NAME

Algorithm::AM - Perl extension for Analogical Modeling using a parallel algorithm

VERSION

version 2.43

AUTHOR

Theron Stanford <shixilun@yahoo.com>, Nathan Glenn <garfieldnate@gmail.com>

COPYRIGHT AND LICENSE

This is free software; you can redistribute it and/or modify it under the same terms as the Perl 5 programming language system itself.

SYNOPSIS

use Algorithm::AM;

my $p = Algorithm::AM->new('finnverb', -commas => 'no');
$p->classify();

DESCRIPTION

Analogical Modeling is an exemplar-based way to model language usage. Algorithm::AM is a Perl module which analyzes data sets using Analogical Modeling.

How to create data sets is not explained here. See the appendices in the "red book", Analogical Modeling: An exemplar-based approach to language, for details on that. See also the "green book", Analogical Modeling of Language, for an explanation of the method in general, and the "blue book", Analogy and Structure, for its mathematical basis.

METHODS

`new`

Arguments: see "Initializing a Project" (TODO: reorganize POD properly)

Creates and returns a subroutine to classify the data in a given project.

`classify`

Using the analogical modeling algorithm, this method classifies the instances in the project and prints the results to STDOUT, as well as to amcpresults in the project directory.

`print_summary` THIS METHOD IS UNDER CONSTRUCTION. Currently it is called by `classify` to print a summary of the classifcation results.

HISTORY

Initially, Analogical Modeling was implemented as a Pascal program. Subsequently, it was ported to Perl, with substantial improvements made in 2000. In 2001, the core of the algorithm was rewritten in C, while the parsing, printing, and statistical routines remained in C; this was accomplished by embedding a Perl interpreter into the C code.

In 2004, the algorithm was again rewritten, this time in order to handle more variables and large data sets. It breaks the supracontextual lattice into the direct product of four smaller ones, which the algorithm manipulates individually before recombining them. Because these lattices could be manipulated in parallel, using the right hardware, the module was named AM::Parallel. Later it was renamed Algorithm::AM to fit better into the CPAN ecostystem.

To provide more flexibility and to more closely follow "the Perl way", the C core is now an XSUB wrapped within a Perl module. Instead of specifying a configuration file, parameters are passed to the new() function of Algorithm::AM. The core functionality of the module has been stripped down; the only reports available are the statistical summary, the analogical set, and the gang listings. However, hooks are provided for users to create their own reports. They can also manipulate various parameters at run time and redirect output.

It is expected that future improvements will maintain a Perl interface to an XSUB. However, the design will remain simple enough that users without much programming experience will still be able to use the module with the least amount of trouble.

PROJECTS

Algorithm::AM assumes the existence of a project, a directory containing the data set, the test set, and the outcome file (named, not surprisingly, data, test, and outcome). Once the project is initialized, the user can set various parameters and run the algorithm.

If no outcome file is given, one is created using the outcomes which appear in the data set. If no test set is given, it is assumed that the data set functions as the test set.

Initializing a Project

A project is initialized using the syntax

$p = Algorithm::AM->new(directory, -commas => commas, ?options?);

The first parameter must be the name of the directory where the files are. It can be an absolute or a relative path. The following parameter is required:

-commas: Tells how to parse the lines of the data file. May be set to either yes or no. Any other value will trigger a warning and stop creation of the project, as will omitting this option entirely. See details in the "red book" to determine how to set this.

The following options are available:

-nulls

Tells how to treat nulls, i.e., variables marked with an equals sign =. Can be include or exclude; any other value will revert back to the default. Default: exclude.

-given

Tells whether or not to include the test item as a data item if it is found in the data set. Can be include or exclude; any other value will revert back to the default. Default: exclude.

-linear

Determines if the analogical set will be computed using occurrences (linearly) or pointers (quadratically). If -linear is set to yes, the analogical set will be computed using occurrences; otherwise, it will be computed using pointers. Default: compute using pointers.

-probability

Sets the probability of including any one data item. Default: undef. (TODO: what's undef do here?)

-repeat

Determines how many times each individual test item will be analyzed. Only makes sense if the probability is less than 1. Default: 1.

-skipset

Determines whether or not the analogical set is printed. Can be yes or no; any other value will revert to the default. Default: yes.

-gangs

Determines whether or not gang effects will be printed. Can be one of the following three values:

yes: Prints which contexts affect the result, how many pointers they contain, and which data items are in them.
summary: Prints which contexts affect the result and how many pointers they contain.
no: Omits any information about gang effects.

Any other value will revert to the default. Default: no.

So, the minimal invocation to initialize a project would be something like

$p = Algorithm::AM->new('finnverb', -commas => 'no');

while something fancier might be

$p = Algorithm::AM->new('negpre', -commas => 'yes',
                       -probability => 0.2, -repeat => 5,
     -skipset => 'no', -gangs => 'summary');

Initializing a project doesn't do anything more than read in the files and prepare them for analysis. To actually do any work, read on.

Running a project

To run an already initialized project with the defaults set at initialization time, use the following:

$p->classify();

Yep, that's all there is to it.

Of course, you can override the defaults. Any of the options set at initialization can be temporarily overridden. So, for instance, you can run your project twice, once including nulls and once excluding them, as follows:

$p->classify(-nulls => 'include');
$p->classify(-nulls => 'exclude');

Or, if you didn't specify a value at initialization time and accepted the default, you can merely use

$p->classify(-nulls => 'include');
$p->classify();

Or you can play with the probabilities:

$p->classify(-probability => 0.5, -repeat => 2);
$p->classify(-probability => 0.2, -repeat => 5);
$p->classify(-probability => 0.1, -repeat => 10);

Output

Output from the program is appended to the file amcpresults in the project directory by default. Internally, Algorithm::AM opens amcpresults at the beginning each run and selects its file handle to be current, so that the output of all print() statements gets directed to it. Directing output elsewhere is possible, but you can't do it the "obvious" way; the following won't work:

## do not use this code -- it is a BAD example
open FH5, ">results05";
open FH2, ">results02";
open FH1, ">results01";
select FH5;
$p->classify(-probability => 0.5, -repeat => 2);
select FH2;
$p->classify(-probability => 0.2, -repeat => 5);
select FH1;
$p->classify(-probability => 0.1, -repeat => 10);
close FH1;
close FH2;
close FH5;

That's because at the very beginning of each run, the code for $p reselects the file handle. However, you can do this using a hook; see -beginhook for a simple example of redirected output and -beginrepeathook for a more complicated one.

Warnings and error messages get sent to STDERR. If there are no fatal errors and the program runs normally, status messages are sent to STDERR. You can see how long the program has been running, what test item it's currently on, and even which iteration of an individual test item it's on if the repeat is set greater than one.

USING HOOKS

Algorithm::AM provides power and flexibility. The power is in the C code; the flexibility is in the hooks provided for the user to interact with the algorithm at various stages.

Hook Placement in `Algorithm::AM`

Hooks are just references to subroutines that can be passed to the project at run time; the subroutine references can be either named or anonymous. They are passed as any other option. The following hooks are currently implemented:

-beginhook

This hook is called before any test items are run.

-endhook

This hook is called after all test items are run.

Example: To send all the output from a run to another file, you can do the following:

$p->classify(-beginhook => sub {open FH, ">myoutput"; select FH;},
     -endhook => sub {close FH;});

-begintesthook

This hook is called at the beginning of each new test item. If a test item will be run more than once, this hook is called just once before the first iteration.

-endtesthook

This hook is called at the end of each test item. If a test item will be run more than once, this hook is called just once after the last iteration.

Example: If each test item is run just once, and you want to keep a running tally of how many test items are correctly predicted, you can use the variables $curTestOutcome, $pointermax, and @sum:

$count = 0;
$countsub = sub {
  ## must use eq instead of == in following statement
  ++$count if $sum[$curTestOutcome] eq $pointermax;
};
$p->classify(-endtesthook => $countsub,
     -endhook => sub {print "Number of correct predictions: $count\n";});

-beginrepeathook

This hook is called at the beginning of each iteration of a test item.

-endrepeathook

This hook is called at the end of each iteration of a test item.

Example: To vary the probability of each iteration through a test item, you can use the variables $probability and $pass:

open FH5, ">results05";
open FH2, ">results02";
$repeatsub = sub {
  $probability = (0.5, 0.2)[$pass];
  select((FH5, FH2)[$pass]);
};
$p->classify(-beginrepeathook => $repeatsub);

Then on iteration 0, the test item is analyzed with the probability of any data item being included set to 0.5, with output sent to file results05, while on iteration 1, the test item is analyzed with the probability of any data item being included set to 0.2, with output sent to file results02.

-datahook

This hook is called for each data item considered during a test item run. Unlike other hooks, which receive no arguments, this hook is passed the index of the data item under consideration. The value of this index ranges from one less than the number of data items to 0 (data items are considered in reverse order in Algorithm::AM for various reasons not gone into here).

The index passed is not a copy but the actual index variable used in Algorithm::AM; be careful not to change it -- for example, by assigning to $_[0] -- unless that is what is intended.

This hook should return a true value (in the Perl sense of true) if the data item should still be included in the test run, and should return a false value otherwise. To ensure this, it's a good idea to end the subroutine assigned to the hook with

return 1;

since

return;

returns an undefined value.

If the probability of including any data item is less than one, this hook is called before a call to rand() to see whether or not to include the item. If you don't like this, set -probability to 1 in the option list and call rand() yourself somewhere within the hook.

Example: The results for sorta- in the "red book" do not match what you get when you run finnverb. That's because the "red book" omitted all data items with outcome a-oi. You can do this using the variables @curTestItem, @outcome, and %outcometonum:

$datasub = sub {
  ## we use @curTestItem because finnverb/test has no specifiers
  return 1 unless join('', @curTestItem) eq 'SO0=SR0=TA';
  return 1 unless $outcome[$_[0]] eq $outcometonum{'a-oi'};
  return 0;
};
$p->classify(-datahook => $datasub);

Hook Variables

Various variables can be read and even manipulated by the hooks.

Note: All hook variables are exported into package main. If you don't know what this means, chances are you don't need to worry about it; if you do know what it means, you'll know how to deal with it.

However, these variables exist in package main only while a project is being run (they are exported using local()). Thus, you can only access them through a hook, and they will not clobber the values of variables of the same name outside of the run.

Variables Fixed at Initialization

These variables should be considered read-only, unless you're really sure what you're doing.

@outcomelist

This array lists all possible outcomes. It is generated either from the outcome file, if it exists, or from the outcomes that appear in the data file. If there is a "short" version and a "long" version of each outcome, @outcomelist contains the "long" version.

Outcomes are assigned positive integer values; outcome 0 is reserved for internal use of Algorithm::AM. (You'll have to look at the source code and its documentation for further details, which most likely you won't need.)

Example: File finnverb/outcome is as follows:

A V-i
B a-oi
C tV-si

During initialization, Algorithm::AM makes a series of assignments equivalent to the following:

@outcomelist = ('', 'V-i', 'a-oi', 'tV-si');

%outcometonum

This hash maps outcome strings (the "long" ones that appear in @outcomelist) to their respective positions in @outcomelist.

@outcome

$outcome[$i] contains the outcome of data item $i as an integer index into @outcomelist.

@data

$data[$i] is a reference to an array containing the variables of data item $i.

@spec

$spec[$i] contains the specifier for data item $i.

Example: Line 80 of file finnverb/data is as follows:

C MU0=SR0=TA MURTA

During initialization, Algorithm::AM makes a series of assignments equivalent to the following:

$outcome[79] = 3;
$data[79] = ['M', 'U', '0', '=', 'S', 'R', '0', '=', 'T', 'A'];
$spec[79] = 'MURTA';

Variables Used for a Specific Test Item

These variables should be considered read-only, unless you're really sure what you're doing.

$curTestOutcome: Contains the outcome index for the outcome of the current test item, as determined by @outcomelist, if an outcome has been specified, and 0 otherwise.
@curTestItem: Contains the variables of the current test item.
$curTestSpec: Contains the specifier of the current test item, if one has been specified, and is empty otherwise.

Variables Used for a Specific Iteration of a Test Item Run

$probability

Setting this changes the likelihood of including any one particular data item in a test run. Note: If the option -probability is not set at either initialization time or at run time, setting the value of $probability inside a hook has no effect. (This is an intentional optimization; see the source code and its documentation for the reason why.) Therefore, if you plan to change the probability during test item runs, make sure to specify a value (1 is a good choice) for the option -probability.

$pass

This variable indicates the current iteration of a test item run; it will range from 0 to one less than the number specified by the -repeat option.

Note: You cannot (easily) change the number of repetitions from within a hook. You can only do this (easily) using the -repeat option at run time. This is because typically you want each test item to be subjected to the same number of repetitions. (But if for some reason you really want to do this, you can increase $pass so that Algorithm::AM will skip some passes. You're on your own figuring out which hook to put this in.)

$datacap

This variable determines how many data items will be considered. It is initially set to scalar @data. However, if it is set smaller, only the first $datacap items in the data file will be considered. Algorithm::AM automatically truncates $datacap if it isn't an integer, so you don't have to.

Example: It is often of interest to see how results change as the number of data items considered decreases. Here's one way to do it:

$repeatsub = sub {
  $datacap = (1, 0.5, 0.25)[$pass] * scalar @data;
};
$p->classify(-repeat => 3, -beginrepeathook => $repeatsub);

Note that this will give different results than the following:

$repeatsub = sub {
  $probability = (1, 0.5, 0.25)[$pass];
};
$p->classify(-probability => 1, -repeat => 3, -beginrepeathook => $repeatsub);

The first way would be useful for modeling how predictions change as more examples are gathered -- say, as a child grows older (though the way it's written, it looks like the child is actually growing younger). The second way would be useful for modeling how predictions change as memory worsens -- say, as an adult grows older. Note that option -probability must be specified at run time if it hasn't been at initialization time; otherwise, calling the hook has no effect.

Variables Available at the End of a Test Run Iteration

Before looking at these variables, it is important to know what they contain.

Algorithm::AM works with really big integers, much larger than what 32 bits can hold. The XSUB uses a special internal format for storing them. (You can read all about it in the usual place: the source code and its documentation.) However, when the XSUB has finished its computations, it converts these integers into something that the Perl code finds more useful.

The scalar values returned from the XSUB are dual-valued scalars; they have different values depending on the context they're called in. In string context, you get a string representation of the integer. In numeric context, you get a double.

For example, if $n and $d are big integers returned from the XSUB, you can write

print $n/$d;

to see the decimal value of the fraction you get when you divide $n by $d, because the division will use the numeric values, while

print "$n/$d";

will let you see this fraction expressed as the quotient of two integers, because the quotation marks will interpolate the string values.

Because of this, you can't use == to test if two big integers have the same value -- they might be so big that the double representation doesn't give enough accuracy to distinguish them. Use eq to test equality.

If you need a comparison operator, you can use bigcmp().

@sum: Contains the number of pointers for each outcome index. (Remember that outcome indices start with 1.)
$pointertotal: Contains the total number of pointers.
$pointermax: Contains the maximum value among all the values in @sum.

Note that there is no variable reporting which outcome has the most pointers. That's because there could be a tie, and different users treat ties in different ways. So, if you want to see which outcomes have the highest number of pointers, try something like this:

@winners = ();
for ($i = 1; $i < @sum; ++$i) {
  push @winners, $i if $sum[$i] eq $pointermax; ## use eq, not ==
}

For another example using these variables, see -endtesthook.

Variables Useful for Formatting

You may want to create your own reports. These variables can help your formatting. (They are also used by Algorithm::AM to format the standard reports.)

$dformat

Leaves enough space to hold an integer equal to the number of data items. Justifies right.

$sformat

Leaves enough space to hold any of the specifiers in the data set. Justifies left.

$oformat

Leaves enough space to hold a "long" outcome. Justifies left.

$vformat

Formats a list of variables. Set -gangs to yes for an example.

$pformat

Leaves enough space to hold the big integer $pointertotal, and thus is big enough to hold $pointermax or any element of @sum as well. Justifies right.

Note: This variable changes with each iteration of a test item.

Hook Function

The following function is also exported into package main and available for use in hooks. This is done with local(), just as with hook variables, so it is not available outside of hooks.

bigcmp()

Compares two big integers, returning 1, 0, or -1 depending on whether the first argument is greater than, equal to, or less than the second argument. Remember that the syntax is different: you must write

bigcmp($a, $b)

instead of $a bigcmp $b.

MORE EXAMPLES

Summarizing a Repeated Test Item

Suppose you run each test item 5 times, each with probability 0.005, and you want to create a statistical analysis summarizing the results for each test item. Here's one way to do it:

$begintest = sub {
  $valid = 0;
  @testPct = ();
  @testPctSq = ();
  $correct = 0;
};
$endrepeat = sub {
  return unless $pointertotal;
  ++$valid;
  ++$correct if $sum[$curTestOutcome] eq $pointermax;
  for ($i = 1; $i < @outcomelist; ++$i) {
    $testPct[$i] += $sum[$i]/$pointertotal;
    $testPctSq[$i] += ($sum[$i]*$sum[$i])/($pointertotal*$pointertotal);
  }
};
$endtest = sub {
  print "Summary for test item: $curTestSpec\n";
  print "Valid runs: $valid out of 5\n\n";
  print "\n" and return unless $valid;
  printf "$oformat    Avg     Std Dev\n", "";
  for ($i = 1; $i < @outcomelist; ++$i) {
    next unless $testPct[$i];
    if ($valid > 1) {
      printf "$oformat  %7.3f%% %7.3f%%\n",
  $outcomelist[$i],
  100 * $testPct[$i]/$valid,
  100 * sqrt(($testPctSq[$i]-$testPct[$i]*$testPct[$i]/$valid)/($valid-1));
    } else {
      printf "$oformat  %7.3f%%\n",
  $outcomelist[$i],
  100 * $testPct[$i]/$valid;
    }
  }
  printf "\nCorrect prediction occurred %7.3f%% (%i/5) of the time\n",
    100 * $correct / 5,
    $correct;
  print "\n\n";
};
$p->classify(-probability => 0.005, -repeat => 5,
     -begintesthook => $begintest, -endrepeathook => $endrepeat, -endtesthook => $endtest);

Creating a Confusion Matrix

Suppose you want to compare correct outcomes with predicted outcomes. Here's one way to do it:

$begin = sub {
  @confusion = ();
};
$endrepeat = sub {
  if (!$pointertotal) {
    ++$confusion[$curTestOutcome][0];
    return;
  }
  if ($sum[$curTestOutcome] eq $pointermax) {
    ++$confusion[$curTestOutcome][$curTestOutcome];
    return;
  }
  my @winners = ();
  my $i;
  for ($i = 1; $i < @outcomelist; ++$i) {
    push @winners, $i if $sum[$i] == $pointermax;
  }
  my $numwinners = scalar @winners;
  foreach (@winners) {
    $confusion[$curTestOutcome][$_] += 1 / $numwinners;
  }
};
$end = sub {
  my($i,$j);
  for ($i = 1; $i < @outcomelist; ++$i) {
    my $total = 0;
    foreach (@{$confusion[$i]}) {
      $total += $_;
    }
    next unless $total;
    printf "Test items with outcome $oformat were predicted as follows:\n",
      $outcomelist[$i];
    for ($j = 1; $j < @outcomelist; ++$j) {
      my $t;
      next unless ($t = $confusion[$i][$j]);
      printf "%7.3f%% $oformat  (%i/%i)\n", 100 * $t / $total, $outcomelist[$j], $t, $total;
    }
    if ($t = $confusion[$i][0]) {
      printf "%7.3f%% could not be predicted (%i/%i)\n", 100 * $t / $total, $t, $total;
    }
    print "\n\n";
  }
};
$p->classify(-probability => 0.005, -repeat => 5,
     -beginhook => $begin, -endrepeathook => $endrepeat, -endhook => $end);

WARNINGS AND ERROR MESSAGES

Project not specified: No project was specified in the call to Algorithm::AM->new. An empty subroutine is returned (so that batch scripts do not break).
Project %s has no data file: The project directory has no file named data. An empty subroutine is returned (so that batch scripts do not break).
Project %s did not specify comma formatting: The required parameter -commas was not provided. An empty subroutine is returned (so that batch scripts do not break).
Project %s did not specify comma formatting correctly: Parameter -commas must be either yes or no. An empty subroutine is returned (so that batch scripts do not break).
Project %s did not specify option -nulls correctly: Parameter -nulls must be either include or exclude. Displayed default value will be used.
Project %s did not specify option -given correctly: Parameter -given must be either include or exclude. Displayed default value will be used.
Project %s did not specify option -skipset correctly: Parameter -skipset must be either yes or no. Displayed default value will be used.
Project %s did not specify option -gangs correctly: Parameter -gangs must be either yes, summary, or no. Displayed default value will be used.
Couldn't open %s/test: Project %s does not have a test file. The data file will be used.

AUTHORS

Theron Stanford <shixilun@yahoo.com>

Nathan Glenn <garfieldnate@gmail.com>

COPYRIGHT

To install Algorithm::AM, copy and paste the appropriate command in to your terminal.

cpanm

cpanm Algorithm::AM

CPAN shell

perl -MCPAN -e shell
install Algorithm::AM

For more information on module installation, please visit the detailed CPAN module installation guide.

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