# [mlpack-svn] r14960 - mlpack/trunk/doc/tutorials/det

fastlab-svn at coffeetalk-1.cc.gatech.edu fastlab-svn at coffeetalk-1.cc.gatech.edu
Thu Apr 25 11:52:20 EDT 2013

Author: rcurtin
Date: 2013-04-25 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	2013-04-25 15:51:24 UTC (rev 14959)
+++ mlpack/trunk/doc/tutorials/det/det.txt	2013-04-25 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