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. +A variant for classification is also sometimes used, a quantity we will meet later. +$$ +L_{\delta }(a)={\begin{cases}{\frac {1}{2}}{a^{2}}&{\text{for }}|a|\leq \delta ,\\\delta (|a|-{\frac {1}{2}}\delta ),&{\text{otherwise.}}\end{cases}}}L_{\delta }(a)={\begin{cases}{\frac {1}{2}}{a^{2}}&{\text{for }}|a|\leq \delta ,\\\delta (|a|-{\frac {1}{2}}\delta ),&{\text{otherwise.}}\end{cases}} +$$
We will discuss in more diff --git a/doc/pub/How2ReadData/html/How2ReadData-reveal.html b/doc/pub/How2ReadData/html/How2ReadData-reveal.html index dbf50c07d..57f2f2221 100644 --- a/doc/pub/How2ReadData/html/How2ReadData-reveal.html +++ b/doc/pub/How2ReadData/html/How2ReadData-reveal.html @@ -1228,7 +1228,12 @@ 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. +A variant for classification is also sometimes used, a quantity we will meet later. +
+$$
+L_{\delta }(a)={\begin{cases}{\frac {1}{2}}{a^{2}}&{\text{for }}|a|\leq \delta ,\\\delta (|a|-{\frac {1}{2}}\delta ),&{\text{otherwise.}}\end{cases}}}L_{\delta }(a)={\begin{cases}{\frac {1}{2}}{a^{2}}&{\text{for }}|a|\leq \delta ,\\\delta (|a|-{\frac {1}{2}}\delta ),&{\text{otherwise.}}\end{cases}}
+$$
+
We will discuss in more diff --git a/doc/pub/How2ReadData/html/How2ReadData-solarized.html b/doc/pub/How2ReadData/html/How2ReadData-solarized.html index 5feadf7ba..2d5f087e3 100644 --- a/doc/pub/How2ReadData/html/How2ReadData-solarized.html +++ b/doc/pub/How2ReadData/html/How2ReadData-solarized.html @@ -1163,7 +1163,10 @@ 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. +A variant for classification is also sometimes used, a quantity we will meet later. +$$ +L_{\delta }(a)={\begin{cases}{\frac {1}{2}}{a^{2}}&{\text{for }}|a|\leq \delta ,\\\delta (|a|-{\frac {1}{2}}\delta ),&{\text{otherwise.}}\end{cases}}}L_{\delta }(a)={\begin{cases}{\frac {1}{2}}{a^{2}}&{\text{for }}|a|\leq \delta ,\\\delta (|a|-{\frac {1}{2}}\delta ),&{\text{otherwise.}}\end{cases}} +$$
We will discuss in more diff --git a/doc/pub/How2ReadData/html/How2ReadData.html b/doc/pub/How2ReadData/html/How2ReadData.html index 154c9bac9..26137487f 100644 --- a/doc/pub/How2ReadData/html/How2ReadData.html +++ b/doc/pub/How2ReadData/html/How2ReadData.html @@ -1168,7 +1168,10 @@ 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. +A variant for classification is also sometimes used, a quantity we will meet later. +$$ +L_{\delta }(a)={\begin{cases}{\frac {1}{2}}{a^{2}}&{\text{for }}|a|\leq \delta ,\\\delta (|a|-{\frac {1}{2}}\delta ),&{\text{otherwise.}}\end{cases}}}L_{\delta }(a)={\begin{cases}{\frac {1}{2}}{a^{2}}&{\text{for }}|a|\leq \delta ,\\\delta (|a|-{\frac {1}{2}}\delta ),&{\text{otherwise.}}\end{cases}} +$$
We will discuss in more diff --git a/doc/pub/How2ReadData/ipynb/How2ReadData.ipynb b/doc/pub/How2ReadData/ipynb/How2ReadData.ipynb index bf0bdf435..dd60965d9 100644 --- a/doc/pub/How2ReadData/ipynb/How2ReadData.ipynb +++ b/doc/pub/How2ReadData/ipynb/How2ReadData.ipynb @@ -1459,10 +1459,22 @@ "\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", - "\n", - "\n", - "\n", + "A variant for classification is also sometimes used, a quantity we will meet later." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "L_{\\delta }(a)={\\begin{cases}{\\frac {1}{2}}{a^{2}}&{\\text{for }}|a|\\leq \\delta ,\\\\\\delta (|a|-{\\frac {1}{2}}\\delta ),&{\\text{otherwise.}}\\end{cases}}}L_{\\delta }(a)={\\begin{cases}{\\frac {1}{2}}{a^{2}}&{\\text{for }}|a|\\leq \\delta ,\\\\\\delta (|a|-{\\frac {1}{2}}\\delta ),&{\\text{otherwise.}}\\end{cases}}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ "We will discuss in more\n", "detail these and other functions in the various lectures. We conclude this part with another example. Instead of \n", "a linear $x$-dependence we study now a cubic polynomial and use the polynomial regression analysis tools of scikit-learn." diff --git a/doc/pub/How2ReadData/ipynb/ipynb-How2ReadData-src.tar.gz b/doc/pub/How2ReadData/ipynb/ipynb-How2ReadData-src.tar.gz index 44fa9526c..c22a7cf62 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 0bf967a68..92658c57d 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 60b64ce20..68c2b07c4 100644 --- a/doc/src/How2ReadData/How2ReadData.do.txt +++ b/doc/src/How2ReadData/How2ReadData.do.txt @@ -940,8 +940,11 @@ 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. - - +!bt +\[ +L_{\delta }(a)={\begin{cases}{\frac {1}{2}}{a^{2}}&{\text{for }}|a|\leq \delta ,\\\delta (|a|-{\frac {1}{2}}\delta ),&{\text{otherwise.}}\end{cases}}}L_{\delta }(a)={\begin{cases}{\frac {1}{2}}{a^{2}}&{\text{for }}|a|\leq \delta ,\\\delta (|a|-{\frac {1}{2}}\delta ),&{\text{otherwise.}}\end{cases}} +\] +!et We will discuss in more detail these and other functions in the various lectures. We conclude this part with another example. Instead of