added about huber cost function
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@@ -148,7 +148,7 @@ MathJax.Hub.Config({
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<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
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<br>
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<p> <br>
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<center><h4>Aug 14, 2019</h4></center> <!-- date -->
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<center><h4>Dec 20, 2019</h4></center> <!-- date -->
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<br>
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<h2 id="___sec0">Introduction </h2>
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@@ -1089,6 +1089,15 @@ $$
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$$
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<p> <br>
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<p>
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The squared cost function results in an arithmetic mean-unbiased
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estimator, and the absolute-value cost function results in a
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median-unbiased estimator (in the one-dimensional case, and a
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geometric median-unbiased estimator for the multi-dimensional
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case). The squared cost function has the disadvantage that it has the tendency
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to be dominated by outliers.
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<p>
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We can modify easily the above Python code and plot the relative error instead
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<p>
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@@ -1202,7 +1211,7 @@ $$
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$$
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<p> <br>
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Finally we present the
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We present the
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squared logarithmic (quadratic) error
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<p> <br>
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$$
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@@ -1216,6 +1225,11 @@ estimate is best to use when targets having exponential growth, such
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as population counts, average sales of a commodity over a span of
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years etc.
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<p>
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Finally, another cost function is the Huber cost function used in robust regression.
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It is less sensitive to outliers in data than the squared error cost function.
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A variant for classification is also sometimes used, a quantity we will meet later.
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<p>
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We will discuss in more
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detail these and other functions in the various lectures. We conclude this part with another example. Instead of
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