[mlpacksvn] r14960  mlpack/trunk/doc/tutorials/det
fastlabsvn at coffeetalk1.cc.gatech.edu
fastlabsvn at coffeetalk1.cc.gatech.edu
Thu Apr 25 11:52:20 EDT 2013
Author: rcurtin
Date: 20130425 11:52:20 0400 (Thu, 25 Apr 2013)
New Revision: 14960
Modified:
mlpack/trunk/doc/tutorials/det/det.txt
Log:
It all has to be one big comment to be a page...
Modified: mlpack/trunk/doc/tutorials/det/det.txt
===================================================================
 mlpack/trunk/doc/tutorials/det/det.txt 20130425 15:51:24 UTC (rev 14959)
+++ mlpack/trunk/doc/tutorials/det/det.txt 20130425 15:52:20 UTC (rev 14960)
@@ 166,44 +166,6 @@
$ ./det t dataset.csv s density_estimates.txt v
@endcode
*/

 this option is not available in DET right now; see #238! 
 at subsection cli_alt_reg_tut Alternate DET regularization

The usual regularized error \f$R_\alpha(t)\f$ of a node \f$t\f$ is given by:
\f$R_\alpha(t) = R(t) + \alpha \tilde{t}\f$ where

\f[
R(t) = \frac{t^2}{N^2 V(t)}.
\f]

\f$V(t)\f$ is the volume of the node \f$t\f$ and \f$\tilde{t}\f$ is
the set of leaves in the subtree rooted at \f$t\f$.

For the purposes of density estimation, there is a different form of
regularization: instead of penalizing the number of leaves in the subtree, we
penalize the sum of the inverse of the volumes of the leaves. With this
regularization, very small volume nodes are discouraged unless the data actually
warrants it. Thus,

\f[
R_\alpha'(t) = R(t) + \alpha I_v(\tilde{t})
\f]

where

\f[
I_v(\tilde{t}) = \sum_{l \in \tilde{t}} \frac{1}{V(l)}.
\f]

To use this form of regularization, use the \c R flag.

 at code
$ det t dataset.csv R v
 at endcode

/*!
@subsection cli_ex2_de_test_tut Estimation on a test set
Often, it is useful to train a density estimation tree on a training set and
@@ 398,3 +360,38 @@
\ref mlpack::det::DTree "complete API documentation".
*/
+
+ this option is not available in DET right now; see #238! 
+ at subsection cli_alt_reg_tut Alternate DET regularization
+
+The usual regularized error \f$R_\alpha(t)\f$ of a node \f$t\f$ is given by:
+\f$R_\alpha(t) = R(t) + \alpha \tilde{t}\f$ where
+
+\f[
+R(t) = \frac{t^2}{N^2 V(t)}.
+\f]
+
+\f$V(t)\f$ is the volume of the node \f$t\f$ and \f$\tilde{t}\f$ is
+the set of leaves in the subtree rooted at \f$t\f$.
+
+For the purposes of density estimation, there is a different form of
+regularization: instead of penalizing the number of leaves in the subtree, we
+penalize the sum of the inverse of the volumes of the leaves. With this
+regularization, very small volume nodes are discouraged unless the data actually
+warrants it. Thus,
+
+\f[
+R_\alpha'(t) = R(t) + \alpha I_v(\tilde{t})
+\f]
+
+where
+
+\f[
+I_v(\tilde{t}) = \sum_{l \in \tilde{t}} \frac{1}{V(l)}.
+\f]
+
+To use this form of regularization, use the \c R flag.
+
+ at code
+$ det t dataset.csv R v
+ at endcode
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