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Clean up DET tutorial significantly. It could still use some work -- but then,

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so could the actual DTree API.
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Ryan Curtin
2013-04-24 21:04:55 +00:00
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@section intro_det_tut Introduction
DETs perform the unsupervised task of density estimation using decision trees.
Using a trained density estimation tree (DET), the density at any particular
point can be estimated very quickly (O(log n) time, where n is the number of
points the tree is built on).
The details of this work is presented in the following paper:
@code
@inproceedings{ram2011density,
title={Density estimation trees},
author={Ram, P. and Gray, A.G.},
booktitle={Proceedings of the 17th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining},
booktitle={Proceedings of the 17th ACM SIGKDD International Conference on
Knowledge Discovery and Data Mining},
pages={627--635},
year={2011},
organization={ACM}
@@ -51,86 +55,77 @@ A list of all the sections this tutorial contains.
The command line arguments of this program can be viewed using the '-h' option:
@code
$ ./det -h
$ det -h
Density Estimation With Density Estimation Trees
Density estimation with DET
This program performs a number of functions related to Density Estimation
Trees. The optimal Density Estimation Tree (DET) can be trained on a set of
data (specified by --train_file) using cross-validation (with number of folds
specified by --folds). In addition, the density of a set of test points
(specified by --test_file) can be estimated, and the importance of each
dimension can be computed. If class labels are given for the training points
(with --labels_file), the class memberships of each leaf in the DET can be
calculated.
This program provides an example use of the Density Estimation Tree for
density estimation. For more details, please look at the paper titled 'Density
Estimation Trees'.
The created DET can be saved to a file, along with the density estimates for
the test set and the variable importances.
Required options:
--input/training_set (-S) [string]
The data set on which to perform density
estimation.
--train_file (-t) [string] The data set on which to build a density
estimation tree.
Options:
--DET/max_leaf_size (-M) [int]
The maximum size of a leaf in the unpruned fully
grown DET. Default value 10.
--DET/min_leaf_size (-N) [int]
The minimum size of a leaf in the unpruned fully
grown DET. Default value 5.
--DET/use_volume_reg (-R) This flag gives the used the option to use a
form of regularization similar to the usual
alpha-pruning in decision tree. But instead of
regularizing on the number of leaves, you
regularize on the sum of the inverse of the
volume of the leaves (meaning you penalize low
volume leaves.
--flag/print_tree (-P) If you just wish to print the tree out on the
command line.
--flag/print_vi (-I) If you just wish to print the variable
importance of each feature out on the command
line.
--folds (-f) [int] The number of folds of cross-validation to
perform for the estimation (0 is LOOCV) Default
value 10.
--help (-h) Default help info.
--info [string] Get help on a specific module or option.
Default value ''.
--input/labels (-L) [string] The labels for the given training data to
--labels_file (-l) [string] The labels for the given training data to
generate the class membership of each leaf (as
an extra statistic) Default value ''.
--input/test_set (-T) [string]
An extra set of test points on which to estimate
the density given the estimator. Default value
''.
--output/leaf_class_table (-l) [string]
--leaf_class_table_file (-L) [string]
The file in which to output the leaf class
membership table. Default value
'leaf_class_membership.txt'.
--output/test_set_estimates (-t) [string]
--max_leaf_size (-M) [int] The maximum size of a leaf in the unpruned,
fully grown DET. Default value 10.
--min_leaf_size (-N) [int] The minimum size of a leaf in the unpruned,
fully grown DET. Default value 5.
--print_tree (-p) Print the tree out on the command line (or in
the file specified with --tree_file).
--print_vi (-I) Print the variable importance of each feature
out on the command line (or in the file
specified with --vi_file).
--test_file (-T) [string] A set of test points to estimate the density of.
Default value ''.
--test_set_estimates_file (-E) [string]
The file in which to output the estimates on the
test set from the final optimally pruned tree.
Default value ''.
--output/training_set_estimates (-s) [string]
The file in which to output the estimates on the
training set from the final optimally pruned
tree. Default value ''.
--output/tree (-p) [string] The file in which to print the final optimally
--training_set_estimates_file (-e) [string]
The file in which to output the density
estimates on the training set from the final
optimally pruned tree. Default value ''.
--tree_file (-r) [string] The file in which to print the final optimally
pruned tree. Default value ''.
--output/unpruned_tree_estimates (-u) [string]
The file in which to output the estimates on the
training set from the large unpruned tree.
Default value ''.
--output/vi (-i) [string] The file to output the variable importance
values for each feature. Default value ''.
--param/folds (-F) [int] The number of folds of cross-validation to
performed for the estimation (enter 0 for LOOCV)
Default value 10.
--param/number_of_classes (-C) [int]
The number of classes present in the 'labels'
set provided Default value 0.
--unpruned_tree_estimates_file (-u) [string]
The file in which to output the density
estimates on the training set from the large
unpruned tree. Default value ''.
--verbose (-v) Display informational messages and the full list
of parameters and timers at the end of
execution.
--vi_file (-i) [string] The file to output the variable importance
values for each feature. Default value ''.
For further information, including relevant papers, citations, and theory,
consult the documentation found at http://www.mlpack.org or included with your
distribution of MLPACK.
@endcode
@subsection cli_ex1_de_tut Plain-vanilla density estimation
We can just train a DET on the provided data set \e S. Like all datasets
@@ -139,228 +134,266 @@ is loaded; internally, the data is column-major -- see \ref matrices "this page"
for more information).
@code
$ ./det -S dataset.csv -v
$ det -t dataset.csv -v
@endcode
By default, det performs 10-fold cross-validation (using the
\f$\alpha\f$-pruning regularization for decision trees). To perform LOOCV
(leave-one-out cross-validation), use the following command:
(leave-one-out cross-validation), which can provide better results but will take
longer, use the following command:
@code
$ ./det -S dataset.csv -F 0 -v
$ det -t dataset.csv -f 0 -v
@endcode
To perform k-fold crossvalidation, use \c -F \c k. There are certain other
options available for training. For example, for the construction of the initial
tree, you can specify the maximum and minimum leaf sizes. By default, they are
10 and 5 respectively, you can set them using the \c -M (\c --maximum_leaf_size)
and the \c -N (\c --minimum_leaf_size) options.
To perform k-fold crossvalidation, use \c -f \c k (or \c --folds \c k). There
are certain other options available for training. For example, in the
construction of the initial tree, you can specify the maximum and minimum leaf
sizes. By default, they are 10 and 5 respectively; you can set them using the \c
-M (\c --max_leaf_size) and the \c -N (\c --min_leaf_size) options.
@code
$ ./det -S dataset.csv -M 20 -N 10
$ det -t dataset.csv -M 20 -N 10
@endcode
In case you want to output the density estimates at the points in the training
set, use the \c -s option to specify the output file.
set, use the \c -e (\c --training_set_estimates_file) option to specify the
output file to which the estimates will be saved. The first line in
density_estimates.txt will correspond to the density at the first point in the
training set. Note that the logarithm of the density estimates are given, which
allows smaller estimates to be saved.
@code
$ ./det -S dataset.csv -s density_estimates.txt -v
$ ./det -t dataset.csv -s density_estimates.txt -v
@endcode
*/
----- this option is not available in DET right now; see #238! -----
@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
\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, I have developed 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. Here really 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 \e -R flag.
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.
@code
$ ./dt_utils -S dataset.csv -R -v
$ det -t dataset.csv -R -v
@endcode
/*!
@subsection cli_ex2_de_test_tut Estimation on a test set
There is the option of training the DET on a certain set and obtaining the
density from the learned estimator at some out of sample (new) test points. The
\e -T option is the set of test points and the \e -t is the file in which the
estimates are to be output.
Often, it is useful to train a density estimation tree on a training set and
then obtain density estimates from the learned estimator for a separate set of
test points. The \c -T (\c --test_file) option allows specification of a set of
test points, and the \c -E (\c --test_set_estimates_file) option allows
specification of the file into which the test set estimates are saved. Note
that the logarithm of the density estimates are saved; this allows smaller
values to be saved.
@code
$ ./det -S dataset.csv -T test_points.csv -t test_density_estimates.txt -v
$ det -t dataset.csv -T test_points.csv -E test_density_estimates.txt -v
@endcode
@subsection cli_ex3_de_p_tut Printing a trained DET
A depth-first visualization of the DET can be obtained by using the \e -P flag.
A depth-first visualization of the DET can be obtained by using the \c -p (\c
--print_tree) flag.
@code
$ ./det -S dataset.csv -P -v
$ det -t dataset.csv -p -v
@endcode
To print this tree in a file, use the \e -p option to specify the output file
along with the \e -P flag.
To print this tree in a file, use the \c -r (\c --tree_file) option to specify
the output file along with the \c -P (\c --print_tree) flag.
@code
$ ./det -S dataset.csv -P -p tree.txt -v
$ det -t dataset.csv -p -r tree.txt -v
@endcode
@subsection cli_ex4_de_vi_tut Computing the variable importance
The variable importance (with respect to density estimation) of the different
features in the data set can be obtained by using the \e -I option. This outputs
the (absolute as opposed to relative) variable importance of the all the
features.
features in the data set can be obtained by using the \c -I (\c --print_vi)
option. This outputs the absolute (as opposed to relative) variable importance
of the all the features.
@code
$ ./det -S dataset.csv -I -v
$ det -t dataset.csv -I -v
@endcode
To print this in a file, use the \e -i option
To print this in a file, use the \c -i (\c --vi_file) option.
@code
$ ./det -S dataset.csv -I -i variable_importance.txt -v
$ det -t dataset.csv -I -i variable_importance.txt -v
@endcode
@subsection cli_ex5_de_lm Leaf Membership
In case the dataset is labeled and you are curious to find the class membership
of the leaves of the DET, there is an option of view the class membership. The
training data has to still be input in an unlabeled format, but an additional
In case the dataset is labeled and you want to find the class membership
of the leaves of the tree, there is an option to print the class membership into
a file. The training data has to still be input in an unlabeled format, but an additional
label file containing the corresponding labels of each point has to be input
using the \e -L option. You are required to specify the number of classes
present in this set using the \e -C option.
using the \c -l (\c --labels_file) option. The file to output the class
memberships into can be specified with \c -L (\c --leaf_class_table_file). If
\c -L is left unspecified, leaf_class_membership.txt is used by default.
@code
$ ./det -S dataset.csv -L labels.csv -C <number-of-classes> -v
@endcode
The leaf membership matrix is output into a file called 'leaf_class_membership.txt' by default. An user-specified file can be used by utilizing the \e -l option.
@code
$ ./det -S dataset.csv -L labels.csv -C <number-of-classes> -l leaf_class_membership_file.txt -v
$ det -t dataset.csv -l labels.csv -v
$ det -t dataset.csv -l labels.csv -l leaf_class_membership_file.txt -v
@endcode
@section dtree_det_tut The 'DTree' class
This class implements the DET.
This class implements density estimation trees. Below is a simple example which
initializes a density estimation tree.
@code
#include <mlpack/methods/det/dtree.hpp>
using namespace mlpack::det;
// The dataset matrix, on which to learn the DET
// The dataset matrix, on which to learn the density estimation tree.
extern arma::Mat<float> data;
// Initializing the class
// This function creates and saves the bounding box of the data.
DTree<>* det = new DTree<>(&data);
// Initialize the tree. This function also creates and saves the bounding box
// of the data. Note that it does not actually build the tree.
DTree<> det(data);
@endcode
@subsection dtree_pub_func_det_tut Public Functions
\b Growing the tree to the full size:
The function \c Grow() greedily grows the tree, adding new points to the tree.
Note that the points in the dataset will be reordered. This should only be run
on a tree which has not already been built. In general, it is more useful to
use the \c Trainer() function found in \ref dtutils_det_tut.
@code
// This keeps track of the data during the shuffle
// that occurs while growing the tree.
arma::Col<size_t>* old_from_new = new arma::Col<size_t>(data.n_cols);
for (size_t i = 0; i < data.n_cols; i++) {
(*old_from_new)[i] = i;
}
// This keeps track of the data during the shuffle that occurs while growing the
// tree.
arma::Col<size_t> oldFromNew(data.n_cols);
for (size_t i = 0; i < data.n_cols; i++)
oldFromNew[i] = i;
// This function grows the tree down to the leaf
// any regularization. It returns the current minimum
// value of the regularization parameter 'alpha'.
bool use_volume_reg = false;
size_t max_leaf_size = 10, min_leaf_size = 5;
// This function grows the tree down to the leaves. It returns the current
// minimum value of the regularization parameter alpha.
size_t maxLeafSize = 10;
size_t minLeafSize = 5;
long double alpha
= det->Grow(&data, old_from_new, use_volume_reg,
max_leaf_size, min_leaf_size);
double alpha = det.Grow(data, oldFromNew, false, maxLeafSize, minLeafSize);
@endcode
One step of \b pruning the tree back up:
Note that the alternate volume regularization should not be used (see ticket
#238).
To estimate the density at a given query point, use the following code. Note
that the logarithm of the density is returned.
@code
// This function performs a single pruning of the
// decision tree for the given value of alpha
// and returns the next minimum value of alpha
// that would induce a pruning
alpha = det->PruneAndUpdate(alpha, use_volume_reg);
@endcode
\b Estimating the density at a given query point:
@code
// for a given query, you can obtain the density estimate
// For a given query, you can obtain the density estimate.
extern arma::Col<float> query;
long double estimate = det->Compute(&query);
extern DTree* det;
double estimate = det->ComputeValue(&query);
@endcode
Computing the \b variable \b importance of each feature for the given DET.
@code
// Initialize the importance of every dimension to zero.
arma::Col<double> v_imps = arma::zeros<arma::Col<double> >(data.n_rows);
// The data matrix and density estimation tree.
extern arma::mat data;
extern DTree* det;
// The variable importances will be saved into this vector.
arma::Col<double> varImps;
// You can obtain the variable importance from the current tree.
det->ComputeVariableImportance(&v_imps);
det->ComputeVariableImportance(varImps);
@endcode
@section dtutils_det_tut 'namespace mlpack::det'
The functions in this namespace allows the user to perform certain tasks with the 'DTree' class.
The functions in this namespace allows the user to perform tasks with the
'DTree' class. Most importantly, the \c Trainer() method allows the full
training of a density estimation tree with cross-validation. There are also
utility functions which allow printing of leaf membership and variable
importance.
@subsection dtutils_util_funcs Utility Functions
\b Training a DET (with cross-validation)
The code below details how to train a density estimation tree with
cross-validation.
@code
#include <mlpack/methods/det/dt_utils.hpp>
using namespace mlpack::det;
// The dataset matrix, on which to learn the DET
// The dataset matrix, on which to learn the density estimation tree.
extern arma::Mat<float> data;
// the number of folds in the cross-validation
size_t folds = 10; // set folds = 0 for LOOCV
// The number of folds for cross-validation.
const size_t folds = 10; // Set folds = 0 for LOOCV.
bool use_volume_reg = false;
size_t max_leaf_size = 10, min_leaf_size = 5;
const size_t maxLeafSize = 10;
const size_t minLeafSize = 5;
// obtain the trained DET
DTree<>* dtree_opt = Trainer(&data, folds, use_volume_reg,
max_leaf_size, min_leaf_size);
// Train the density estimation tree with cross-validation.
DTree<>* dtree_opt = Trainer(data, folds, false, maxLeafSize, minLeafSize);
@endcode
Generating \b leaf-class \b membership
Note that the alternate volume regularization should be set to false because it
has known bugs (see #238).
To print the class membership of leaves in the tree into a file, see the
following code.
@code
extern arma::Mat<int> labels;
size_t number_of_classes = 3; // this is required
extern arma::Mat<size_t> labels;
extern DTree* det;
const size_t numClasses = 3; // The number of classes must be known.
extern string leaf_class_membership_file;
extern string leafClassMembershipFile;
PrintLeafMembership(dtree_opt, data, labels, number_of_classes,
leaf_class_membership_file);
PrintLeafMembership(det, data, labels, numClasses, leafClassMembershipFile);
@endcode
Generating \b variable \bimportance
Note that you can find the number of classes with \c max(labels) \c + \c 1.
The variable importance can also be printed to a file in a similar manner.
@code
extern string variable_importance_file;
size_t number_of_features = data.n_rows;
extern DTree* det;
PrintVariableImportance(dtree_opt, nunmber_of_features,
variable_importance_file);
extern string variableImportanceFile;
const size_t numFeatures = data.n_rows;
PrintVariableImportance(det, numFeatures, variableImportanceFile);
@endcode
@section further_doc_det_tut Further Documentation
For further documentation on the DTree class, consult the
\ref mlpack::det::DTree "complete API documentation".