added about huber cost function

This commit is contained in:
mhjensen
2019-12-20 22:36:34 +01:00
parent 38e5126383
commit a70aa87228
8 changed files with 242 additions and 1112 deletions
@@ -148,7 +148,7 @@ MathJax.Hub.Config({
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
<br>
<p>&nbsp;<br>
<center><h4>Aug 14, 2019</h4></center> <!-- date -->
<center><h4>Dec 20, 2019</h4></center> <!-- date -->
<br>
<h2 id="___sec0">Introduction </h2>
@@ -1089,6 +1089,15 @@ $$
$$
<p>&nbsp;<br>
<p>
The squared cost function results in an arithmetic mean-unbiased
estimator, and the absolute-value cost function results in a
median-unbiased estimator (in the one-dimensional case, and a
geometric median-unbiased estimator for the multi-dimensional
case). The squared cost function has the disadvantage that it has the tendency
to be dominated by outliers.
<p>
We can modify easily the above Python code and plot the relative error instead
<p>
@@ -1202,7 +1211,7 @@ $$
$$
<p>&nbsp;<br>
Finally we present the
We present the
squared logarithmic (quadratic) error
<p>&nbsp;<br>
$$
@@ -1216,6 +1225,11 @@ estimate is best to use when targets having exponential growth, such
as population counts, average sales of a commodity over a span of
years etc.
<p>
Finally, another cost function is the Huber cost function used in robust regression.
It is less sensitive to outliers in data than the squared error cost function.
A variant for classification is also sometimes used, a quantity we will meet later.
<p>
We will discuss in more
detail these and other functions in the various lectures. We conclude this part with another example. Instead of