specific style estimator block */
#sk-container-id-2 div.sk-parallel-item::after {
content: "";
width: 100%;
border-bottom: 2px solid var(--sklearn-color-text-on-default-background);
flex-grow: 1;
}
#sk-container-id-2 div.sk-parallel {
display: flex;
align-items: stretch;
justify-content: center;
background-color: var(--sklearn-color-background);
position: relative;
}
#sk-container-id-2 div.sk-parallel-item {
display: flex;
flex-direction: column;
}
#sk-container-id-2 div.sk-parallel-item:first-child::after {
align-self: flex-end;
width: 50%;
}
#sk-container-id-2 div.sk-parallel-item:last-child::after {
align-self: flex-start;
width: 50%;
}
#sk-container-id-2 div.sk-parallel-item:only-child::after {
width: 0;
}
/* Serial-specific style estimator block */
#sk-container-id-2 div.sk-serial {
display: flex;
flex-direction: column;
align-items: center;
background-color: var(--sklearn-color-background);
padding-right: 1em;
padding-left: 1em;
}
/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is
clickable and can be expanded/collapsed.
- Pipeline and ColumnTransformer use this feature and define the default style
- Estimators will overwrite some part of the style using the `sk-estimator` class
*/
/* Pipeline and ColumnTransformer style (default) */
#sk-container-id-2 div.sk-toggleable {
/* Default theme specific background. It is overwritten whether we have a
specific estimator or a Pipeline/ColumnTransformer */