`glicko2_ranker`

Glicko-2 pairwise preference ranker. It applies the standard Glicko-2 rating, rating-deviation, and volatility update equations over a single synthetic rating period built from the aggregated pairwise outcomes of the dataset.

The library implements the ranker_protocol defined in the ranking_protocols library. It provides predicates for learning a ranker from pairwise preferences, 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 pairwise_ranking_dataset_protocol protocol from the ranking_protocols library. See the test_datasets directory for examples. The current implementation requires a well-formed connected pairwise dataset so that learned ratings remain globally comparable across all ranked items.

API documentation

Open the ../../apis/library_index.html#glicko2_ranker link in a web browser.

Loading

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

| ?- logtalk_load(glicko2_ranker(loader)).

Testing

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

| ?- logtalk_load(glicko2_ranker(tester)).

Features

Pairwise Preference Learning: Learns one deterministic rating per item from pairwise outcomes.
Deterministic Single-Period Glicko-2 Semantics: Applies the standard Glicko-2 rating-period update equations over one synthetic rating period built from the aggregated pairwise results.
Configurable Rating Parameters: Exposes the initial rating, initial rating deviation, initial volatility, volatility constraint parameter, and volatility-solver tolerance as user options.
Integer Weight Fidelity: Preference weights must be positive integers and are interpreted as repeated unit outcomes inside the same rating period.
Deterministic Ranking: Orders candidate items by learned rating with deterministic tie-breaking.
Strict Dataset Validation: Rejects duplicate items, undeclared items, self-preferences, non-positive weights, and disconnected comparison graphs.
Extended Diagnostics: Preserves per-item rating deviations and volatilities 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 a deterministic batch interpretation of Glicko-2. The whole dataset is treated as a single synthetic rating period because the current pairwise dataset protocol does not encode timestamps or rating-period boundaries.

The implementation converts ratings and rating deviations to the internal Glicko-2 scale, applies the standard opponent-scaling factor g(phi), expected-score function, variance term v, improvement estimate delta, and volatility update iteration, and then converts the updated ratings and deviations back to the conventional Glicko scale.

Positive integer preference weights are replayed as repeated unit outcomes. Datasets using non-integer preference weights are rejected because they do not map cleanly to standard Glicko-2 update semantics.

Usage

Learning a ranker

% Learn from a pairwise ranking dataset object
| ?- glicko2_ranker::learn(my_dataset, Ranker).
...

% Learn with custom Glicko-2 parameters
| ?- glicko2_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 dataset metadata
| ?- glicko2_ranker::learn(my_dataset, Ranker),
     glicko2_ranker::diagnostics(Ranker, Diagnostics).
Diagnostics = [...]
...

Ranking candidate items

% Rank a candidate set from most preferred to least preferred
| ?- glicko2_ranker::learn(my_dataset, Ranker),
     glicko2_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_ranker::learn(my_dataset, Ranker),
     glicko2_ranker::export_to_clauses(my_dataset, Ranker, my_ranker, Clauses).
Clauses = [my_ranker(glicko2_ranker(...))]
...

% Export to a file
| ?- glicko2_ranker::learn(my_dataset, Ranker),
     glicko2_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 every item.
initial_deviation(Deviation): Initial rating deviation assigned to every item.
initial_volatility(Volatility): Initial volatility assigned to every item.
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 positive integer preference weights. Non-integer weights are rejected.

Diagnostics syntax

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

[
    model(glicko2_ranker),
    options(Options),
    rating_deviations(Deviations),
    volatilities(Volatilities),
    dataset_summary(DatasetSummary)
]

Ranker representation

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

glicko2_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, and dataset summary.

References

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

glicko2_ranker