jammy (3) Statistics::Contingency.3pm.gz
NAME
Statistics::Contingency - Calculate precision, recall, F1, accuracy, etc.
VERSION
version 0.09
SYNOPSIS
use Statistics::Contingency;
my $s = new Statistics::Contingency(categories => \@all_categories);
while (...something...) {
...
$s->add_result($assigned_categories, $correct_categories);
}
print "Micro F1: ", $s->micro_F1, "\n"; # Access a single statistic
print $s->stats_table; # Show several stats in table form
DESCRIPTION
The "Statistics::Contingency" class helps you calculate several useful statistical measures based on 2x2
"contingency tables". I use these measures to help judge the results of automatic text categorization
experiments, but they are useful in other situations as well.
The general usage flow is to tally a whole bunch of results in the "Statistics::Contingency" object, then
query that object to obtain the measures you are interested in. When all results have been collected,
you can get a report on accuracy, precision, recall, F1, and so on, with both macro-averaging and micro-
averaging over categories.
Macro vs. Micro Statistics
All of the statistics offered by this module can be calculated for each category and then averaged, or
can be calculated over all decisions and then averaged. The former is called macro-averaging
(specifically, macro-averaging with respect to category), and the latter is called micro-averaging. The
two procedures bias the results differently - micro-averaging tends to over-emphasize the performance on
the largest categories, while macro-averaging over-emphasizes the performance on the smallest. It's
often best to look at both of them to get a good idea of how your data distributes across categories.
Statistics available
All of the statistics are calculated based on a so-called "contingency table", which looks like this:
Correct=Y Correct=N
+-----------+-----------+
Assigned=Y | a | b |
+-----------+-----------+
Assigned=N | c | d |
+-----------+-----------+
a, b, c, and d are counts that reflect how the assigned categories matched the correct categories.
Depending on whether a macro-statistic or a micro-statistic is being calculated, these numbers will be
tallied per-category or for the entire result set.
The following statistics are available:
• accuracy
This measures the portion of all decisions that were correct decisions. It is defined as
"(a+d)/(a+b+c+d)". It falls in the range from 0 to 1, with 1 being the best score.
Note that macro-accuracy and micro-accuracy will always give the same number.
• error
This measures the portion of all decisions that were incorrect decisions. It is defined as
"(b+c)/(a+b+c+d)". It falls in the range from 0 to 1, with 0 being the best score.
Note that macro-error and micro-error will always give the same number.
• precision
This measures the portion of the assigned categories that were correct. It is defined as "a/(a+b)".
It falls in the range from 0 to 1, with 1 being the best score.
• recall
This measures the portion of the correct categories that were assigned. It is defined as "a/(a+c)".
It falls in the range from 0 to 1, with 1 being the best score.
• F1
This measures an even combination of precision and recall. It is defined as "2*p*r/(p+r)". In terms
of a, b, and c, it may be expressed as "2a/(2a+b+c)". It falls in the range from 0 to 1, with 1
being the best score.
The F1 measure is often the only simple measure that is worth trying to maximize on its own - consider
the fact that you can get a perfect precision score by always assigning zero categories, or a perfect
recall score by always assigning every category. A truly smart system will assign the correct categories
and only the correct categories, maximizing precision and recall at the same time, and therefore
maximizing the F1 score.
Sometimes it's worth trying to maximize the accuracy score, but accuracy (and its counterpart error) are
considered fairly crude scores that don't give much information about the performance of a categorizer.
METHODS
The general execution flow when using this class is to create a "Statistics::Contingency" object, add a
bunch of results to it, and then report on the results.
• $e = Statistics::Contingency->new()
Returns a new "Statistics::Contingency" object. Expects a "categories" parameter specifying the
entire set of categories that may be assigned during this experiment. Also accepts a "verbose"
parameter - if true, some diagnostic status information will be displayed when certain actions are
performed.
• $e->add_result($assigned_categories, $correct_categories, $name)
Adds a new result to the experiment. The lists of assigned and correct categories can be given as an
array of category names (strings), as a hash whose keys are the category names and whose values are
anything logically true, or as a single string if there is only one category.
If you've already got the lists in hash form, this will be the fastest way to pass them. Otherwise,
the current implementation will convert them to hash form internally in order to make its
calculations efficient.
The $name parameter is an optional name for this result. It will only be used in error messages or
debugging/progress output.
In the current implementation, we only store the contingency tables per category, as well as a table
for the entire result set. This means that you can't recover information about any particular single
result from the "Statistics::Contingency" object.
• $e->set_entries($a, $b, $c, $d)
If you don't wish to use the c<add_result()> interface, but still take advantage of the calculation
methods and the various edge cases they handle, you can directly set the four elements of the
contingency table with this method.
• $e->micro_accuracy
Returns the micro-averaged accuracy for the data set.
• $e->micro_error
Returns the micro-averaged error for the data set.
• $e->micro_precision
Returns the micro-averaged precision for the data set.
• $e->micro_recall
Returns the micro-averaged recall for the data set.
• $e->micro_F1
Returns the micro-averaged F1 for the data set.
• $e->macro_accuracy
Returns the macro-averaged accuracy for the data set.
• $e->macro_error
Returns the macro-averaged error for the data set.
• $e->macro_precision
Returns the macro-averaged precision for the data set.
• $e->macro_recall
Returns the macro-averaged recall for the data set.
• $e->macro_F1
Returns the macro-averaged F1 for the data set.
• $e->stats_table
Returns a string combining several statistics in one graphic table. Since accuracy is 1 minus error,
we only report error since it takes less space to print. An optional argument specifies the number
of significant digits to show in the data - the default is 3 significant digits.
• $e->category_stats
Returns a hash reference whose keys are the names of each category, and whose values contain the
various statistical measures (accuracy, error, precision, recall, or F1) about each category as a
hash reference. For example, to print a single statistic:
print $e->category_stats->{sports}{recall}, "\n";
Or to print certain statistics for all categtories:
my $stats = $e->category_stats;
while (my ($cat, $value) = each %$stats) {
print "Category '$cat': \n";
print " Accuracy: $value->{accuracy}\n";
print " Precision: $value->{precision}\n";
print " F1: $value->{F1}\n";
}
AUTHOR
Ken Williams <kwilliams@cpan.org>
COPYRIGHT
Copyright 2002-2008 Ken Williams. All rights reserved.
This distribution is free software; you can redistribute it and/or modify it under the same terms as Perl
itself.