# `elo_ranker`

Elo pairwise preference ranker. Processes the pairwise preference stream in dataset enumeration order using the standard Elo expected-score formula and symmetric rating updates after each observed result.

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#elo_ranker link in a web browser.

## Loading

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

    | ?- logtalk_load(elo_ranker(loader)).

## Testing

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

    | ?- logtalk_load(elo_ranker(tester)).

## Features

- Pairwise Preference Learning: Learns one deterministic rating per item from pairwise outcomes.

- Deterministic Batch Elo Semantics: Replays the dataset preference stream in enumeration order using the standard Elo expected-score formula. Because the current pairwise dataset protocol does not record historical timestamps, the implementation is a deterministic batch interpretation of that enumeration order rather than a reconstruction of a literal chronological competition log.

- Configurable Rating Parameters: Exposes the initial rating, K-factor, and rating scale as user options.

- Integer Weight Fidelity: Preference weights must be positive integers and are replayed as repeated unit outcomes in dataset enumeration order.

- 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.

- 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, export, and candidate ranking.

## Rating semantics

This implementation uses a deterministic batch Elo interpretation over the pairwise preference stream. Each preference is processed in dataset enumeration order. For a winner with rating `R_w` and a loser with rating `R_l`, the expected winner score is computed as

    1 / (1 + 10^((R_l - R_w)/Scale))

and the winner receives a rating update of

    K * (1 - ExpectedWinnerScore)

with the loser receiving the symmetric negative update.

Because the current pairwise dataset protocol does not encode timestamps, this is a deterministic batch Elo variant rather than a literal historical competition-log replay.

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 Elo update semantics.

## Usage

### Learning a ranker

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

    % Learn with custom Elo parameters
    | ?- elo_ranker::learn(my_dataset, Ranker, [initial_rating(1400.0), k_factor(24.0), rating_scale(200.0)]).
    ...

### Inspecting diagnostics

    % Inspect model, options, and dataset summary metadata
    | ?- elo_ranker::learn(my_dataset, Ranker),
         elo_ranker::diagnostics(Ranker, Diagnostics).
    Diagnostics = [...]
    ...

### Ranking candidate items

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

    % Export to a file
    | ?- elo_ranker::learn(my_dataset, Ranker),
         elo_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.

- `k_factor(KFactor)`: Positive Elo K-factor.

- `rating_scale(Scale)`: Positive rating-scale denominator used in the expected-score formula.

Datasets supplied to the ranker must use positive integer preference weights. Non-integer weights are rejected.

## Ranker representation

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

    elo_ranker(Items, Ratings, Diagnostics)

Where:

- `Items`: List of ranked items.

- `Scores`: List of `Item-Rating` pairs.

- `Diagnostics`: List of metadata terms, including the effective options and dataset summary.

## References

1. Elo, A. E. (1978). The Rating of Chessplayers, Past and Present. Arco.