NAME
MaxEntropy - Perl5 module for Maximum Entropy Modeling and
Feature Induction
SYNOPSIS
use Statistics::MaxEntropy;
# debugging messages; default 0
$Statistics::MaxEntropy::debug = 0;
# maximum number of iterations for IIS; default 100
$Statistics::MaxEntropy::NEWTON_max_it = 100;
# minimal distance between new and old x for Newton's method;
# default 0.001
$Statistics::MaxEntropy::NEWTON_min = 0.001;
# maximum number of iterations for Newton's method; default 100
$Statistics::MaxEntropy::KL_max_it = 100;
# minimal distance between new and old x; default 0.001
$Statistics::MaxEntropy::KL_min = 0.001;
# the size of Monte Carlo samples; default 1000
$Statistics::MaxEntropy::SAMPLE_size = 1000;
# creation of a new event space from an events file
$events = Statistics::MaxEntropy::new($vectype, $file);
# Generalised Iterative Scaling, "corpus" means no sampling
$events->scale("corpus", "gis");
# Improved Iterative Scaling, "mc" means Monte Carlo sampling
$events->scale("mc", "iis");
# Feature Induction algorithm, also see Statistics::Candidates POD
$candidates = Statistics::Candidates->new($candidates_file);
$events->fi("iis", $candidates, $nr_to_add, "mc");
# writing new events, candidates, and parameters files
$events->write($some_other_file);
$events->write_parameters($file);
$events->write_parameters_with_names($file);
# dump/undump the event space to/from a file
$events->dump($file);
$events->undump($file);
DESCRIPTION
This module is an implementation of the Generalised and Improved
Iterative Scaling (GIS, IIS) algorithms and the Feature
Induction (FI) algorithm as defined in (Darroch and Ratcliff
1972) and (Della Pietra et al. 1997). The purpose of the scaling
algorithms is to find the maximum entropy distribution given a
set of events and (optionally) an initial distribution. Also a
set of candidate features may be specified; then the FI
algorithm may be applied to find and add the candidate
feature(s) that give the largest `gain' in terms of Kullback
Leibler divergence when it is added to the current set of
features.
Events are specified in terms of a set of feature functions
(properties) f_1...f_k that map each event to {0,1} or to the
natural numbers: an event is a string of bits. In addition, the
frequency of each event is given. We assume the event space to
have a probability distribution that can be described by
p(x) = 1/Z e^{sum_i alpha_i f_i(x)}
If you have a Perl earlier than 5.005, then you need
`Data::Dumper' module by Gurusamy Sarathy. It can be obtained
from CPAN just like this module.
CONFIGURATION VARIABLES
`$Statistics::MaxEntropy::debug'
If set to `1', lots of debug information, and intermediate
results will be output. Default: `0'
`$Statistics::MaxEntropy::NEWTON_max_it'
Sets the maximum number of iterations in Newton's method.
Newton's method is applied to find the new parameters
\alpha_i of the features `f_i'. Default: `100'.
`$Statistics::MaxEntropy::NEWTON_min'
Sets the minimum difference between x' and x in Newton's
method (used for computing parameter updates in IIS); if
either the maximum number of iterations is reached or the
difference between x' and x is small enough, the iteration
is stopped. Default: `0.001'. Sometimes features have
Infinity or -Infinity as a solution; these features are
excluded from future iterations.
`$Statistics::MaxEntropy::KL_max_it'
Sets the maximum number of iterations applied in the IIS
algorithm. Default: `100'.
`$Statistics::MaxEntropy::KL_min'
Sets the minimum difference between KL divergences of two
distributions in the IIS algorithm; if either the maximum
number of iterations is reached or the difference between
the divergences is enough, the iteration is stopped.
Default: `0.001'.
`$Statistics::MaxEntropy::SAMPLE_size'
Determines the number of (unique) events a sample should
contain. Only makes sense if for sampling "mc" is selected
(see below). Its default is `1000'.
METHODS
`new'
$vectype = "binary"; # or "integer"
$events = Statistics::MaxEntropy::new($vectype, $events_file);
A new event space is created, and the events are read from
`$file'. The events file is not required. The syntax of
events files is described in the section on "FILE SYNTAX".
The `$vectype' parameter specifies how nonzero feature
values should be interpreted as binary values or not.
`write'
$events->write($file);
Writes the events to a file. Its syntax is described in the
section on "FILE SYNTAX".
`scale'
$events->scale($sample, $scaler);
If `$scaler' equals `"gis"', the Generalised Iterative
Scaling algorithm (Darroch and Ratcliff 1972) is applied on
the event space; `$scaler' equals `"iis"', the Improved
Iterative Scaling Algorithm (Della Pietra et al. 1997) is
used. If `$sample' is `"corpus"', there is no sampling done
to re-estimate the parameters (the events previously read
are considered a good sample); if it equals `"mc"' Monte
Carlo (Metropolis-Hastings) sampling is performed to obtain
a random sample; if `$sample' is `"enum"' the complete event
space is enumerated.
`fi'
fi($scaler, $candidates, $nr_to_add, $sampling);
Calls the Feature Induction algorithm. The parameter
`$nr_to_add' is for the number of candidates it should add.
If this number is greater than the number of candidates, all
candidates are added. Meaningfull values for `$scaler' are
`"gis"' and `"iis"'; default is `"gis"' (see previous item).
`$sampling' should be one of `"corpus"', `"mc"', `"enum"'.
`$candidates' should be in the `Statistics::Candidates'
class:
$candidates = Statistics::Candidates->new($file);
See the Statistics::Candidates manpage.
`write_parameters'
$events->write_parameters($file);
`write_parameters_with_names'
$events->write_parameters_with_names($file);
`dump'
$events->dump($file);
`$events' is written to `$file' using `Data::Dumper'.
`undump'
$events = Statistics::MaxEntropy->undump($file);
The contents of file `$file' is read and eval'ed into
`$events'.
FILE SYNTAX
Lines that start with a `#' and empty lines are ignored.
Below we give the syntax of in and output files.
EVENTS FILE (input/output)
Syntax of the event file (`n' features, and `m' events); the
following holds for features:
* each line is an event;
* each column represents a feature function; the co-domain of a
feature function is N;
* constant features (i.e. columns that are completely 0 or 1) are
forbidden;
* 2 or more events should be specified (this is in fact a
consequence of the previous requirement;
The frequency of each event precedes the feature columns.
Features are indexed from right to left. Each `f_ij' and each
`freq_i' is an integer:
name_1 name_2 ... name_n-1 name_n
freq_1 f_11 f12 ... f_1n-1 f_1n
. .
. .
. .
freq_i f_i1 fi2 ... f_in-1 f_in
. .
. .
. .
freq_m f_m1 fm2 ... f_mn-1 f_mn
(`m' events, `n' features) The feature names are separated by
tabs, not white space. The line containing the feature names
will be split on tabs; this implies that (non-tab) white space
may be part of the feature names. The distinction between binary
and integer feature functions is a matter of interpretation. If
vector type `"binary"' is used, nonzero values are interpreted
as 1.
PARAMETERS FILE (input/output)
Syntax of the initial parameters file; one parameter per line:
par_1
.
.
.
par_i
.
.
.
par_n
The syntax of the output distribution is the same. The
alternative procedure for saving parameters to a file
`write_parameters_with_names' writes files that have the
following syntax
n
name_1 par_1
.
.
.
name_i par_i
.
.
.
name_n par_n
bitmask
where bitmask can be used to tell other programs what features
to use in computing probabilities. Features that were ignored
during scaling or because they are constant functions, receive a
`0' bit.
DUMP FILE (input/output)
A dump file contains the event space (which is a hash blessed
into class `Statistics::MaxEntropy') as a Perl expression that
can be evaluated with eval.
BUGS
It's slow.
SEE ALSO
the perl(1) manpage, the Statistics::Candidates manpage, the
Statistics::SparseVector manpage, the POSIX manpage, the Carp
manpage.
DIAGNOSTICS
The module dies with an appropriate message if
* it cannot open a specified events file;
* if you specified a constant feature function (in the events file
or the candidates file);
* If the events file, candidates file, or the parameters file is
not consistent. Possible causes are (a.o.):
* insufficient or too many features for some event;
* inconsistent candidate lines;
* insufficient, or to many event lines in the candidates file.
* it is tried to do feature induction with integer feature
functions.
The module captures `SIGQUIT' and `SIGINT'. On a `SIGINT'
(typically it will dump the current event space(s)
and die. If a `SIGQUIT' () occurs it dumps
the current event space as soon as possible after the first
iteration it finishes.
REFERENCES
(Abney 1997)
Steven P. Abney, Stochastic Attribute Value Grammar,
Computational Linguistics 23(4).
(Darroch and Ratcliff 1972)
J. Darroch and D. Ratcliff, Generalised Iterative Scaling
for log-linear models, Ann. Math. Statist., 43, 1470-1480,
1972.
(Jaynes 1983)
E.T. Jaynes, Papers on probability, statistics, and
statistical physics. Ed.: R.D. Rosenkrantz. Kluwer Academic
Publishers, 1983.
(Jaynes 1997)
E.T. Jaynes, Probability theory: the logic of science, 1997,
unpublished manuscript.
`URL:http://omega.math.albany.edu:8008/JaynesBook.html'
(Della Pietra et al. 1997)
Stephen Della Pietra, Vincent Della Pietra, and John
Lafferty, Inducing features of random fields, In:
Transactions Pattern Analysis and Machine Intelligence,
19(4), April 1997.
VERSION
Version 1.0.
AUTHOR
Hugo WL ter Doest, terdoest@cs.utwente.nl
COPYRIGHT
`Statistics::MaxEntropy' comes with ABSOLUTELY NO WARRANTY and
may be copied only under the terms of the GNU Library General
Public License (version 2, or later), which may be found in the
distribution.