-
@@ -1202,8 +1202,15 @@ years etc.
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. + +
+The rationale behind this possible cost function is its reduced +sensitivity to outliers in the data set. In our discussions on +dimensionality reduction and normalization of data we will meet other +ways of dealing with outliers. + +
+The Huber cost function is defined as $$ H_{\delta}(a)={\begin{cases}{\frac {1}{2}}{a^{2}}&{\text{for }}|a|\leq \delta ,\\\delta (|a|-{\frac {1}{2}}\delta ),&{\text{otherwise.}}\end{cases}}}. $$ diff --git a/doc/pub/How2ReadData/html/How2ReadData-reveal.html b/doc/pub/How2ReadData/html/How2ReadData-reveal.html index aa3250a20..fca65e9cc 100644 --- a/doc/pub/How2ReadData/html/How2ReadData-reveal.html +++ b/doc/pub/How2ReadData/html/How2ReadData-reveal.html @@ -148,7 +148,7 @@ MathJax.Hub.Config({
-
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. + +
+The rationale behind this possible cost function is its reduced +sensitivity to outliers in the data set. In our discussions on +dimensionality reduction and normalization of data we will meet other +ways of dealing with outliers. + +
+The Huber cost function is defined as
$$
H_{\delta}(a)={\begin{cases}{\frac {1}{2}}{a^{2}}&{\text{for }}|a|\leq \delta ,\\\delta (|a|-{\frac {1}{2}}\delta ),&{\text{otherwise.}}\end{cases}}}.
diff --git a/doc/pub/How2ReadData/html/How2ReadData-solarized.html b/doc/pub/How2ReadData/html/How2ReadData-solarized.html
index 19a89ca88..a94087cb1 100644
--- a/doc/pub/How2ReadData/html/How2ReadData-solarized.html
+++ b/doc/pub/How2ReadData/html/How2ReadData-solarized.html
@@ -135,7 +135,7 @@ MathJax.Hub.Config({
-
Finally, another cost function is the Huber cost function used in robust regression. -It is less sensitive to outliers in data than the squared error cost function. -A variant for classification is also sometimes used, a quantity we will meet later. + +
+The rationale behind this possible cost function is its reduced +sensitivity to outliers in the data set. In our discussions on +dimensionality reduction and normalization of data we will meet other +ways of dealing with outliers. + +
+The Huber cost function is defined as $$ H_{\delta}(a)={\begin{cases}{\frac {1}{2}}{a^{2}}&{\text{for }}|a|\leq \delta ,\\\delta (|a|-{\frac {1}{2}}\delta ),&{\text{otherwise.}}\end{cases}}}. $$ diff --git a/doc/pub/How2ReadData/html/How2ReadData.html b/doc/pub/How2ReadData/html/How2ReadData.html index f26cca548..592f193f8 100644 --- a/doc/pub/How2ReadData/html/How2ReadData.html +++ b/doc/pub/How2ReadData/html/How2ReadData.html @@ -140,7 +140,7 @@ MathJax.Hub.Config({
-
Finally, another cost function is the Huber cost function used in robust regression. -It is less sensitive to outliers in data than the squared error cost function. -A variant for classification is also sometimes used, a quantity we will meet later. + +
+The rationale behind this possible cost function is its reduced +sensitivity to outliers in the data set. In our discussions on +dimensionality reduction and normalization of data we will meet other +ways of dealing with outliers. + +
+The Huber cost function is defined as $$ H_{\delta}(a)={\begin{cases}{\frac {1}{2}}{a^{2}}&{\text{for }}|a|\leq \delta ,\\\delta (|a|-{\frac {1}{2}}\delta ),&{\text{otherwise.}}\end{cases}}}. $$ diff --git a/doc/pub/How2ReadData/ipynb/How2ReadData.ipynb b/doc/pub/How2ReadData/ipynb/How2ReadData.ipynb index c940c1063..8713448e5 100644 --- a/doc/pub/How2ReadData/ipynb/How2ReadData.ipynb +++ b/doc/pub/How2ReadData/ipynb/How2ReadData.ipynb @@ -10,7 +10,7 @@ " \n", "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n", "\n", - "Date: **Dec 24, 2019**\n", + "Date: **Dec 25, 2019**\n", "\n", "Copyright 1999-2019, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n", "\n", @@ -1458,8 +1458,13 @@ "\n", "\n", "Finally, another cost function is the Huber cost function used in robust regression.\n", - "It is less sensitive to outliers in data than the squared error cost function.\n", - "A variant for classification is also sometimes used, a quantity we will meet later." + "\n", + "The rationale behind this possible cost function is its reduced\n", + "sensitivity to outliers in the data set. In our discussions on\n", + "dimensionality reduction and normalization of data we will meet other\n", + "ways of dealing with outliers.\n", + "\n", + "The Huber cost function is defined as" ] }, { diff --git a/doc/pub/How2ReadData/ipynb/ipynb-How2ReadData-src.tar.gz b/doc/pub/How2ReadData/ipynb/ipynb-How2ReadData-src.tar.gz index 453cc2ce1..7900604e4 100644 Binary files a/doc/pub/How2ReadData/ipynb/ipynb-How2ReadData-src.tar.gz and b/doc/pub/How2ReadData/ipynb/ipynb-How2ReadData-src.tar.gz differ diff --git a/doc/pub/How2ReadData/pdf/How2ReadData-minted.pdf b/doc/pub/How2ReadData/pdf/How2ReadData-minted.pdf index b58b71f46..7692b4334 100644 Binary files a/doc/pub/How2ReadData/pdf/How2ReadData-minted.pdf and b/doc/pub/How2ReadData/pdf/How2ReadData-minted.pdf differ diff --git a/doc/src/How2ReadData/How2ReadData.do.txt b/doc/src/How2ReadData/How2ReadData.do.txt index 52452c11d..4c4e0463e 100644 --- a/doc/src/How2ReadData/How2ReadData.do.txt +++ b/doc/src/How2ReadData/How2ReadData.do.txt @@ -938,8 +938,13 @@ years etc. 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. + +The rationale behind this possible cost function is its reduced +sensitivity to outliers in the data set. In our discussions on +dimensionality reduction and normalization of data we will meet other +ways of dealing with outliers. + +The Huber cost function is defined as !bt \[ H_{\delta}(a)={\begin{cases}{\frac {1}{2}}{a^{2}}&{\text{for }}|a|\leq \delta ,\\\delta (|a|-{\frac {1}{2}}\delta ),&{\text{otherwise.}}\end{cases}}}.