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
      $events = Statistics::MaxEntropy::new($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}: an event is a string of bits. In addition of each event its frequency 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)}

The module requires the `Bit::SparseVector' module by Steffen Beyer and the `Data::Dumper' module by Gurusamy Sarathy. Both 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'

$events = Statistics::MaxEntropy::new($events_file);

        A new event space is created, and the events are read from
        `$file'. The events file is required, its syntax is
        described in the section on "FILE SYNTAX".

`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 {0,1};
no space between feature columns;
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. This is a consequence of how `Bit::SparseVector' reads bit strings. Each `f_ij' is a bit and `freq_i' an integer in the following schema:

        name_n <tab> name_n-1 ... name_2 <tab> name_1 <newline>
        freq_1 <white> f_1n ... f_13 f_12 f_11 <newline>
          .                     .
          .                     .
          .                     .
        freq_i <white> f_in ... f_i3 f_i2 f_i1 <newline>
          .                     .
          .                     .
          .                     .
        freq_m <white> f_mn ... f_m3 f_m2 f_m1

(`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.

PARAMETERS FILE (input/output)

Syntax of the initial parameters file; one parameter per line:

par_1 <newline>

         .
         .
        par_i <newline>
         .
         .
         .
        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 <newline>
        name_1 <tab> par_1 <newline>
         .
         .
         .
        name_i <tab> par_i <newline>
         .
         .
         .
        name_n <tab> par_n <newline>
        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 Bit::Vector manpage, the Data::Dumper 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.

The module captures `SIGQUIT' and `SIGINT'. On a `SIGINT' (typically <CONTROL-C> it will dump the current event space(s) and die. If a `SIGQUIT' (<CONTROL-BACKSLASH>) 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 0.8.

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.