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    <p class="toc_title"><i class="fas fa-list"></i>Contents</p>
    <ul class="toc_list">
        <li><a href="#Sample data description"><span class="toc_label">0</span>Sample data description</a></li>
        <li><a href="#Multiple linear regression"><span class="toc_label">1</span>Multiple linear regression</a></li>
        <ul>
            <li><a href="#Data encoding - regression with categorical variables"><span class="toc_label">Notes:</span>Data encoding - regression with categorical variables</a></li>
            <li><a href="#2D linear regression with scikit-learn"><span class="toc_label">Pythonic Tip:</span>2D regression with scikit-learn</a></li>
            <li><a href="#Forcing zero y-intercept"><span class="toc_label">Pythonic Tip:</span>Forcing zero y-intercept</a></li>
            <li><a href="#3D+ linear regression with scikit-learn"><span class="toc_label">Pythonic Tip:</span>3D+ regression with scikit-learn</a></li>
        </ul>
        <li><a href="#Introduction to multicollinearity"><span class="toc_label">2</span>Introduction to multicollinearity</a></li>
    </ul>
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    <p class="toc_title"><i class="fas fa-list"></i>Contents</p>
    <ul class="toc_list">
        <li><a href="#1.-Review-on-Word2Vec-Skip-Gram"><span class="toc_label">1.</span>
            Review on Word2Vec Skip-Gram</a></li>
        <ul>
            <li><a href="#1.1.-Review-on-Softmax"><span class="toc_label">1.1.</span>
                Review on Softmax</a></li>
            <li><a href="#1.2.-Softmax-is-computationally-very-expensive"><span class="toc_label">1.2.</span>
                Softmax is computationally very expensive</a></li>
        </ul>
        <li><a href="#2.-Skip-Gram-Negative-Sampling"><span class="toc_label">2.</span>
            Skip-Gram negative sampling</a></li>
        <li><a href="#sample_pop_var"><span class="toc_label">Notes:</span>Population variance $\sigma^2$ vs. Sample variance $s^2$</a></li>
        <ul>
            <li><a href="#2.1.-How-does-negative-sampling-work?"><span class="toc_label">2.1.</span>
                How does negative sampling work?</a></li>
                 <ul>
                    <li><a href="#2.1.1.-What-is-a-positive-word-$c_{pos}$?"><span class="toc_label">2.1.1.</span>
                        What is a positive word $c_{pos}$?</a></li>
                    <li><a href="#2.1.2.-What-is-a-negative-word-$c_{neg}$?"><span class="toc_label">2.1.2.</span>
                        What is a negative word $c_{neg}$?</a></li>
                    <li><a href="#2.1.3.-What-is-a-noise-distribution-$P_n(w)$?"><span class="toc_label">2.1.3.</span>
                        What is a noise distribution $P_n(w)$?</a></li>
                    <li><a href="#2.1.4.-How-are-negative-samples-drawn?"><span class="toc_label">2.1.4.</span>
                        How are negative samples drawn?</a></li>
                </ul>
            <li><a href="#2.2.-Derivation-of-Cost-Function-in-Negative-Sampling"><span class="toc_label">2.2.</span>
                Derivation of cost function in negative sampling</a></li>
            <li><a href="#2.3.-Derivation-of-gradients"><span class="toc_label">2.3.</span>
                Derivation of gradients</a></li>
                 <ul>
                    <li><a href="#2.3.1.-Gradients-with-respect-to-output-weight-matrix-$\frac{\partial-J}{\partial-W_{output}}$"><span class="toc_label">2.3.1.</span>
                        Gradients with respect to output weight matrix $\frac{\partial-J}{\partial-W_{output}}$</a></li>
                    <li><a href="#2.3.2.-Gradients-with-respect-to-input-weight-matrix-$\frac{\partial-J}{\partial-W_{input}}$"><span class="toc_label">2.3.2.</span>
                        Gradients with respect to input weight matrix $\frac{\partial-J}{\partial-W_{input}}$</a></li>
                </ul>
            <li><a href="#2.4-Negative-Sampling-Algorithm"><span class="toc_label">2.4.</span>
                Negative sampling algorithm</a></li>
            <li><a href="#2.5.-Numerical-Demonstration"><span class="toc_label">2.5.</span>
                Numerical demonstration</a></li>
        </ul>
    </ul>
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    <p class="toc_title"><i class="fas fa-list"></i>Contents</p>
    <ul class="toc_list">
        <li><a href="#Understanding confidence interval with analogy"><span class="toc_label">1</span>Understandingconfidence interval with analogy</a></li>
    </ul>
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