NAME
Algorithm::Viterbi - Compute Viterbi path and probability
SYNOPSIS
use Algorithm::Viterbi;
my $start_probability = { 'Rainy'=> 0.6, 'Sunny'=> 0.4 };
my $transition_probability = {
'Rainy' => {'Rainy'=> 0.7, 'Sunny'=> 0.3},
'Sunny' => {'Rainy'=> 0.4, 'Sunny'=> 0.6},
};
my $emission = {
'shop' => { 'Sunny' => '0.3', 'Rainy' => '0.4' },
'walk' => { 'Sunny' => '0.6', 'Rainy' => '0.1' },
'clean' => { 'Sunny' => '0.1', 'Rainy' => '0.5' }
};
my $v = Algorithm::Viterbi->new();
$v->start($start_probability);
$v->transition($transition_probability);
$v->emission($emission_probability);
my $observations = [ 'walk', 'shop', 'clean' ];
my ($prob, $v_path, $v_prob) = $v->forward_viterbi($observations);
-- or --
my $training_data = [
[ 'walk', 'Sunny' ],
[ 'walk', 'Sunny' ],
[ 'walk', 'Rainy' ],
[ 'shop', 'Rainy' ],
[ 'clean', 'Rainy' ],
[ 'clean', 'Rainy' ],
...
];
$v->train($training_data);
my ($prob, $v_path, $v_prob) = $v->forward_viterbi($observations);
DESCRIPTION
Algorithm::Viterbi computes the forward probability, the Viterbi path
and the Viterbi probability of a sequence of observations, based on a
given start, emission and transition probability. Alternatively, the
start, emission and transition probability can be computed from a set of
training data.
The whole idea of this module is inspired by an article on the Viterbi
algorithm in Wikipedia, the free encyclopedia. Rather than copying all
text, I'm just including the link to the Wikipedia page:
. I think the page is
well-written and I see no need to repeat the theory here. Reading it may
clarify the documentation below.
METHODS
new Creates a new "Algorithm::Viterbi" object. The following
attributes can be set with the constructor:
my $v = Algorthm::Viterbi->new(
start_state => '$',
unknown_emission_prob => undef,
unknown_transition_prob => 0);
The values of the attributes in the example are the default
values. For a detailed description and use of these attributes,
see below.
train This method computes the start, emission and transition
probabilities from a set of observations and their associated
states. The probabilities are simple averages of the passed
observations, so if you require sophisticated smoothing on the
emission, start and/or transition, then you're better off
rolling your own.
The value of member start_state is a bogus state used to define
the begin state of the first transition. By default, this state
is set to '$'. You can change this by setting the variable in
the constructor or later by accessing the member directly. See
example below.
This state can also be used as a separator between the beginning
and end of a sequence of observations. For example, you could
assign this state (tag) to every end-of-sentence symbol when
training on a pre-tagged corpus.
The set of observations is passed as a reference to an array as
shown in the following example:
use strict;
use Algorithm::Viterbi;
use Data::Dumper;
my $observations = [
[ 'work', 'rainy' ],
[ 'work', 'sunny' ],
[ 'walk', 'sunny' ],
[ 'walk', 'rainy' ],
[ 'shop', 'rainy' ],
[ 'work', 'rainy' ],
];
my $v = Algorithm::Viterbi->new(start_state => '###');
$v->train($observations);
print Dumper($v);
will produce:
$VAR1 = bless( {
'transition' => {
'sunny' => {
'sunny' => '0.5',
'rainy' => '0.25'
},
'rainy' => {
'sunny' => '0.5',
'rainy' => '0.5'
},
'###' => {
'rainy' => '0.25'
}
},
'emission' => {
'shop' => {
'rainy' => '0.25'
},
'walk' => {
'sunny' => '0.5',
'rainy' => '0.25'
},
'work' => {
'sunny' => '0.5',
'rainy' => '0.5'
}
},
'start_state' => '###',
'states' => [
'sunny',
'rainy'
],
'unknown_transition_prob' => 0,
'start' => {
'sunny' => '0.333333333333333',
'rainy' => '0.666666666666667'
}
}, 'Algorithm::Viterbi' );
start Initializes the start probabilities. The start probabilities are
passed as a reference to a hash, as shown in this example:
my $start_probability = { 'Rainy'=> 0.6, 'Sunny'=> 0.4 };
my $v = Algorithm::Viterbi->new();
$v->start($start_probability);
From the start probabilities, all possible states are derived,
by copying the keys of the start hash. This list of states is
used by the forward_viterbi method. It is therefore important to
mention all possible states in the start hash.
Returns the start probabilities.
emission
Initializes the emission probabilities. The emission is passed
as a reference to a hash, as shown in this example:
my $emission_probability = {
'shop' => { 'Sunny' => '0.3', 'Rainy' => '0.4' },
'swim' => { 'Sunny' => '0.1' },
'walk' => { 'Sunny' => '0.5', 'Rainy' => '0.1' },
'clean' => { 'Sunny' => '0.1', 'Rainy' => '0.5' }
};
my $v = Algorithm::Viterbi->new();
$v->emission($emission_probability);
The keys of the emission hash constitute the dictionary, which
is used to determine whether an observation is a known or an
unknown observation.
Returns the emission probabilities.
transition
Initializes the transition probabilities. The transition is
passed as a reference to a hash, as shown in this example:
my $transition_probability = {
'Rainy' => {'Rainy'=> 0.7, 'Sunny'=> 0.3},
'Sunny' => {'Rainy'=> 0.4, 'Sunny'=> 0.6},
};
my $v = Algorithm::Viterbi->new();
$v->transition($transition_probability);
The transition hash can be 'sparse': it is sufficient to include
only known transitions between states. See method
get_transition.
Returns the transition probabilities.
forward_viterbi
This method calculates the forward probability, the Viterbi path
and the Viterbi probability of a given sequence of observations.
For a detailed description of the Algorithm, see the Wikipedia
page .
The difference with the algorithm described in the web page
above, is that the emission and the transition are calculated
somewhat differently. See methods get_emission and
get_transition.
Example:
use strict;
use Algorithm::Viterbi;
use Data::Dumper;
my $observations = [ 'walk', 'shop', 'clean' ];
my $start = { 'Rainy'=> 0.6, 'Sunny'=> 0.4 };
my $transition = {
'Rainy' => {'Rainy'=> 0.7, 'Sunny'=> 0.3},
'Sunny' => {'Rainy'=> 0.4, 'Sunny'=> 0.6},
};
my $emission = {
'shop' => {
'Sunny' => '0.3',
'Rainy' => '0.4',
},
'walk' => {
'Sunny' => '0.6',
'Rainy' => '0.1'
},
'clean' => {
'Sunny' => '0.1',
'Rainy' => '0.5'
}
};
my $v = Algorithm::Viterbi->new();
$v->emission($emission);
$v->transition($transition);
$v->start($start);
print Dumper ($v->forward_viterbi($observations));
produces:
$VAR1 = '0.033612';
$VAR2 = [
'Sunny',
'Rainy',
'Rainy',
'Rainy'
];
$VAR3 = '0.009408';
get_emission
Usage: $v->get_emission($observation, $state);
Returns the emission probability for a given observation and
state. This method is primarily for internal usage and is called
by the forward_viterbi method.
The dictionary consists of the keys of the emission table, e.g.
a list of known observations.
If $observation is a known observation in the dictionary and
$state exists as a state for the observation in the emission
table, then return the probability associated with $observation
and $state.
If the observation exists in the dictionary, but $state is a
state not connected to the observation, then return 0.
If the observation does not exist in the dictionary and
$v->{unknown_emission_prob} is defined, then return
$v->{unknown_emission_prob}. Setting $v->{unknown_emission_prob}
= 1 actually means that you are returning all possible states
for an unknown observation.
If the observation is unknown in the dictionary and
$v->{unknown_emission_prob} is not defined, then return the
start probability of $state.
Example:
my $emission = {
'shop' => {
'Sunny' => '0.3',
'Rainy' => '0.4'
},
'swim' => {
'Sunny' => '0.1'
},
'walk' => {
'Sunny' => '0.5',
'Rainy' => '0.1'
},
'clean' => {
'Sunny' => '0.1',
'Rainy' => '0.5'
}
};
my $start = { 'Rainy'=> 0.6, 'Sunny'=> 0.4 };
my $v = Algorithm::Viterbi->new();
$v->emission($emission);
$v->start($start);
my $e;
$e = get_emission('shop', 'Rainy'); # $e = 0.4
$e = get_emission('swim', 'Rainy'); # $e = 0
$e = get_emission('hack', 'Rainy'); # $e = 0.6
$v->{unknown_emission_prob} = 1;
$e = get_emission('hack', 'Rainy'); # $e = 1
get_transition
Usage: $v->get_transition($state, $next_state);
Returns the transition probability between a state and the next
state. This method is primarily for internal usage and is called
by the forward_viterbi method.
If the transition between $state and $next_state is defined,
then return the probability associated with it.
If the transition between $state and $next_state does not exist,
then return the value of $v->unknown_transition_prob, which will
be 0 unless otherwise defined. Setting this attribute to a very
small value allows you to still obtain a Viterbi path, although
no suitable transitions were found between states of a given
observation.
Example:
use Algorithm::Viterbi;
my $observations = [ 'walk', 'shop', 'read' ];
my $start = { 'Rainy'=> 0.5, 'Sunny'=> 0.4, 'Stormy'=> 0.1 };
my $transition = {
'Rainy' => {'Rainy'=> 0.7, 'Sunny'=> 0.3},
'Sunny' => {'Rainy'=> 0.4, 'Sunny'=> 0.5, 'Stormy'=>.1},
};
my $emission = {
'shop' => {
'Sunny' => '0.4',
'Rainy' => '0.9'
},
'read' => {
'Stormy' => '1'
},
'walk' => {
'Sunny' => '0.6',
'Rainy' => '0.1'
},
};
my $v = Algorithm::Viterbi->new();
$v->emission($emission);
$v->transition($transition);
$v->start($start);
my ($prob, $v_path, $v_prob) = $v->forward_viterbi($observations);
# returns 0, [], 0
$v->{unknown_transition_prob} = 1e-100;
($prob, $v_path, $v_prob) = $v->forward_viterbi($observations);
# returns 1.62e-102, ['Sunny', 'Sunny', 'Stormy', 'Stormy' ], 4.8e-103;
AUTHOR
Koen Dejonghe koen@fietsoverland.com Copyright (c) 2006 Koen
Dejonghe. All rights reserved. This program is free software;
you can redistribute it and/or modify it under the same terms as
Perl itself.
VERSION
Version 0.01 (2006-Nov-07)