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    Explaining the algorithm's output
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    <p>
        In order to understand how ML algorithms arrive at a certain output value (forecast), it can be helpful to determine the importance of
        features used by the algorithm. The here introduced method to determine feature importance for
        complex ML algorithms is based on mathematical game theory. The method is capable of providing the <strong>feature importance
        for a single data point</strong> (e.g. the next one to predict) at a time and is hence a local method. The importance
        assigned to a single feature can vary from data point to data point (from one day to predict to another day to predict).
        <br/>
        <br/>
        The graph below shows how the feature importance with the respective impact on the algorithm's output can be visualized.
        <ul>
            <li>The <strong>"base value"</strong> is the average output value of the ML algorithm for all data points trained on before the experiment. </li>
            <li>The <strong>"output value"</strong> is the forecast of the ML algorithm. </li>
            <li>Starting from the "base value", the <strong>features with arrows pointing to the right</strong> "push" the actual output to higher values. </li>
            <li>Starting from the "base value", the <strong>features with arrows pointing to the left</strong> "push" the actual output to lower values. </li>
            <li>All positive and negative "pushing" adds up and hence cancels out partly. <strong>The result of the "pushing" is where the "output value" ends up</strong>. </li>
            <li>The <strong>importance of features</strong>, indicated by the bar segment size, <strong>is largest for the ones in the middle</strong> (next to the "output value"). The feature importance decreases towards both, the left and right end.</li>
            <li>Only <strong>features of which the importance amounts to at least 10%</strong> of the total length of the black bar are depicted in written form. A single feature's importance might change from data point to data point. </li>


        </ul>
    </p>

<img src="{% static "global/x/xplain.png" %}" width="950"/>


    <p>
        <h5>Example statements for the depicted graph</h5>
        <ul>
            <li>The "base value" is <strong>104.71</strong>. </li>
            <li>The "output value" is <strong>101.85</strong>. </li>
            <li>The <strong>6 features</strong> one can see amount to an <strong>importance of 10% or more</strong>. The other 9 features are not displayed as are less important.</li>
            <li>The features <strong>"Avg_weekday"</strong>, <strong>"1_year_ago"</strong> and <strong>"1_week_ago"</strong>>
                have values of <strong>100.52</strong>, <strong>102.0</strong> and <strong>110.0</strong> and "push" the output value to <strong>higher values</strong>.</li>
            <li>The features <strong>"Avg_year"</strong>, <strong>"Avg_month"</strong> and <strong>"Avg_week"</strong>
                have values of <strong>124.09</strong>, <strong>78.56</strong> and <strong>81.2</strong> and "push" the output value to <strong>lower values</strong>.</li>
            <li>In total, the importance of features "pushing" to lower values is larger than that of the ones "pushing"
                to higher values. Hence, the <strong>output value is below the base value</strong>.</li>
        </ul>
    </p>


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