glicko2_periodic_ranker

Multi-period Glicko-2 ranker over temporal pairwise game datasets. Applies the standard Glicko-2 rating, rating-deviation, and volatility update equations period by period using simultaneous player updates inside each declared rating period.

This library implements the ranker_protocol defined in the ranking_protocols library. It learns one rating per item from datasets implementing the temporal_pairwise_ranking_dataset_protocol protocol, processing declared rating periods in order and applying simultaneous Glicko-2 player updates inside each period using the standard Glicko-2 rating, rating-deviation, and volatility update equations.

Draws are represented directly using game scores on the set {0.0, 0.5, 1.0}. Players who are inactive in a declared period keep their rating and volatility while their rating deviation is inflated for that period.

Players are initialized when they first play instead of being forced to appear in the first declared period.

The library provides predicates for learning a ranker from temporal pairwise games, using it to order candidate items, and exporting it as a list of predicate clauses or to a file.

Datasets are represented as objects implementing the temporal_pairwise_ranking_dataset_protocol protocol from the ranking_protocols library. See the test_datasets directory for examples.

API documentation

Open the ../../apis/library_index.html#glicko2_periodic_ranker link in a web browser.

Loading

To load this library, load the loader.lgt file:

| ?- logtalk_load(glicko2_periodic_ranker(loader)).

Testing

To test this library predicates, load the tester.lgt file:

| ?- logtalk_load(glicko2_periodic_ranker(tester)).

Features

  • Temporal Pairwise Game Learning: Learns one deterministic rating per item from temporal pairwise game results.

  • Deterministic Multi-Period Glicko-2 Semantics: Processes the declared rating periods in order and applies simultaneous Glicko-2 player updates within each period.

  • Direct Draw Support: Uses explicit game scores on the set {0.0, 0.5, 1.0}, allowing wins, draws, and losses to be represented directly.

  • Inactive-Period Deviation Inflation: Players who do not play in a declared period keep their rating and volatility while their rating deviation is inflated for that period.

  • Late Player Initialization: Players are initialized when they first appear in the dataset instead of being forced to play in the first declared period.

  • Configurable Rating Parameters: Exposes the initial rating, initial rating deviation, initial volatility, volatility constraint parameter, and volatility-solver tolerance as user options.

  • Deterministic Ranking: Orders candidate items by learned rating with deterministic tie-breaking.

  • Strict Dataset Validation: Rejects duplicate periods, unknown periods, undeclared items, self-games, illegal scores, and disconnected comparison graphs.

  • Extended Diagnostics: Preserves per-item rating deviations, volatilities, processed period count, and final period metadata in the learned ranker diagnostics.

  • Ranker Export: Learned rankers can be exported as self-contained terms.

  • Shared Ranking Infrastructure: Reuses the ranking_protocols helpers for option processing, dataset validation, diagnostics access, export, and candidate ranking.

Rating semantics

This implementation uses the standard Glicko-2 update equations over explicit rating periods supplied by the dataset. The declared periods are processed in order, and all active players in a period are updated simultaneously from the pre-period ratings, deviations, and volatilities.

Game results are represented directly using scores in the set {0.0, 0.5, 1.0}. A score of 0.5 denotes a draw. Players who are inactive in a period keep their rating and volatility, but their rating deviation is inflated for that period according to the Glicko-2 inactivity rule.

Players are initialized when they first appear in a game rather than being required to occur in the first declared period. Items declared by the dataset but never seen in a game are initialized after training so they remain present in the learned ranker with the configured initial parameters.

Usage

Learning a ranker

% Learn from a temporal pairwise ranking dataset object
| ?- glicko2_periodic_ranker::learn(my_dataset, Ranker).
...

% Learn with custom Glicko-2 parameters
| ?- glicko2_periodic_ranker::learn(my_dataset, Ranker, [initial_rating(1400.0), initial_deviation(300.0), initial_volatility(0.07), tau(0.4)]).
...

Inspecting diagnostics

% Inspect model, options, deviations, volatilities, and period metadata
| ?- glicko2_periodic_ranker::learn(my_dataset, Ranker),
     glicko2_periodic_ranker::diagnostics(Ranker, Diagnostics).
Diagnostics = [...]
...

Ranking candidate items

% Rank a candidate set from most preferred to least preferred
| ?- glicko2_periodic_ranker::learn(my_dataset, Ranker),
     glicko2_periodic_ranker::rank(Ranker, [item_a, item_b, item_c], Ranking).
Ranking = [...]
...

Candidate lists must be proper lists of unique, ground items declared by the training dataset. Invalid ranker terms, duplicate candidates, and candidates containing variables are rejected with errors instead of being silently accepted.

Exporting the ranker

Learned rankers can be exported as a list of clauses or to a file for later use.

% Export as predicate clauses
| ?- glicko2_periodic_ranker::learn(my_dataset, Ranker),
     glicko2_periodic_ranker::export_to_clauses(my_dataset, Ranker, my_ranker, Clauses).
Clauses = [my_ranker(glicko2_periodic_ranker(...))]
...

% Export to a file
| ?- glicko2_periodic_ranker::learn(my_dataset, Ranker),
     glicko2_periodic_ranker::export_to_file(my_dataset, Ranker, my_ranker, 'ranker.pl').
...

Options

The following options can be passed to the learn/3 predicate:

  • initial_rating(Rating): Initial rating assigned to a player when it is first initialized.

  • initial_deviation(Deviation): Initial rating deviation assigned to a player when it is first initialized.

  • initial_volatility(Volatility): Initial volatility assigned to a player when it is first initialized.

  • tau(Tau): Positive volatility-constraint parameter used by the Glicko-2 update.

  • volatility_tolerance(Tolerance): Positive stopping tolerance used by the volatility root-finding iteration.

Datasets supplied to the ranker must use legal game scores from the set {0.0, 0.5, 1.0}.

Diagnostics syntax

The diagnostics/2 predicate returns a list of metadata terms with the form:

[
    model(glicko2_periodic_ranker),
    options(Options),
    rating_deviations(Deviations),
    volatilities(Volatilities),
    periods_processed(PeriodsProcessed),
    final_period(FinalPeriod),
    dataset_summary(DatasetSummary)
]

Ranker representation

The learned ranker is represented by a compound term of the form:

glicko2_periodic_ranker(Items, Ratings, Diagnostics)

Where:

  • Items: List of ranked items.

  • Ratings: List of Item-Rating pairs.

  • Diagnostics: List of metadata terms, including the effective options, per-item rating deviations, per-item volatilities, processed period count, final period, and dataset summary.

References

  1. Glickman, M. E. (2012). Example of the Glicko-2 system.