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NAME
    AI::MaxEntropy - Perl extension for learning Maximum Entropy Models

SYNOPSIS
      use AI::MaxEntropy;

      # create a maximum entropy learner
      my $me = AI::MaxEntropy->new; 
  
      # the learner see 2 red round smooth apples
      $me->see(['round', 'smooth', 'red'] => 'apple' => 2);
  
      # the learner see 3 yellow long smooth bananas
      $me->see(['long', 'smooth', 'yellow'] => 'banana' => 3);

      # and more

      # samples needn't have the same numbers of active features
      $me->see(['rough', 'big'] => 'pomelo');

      # the order of active features is not concerned, too
      $me->see(['big', 'rough'] => 'pomelo');

      # ...

      # and, let it learn
      my $model = $me->learn;

      # then, we can make predictions on unseen data

      # ask what a red thing is most likely to be
      print $model->predict(['red'])."\n";
      # the answer is apple, because all red things the learner have ever seen
      # are apples
  
      # ask what a smooth thing is most likely to be
      print $model->predict(['smooth'])."\n";
      # the answer is banana, because the learner have seen more smooth bananas
      # (weighted 3) than smooth apples (weighted 2)

      # ask what a red, long thing is most likely to be
      print $model->predict(['red', 'long'])."\n";
      # the answer is banana, because the learner have seen more long bananas
      # (weighted 3) than red apples (weighted 2)

      # print out scores of all possible answers to the feature round and red
      for ($model->all_labels) {
          my $s = $model->score(['round', 'red'] => $_);
          print "$_: $s\n";
      }
  
      # save the model
      $model->save('model_file');

      # load the model
      $model->load('model_file');

CONCEPTS
  What is a Maximum Entropy model?
    Maximum Entropy (ME) model is a popular approach for machine learning.
    From a user's view, it just behaves like a classifier which classify
    things according to the previously learnt things.

    Theorically, a ME learner try to recover the real probability
    distribution of the data based on limited number of observations, by
    applying the principle of maximum entropy.

    You can find some good tutorials on Maximum Entropy model here:

    <http://homepages.inf.ed.ac.uk/s0450736/maxent.html>

  Features
    Generally, a feature is a binary function answers a yes-no question on a
    specified piece of data.

    For examples,

      "Is it a red apple?"

      "Is it a yellow banana?"

    If the answer is yes, we say this feature is active on that piece of
    data.

    In practise, a feature is usually represented as a tuple "<x, y>". For
    examples, the above two features can be represented as

      <red, apple>

      <yellow, banana>

  Samples
    A sample is a set of active features, all of which share a common "y".
    This common "y" is sometimes called label or tag. For example, we have a
    big round red apple, the correpsonding sample is

      {<big, apple>, <round, apple>, <red, apple>}

    In this module, a samples is denoted in Perl code as

      $xs => $y => $w

    $xs is an array ref holding all "x", $y is a scalar holding the label
    and $w is the weight of the sample, which tells how many times the
    sample occurs.

    Therefore, the above sample can be denoted as

      ['big', 'round', 'red'] => 'apple' => 1.0

    The weight $w can be ommited when it equals to 1.0, so the above
    denotation can be shorten to

      ['big', 'round', 'red'] => 'apple'

  Models
    With a set of samples, a model can be learnt for future predictions. The
    model (the lambda vector essentailly) is a knowledge representation of
    the samples that it have seen before. By applying the model, we can
    calculate the probability of each possible label for a certain sample.
    And choose the most possible one according to these probabilities.

FUNCTIONS
    NOTE: This is still an alpha version, the APIs may be changed in future
    versions.

  new
    Create a Maximum Entropy learner. Optionally, initial values of
    properties can be specified.

      my $me1 = AI::MaxEntropy->new;
      my $me2 = AI::MaxEntropy->new(
          algorithm => { epsilon => 1e-6 });
      my $me3 = AI::MaxEntropy->new(
          algorithm => { m => 7, epsilon => 1e-4 },
          smoother => { type => 'gaussian', sigma => 0.8 }
      );

  see
    Let the Maximum Entropy learner see a sample.

      my $me = AI::MaxEntropy->new;

      # see a sample with default weight 1.0
      $me->see(['red', 'round'] => 'apple');
  
      # see a sample with specified weight 0.5
      $me->see(['yellow', 'long'] => 'banana' => 0.5);

    The sample can be also represented in the attribute-value form, which
    like

      $me->see({color => 'yellow', shape => 'long'} => 'banana');
      $me->see({color => ['red', 'green'], shape => 'round'} => 'apple');

    Actually, the two samples above are converted internally to,

      $me->see(['color:yellow', 'shape:long'] => 'banana');
      $me->see(['color:red', 'color:green', 'shape:round'] => 'apple');

  forget_all
    Forget all samples the learner have seen previously.

  cut
    Cut the features that occur less than the specified number.

    For example,

      ...
      $me->cut(1)

    will cut all features that occur less than one time.

  learn
    Learn a model from all the samples that the learner have seen so far,
    returns an AI::MaxEntropy::Model object, which can be used to make
    prediction on unlabeled samples.

      ...

      my $model = $me->learn;

      print $model->predict(['x1', 'x2', ...]);

PROPERTIES
  algorithm
    This property enables client program to choose different algorithms for
    learning the ME model and set their parameters.

    There are mainly 3 algorithm for learning ME models, they are GIS, IIS
    and L-BFGS. This module implements 2 of them, namely, L-BFGS and GIS.
    L-BFGS provides full functionality, while GIS runs faster, but only
    applicable on limited scenarios.

    To use GIS, the following conditions must be satisified:

    1. All samples have same number of active features

    2. No feature has been cut

    3. No smoother is used (in fact, the property "smoother" is simplly
    ignored when the type of algorithm equal to 'gis').

    This property "algorithm" is supposed to be a hash ref, like

      {
        type => ...,
        progress_cb => ...,
        param_1 => ...,
        param_2 => ...,
        ...,
        param_n => ...
      }

   type
    The entry "type => ..." specifies which algorithm is used for the
    optimization. Valid values include:

      'lbfgs'       Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS)
      'gis'         General Iterative Scaling (GIS)

    If ommited, 'lbfgs' is used by default.

   progress_cb
    The entry "progress_cb => ..." specifies the progress callback
    subroutine which is used to trace the process of the algorithm. The
    specified callback routine will be called at each iteration of the
    algorithm.

    For L-BFGS, "progress_cb" will be directly passed to "fmin" in
    Algorithm::LBFGS. f(x) is the negative log-likelihood of current lambda
    vector.

    For GIS, the "progress_cb" is supposed to have a prototype like

      progress_cb(i, lambda, d_lambda, lambda_norm, d_lambda_norm)

    "i" is the number of the iterations, "lambda" is an array ref containing
    the current lambda vector, "d_lambda" is an array ref containing the
    delta of the lambda vector in current iteration, "lambda_norm" and
    "d_lambda_norm" are Euclid norms of "lambda" and "d_lambda"
    respectively.

    For both L-BFGS and GIS, the client program can also pass a string
    'verbose' to "progress_cb" to use a default progress callback which
    simply print out the progress on the screen.

    "progress_cb" can also be omitted if the client program do not want to
    trace the progress.

   parameters
    The rest entries are parameters for the specified algorithm. Each
    parameter will be assigned with its default value when it is not given
    explicitly.

    For L-BFGS, the parameters will be directly passed to Algorithm::LBFGS
    object, please refer to "Parameters" in Algorithm::LBFGS for details.

    For GIS, there is only one parameter "epsilon", which controls the