# `modified_z_score_anomaly_detector`

Statistical modified Z-score anomaly detector for continuous datasets. It is a statistical anomaly-detection method based on the modified Z-score defined by Iglewicz and Hoaglin (1993): for each known continuous attribute value `x`, the detector computes `0.6745 * (x - median) / mad`, where `median` is the learned sample median and `mad` is the learned median absolute deviation, and then aggregates the per-attribute modified Z-scores using the selected learn-time `score_mode/1` option.

The library implements the `anomaly_detector_protocol` defined in the `anomaly_detection_protocols` library. It learns a detector from a continuous dataset, computes anomaly scores for new instances, predicts `normal` or `anomaly`, and exports learned detectors as clauses or files.

Datasets are represented as objects implementing the `anomaly_dataset_protocol` protocol from the `anomaly_detection_protocols` library. See the `anomaly_detection_protocols/test_datasets` directory for examples.

## API documentation

Open the ../../apis/library_index.html#modified-z-score link in a web browser.

## Loading

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

    | ?- logtalk_load(modified_z_score_anomaly_detector(loader)).

## Testing

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

    | ?- logtalk_load(modified_z_score_anomaly_detector(tester)).

## Features

- Statistical method: implements robust anomaly detection based on the modified Z-score described by Iglewicz and Hoaglin (1993), using the sample median and median absolute deviation of each continuous attribute to measure how far new observations deviate from the training data distribution.

- Classical per-attribute modified Z-score: for each known attribute value `x`, the library computes the standard robust score `0.6745 * (x - median) / mad`, where `median` is the learned sample median for that attribute and `mad` is the learned median absolute deviation.

- Continuous features only: accepts datasets whose declared attributes are all `continuous`.

- Robust statistics: reuses the `statistics` library `sample` object to compute per-attribute medians and the median of absolute deviations.

- Baseline training selection: supports learn-time `baseline_class_values(ClassValues)` and `baseline_selection_policy(Policy)` options. The default baseline class values are `[normal]`. The default `reject` policy throws an error if non-baseline examples are present, while `filter` removes them before fitting.

- Missing-value tolerant: ignores missing values when fitting attribute statistics. During scoring, queries must provide at least one known value. In the default `score_mode(root_mean_square)`, the raw score is normalized by the number of known values so that scores remain comparable across different missing-value patterns.

- Configurable scoring semantics: supports both dense multivariate deviation scoring using `score_mode(root_mean_square)` and sparse anomaly detection using `score_mode(any_feature_extreme)`. The default root-mean-square mode reuses the `numberlist` library Euclidean norm predicate as part of the computation. The `score_mode/1` option only controls how the per-attribute modified Z-scores are aggregated into a single raw anomaly score.

- Bounded scoring: maps the raw multivariate modified Z-score to `[0.0, 1.0)` using `Score = Raw / (1 + Raw)`.

- Default threshold: the default `anomaly_threshold(0.7777777777777778)` corresponds to the classical raw modified Z-score cutoff `3.5` recommended by Iglewicz and Hoaglin (1993), while remaining overrideable in `learn/3` and `predict/4`.

- Learn-time score mode: `score_mode/1` is recorded in the learned detector and reused for subsequent scoring and prediction. Passing a `score_mode/1` option to `predict/4` does not override the learned mode.

- All-missing queries rejected: scoring and prediction throw a `domain_error(non_empty_known_values, AttributeNames)` exception when every declared feature is missing in the query.

- Featureless datasets rejected: datasets must declare at least one continuous feature; otherwise `learn/2-3` throws a `domain_error(non_empty_features, Dataset)` exception.

- Detector export: learned detectors can be exported as predicate clauses.

- Explicit validation and diagnostics: supports the shared `check_anomaly_detector/1`, `valid_anomaly_detector/1`, `diagnostics/2`, `diagnostic/2`, and `anomaly_detector_options/2` predicates.

## Options

The following options are supported by the public API:

- `anomaly_threshold(Threshold)`: Threshold for `predict/3-4` (default: `0.7777777777777778`)

- `baseline_class_values(ClassValues)`: Learn-time class labels that are admissible for baseline fitting (default: `[normal]`)

- `baseline_selection_policy(Policy)`: Learn-time handling of examples whose class is not listed in `baseline_class_values/1`. Supported values are `filter` and `reject` (default: `reject`)

- `score_mode(Mode)`: Learn-time score aggregation mode for `learn/3`. Supported values are `root_mean_square` and `any_feature_extreme` (default: `root_mean_square`). If passed to `predict/4`, it is ignored and the value stored in the learned detector is used.

## Detector representation

The learned detector is represented by default as:

    modified_z_score_detector(TrainingDataset, Encoders, Diagnostics)

Where:

- `TrainingDataset`: training dataset object identifier

- `Encoders`: list of `modified_zscore(Attribute, Median, Scale)` records

- `Diagnostics`: learned metadata terms including `model/1`, `training_dataset/1`, `attribute_names/1`, `feature_count/1`, `example_count/1`, and `options/1`

When exported using `export_to_clauses/4` or `export_to_file/4`, this detector term is serialized directly as the single argument of the generated predicate clause so that the exported model can be loaded and reused as-is.

## Notes

Scoring has three stages. First, the detector computes one classical per-attribute modified Z-score for each known attribute value using `0.6745 * (x - median) / mad`. Second, those per-attribute modified Z-scores are aggregated into a single raw anomaly score according to the learned `score_mode/1` option. Third, the raw score is mapped to the interval `[0.0, 1.0)` using `Score = Raw / (1 + Raw)`.

The `score_mode/1` option does not change the classical per-attribute formula. It only changes the aggregation step. With `score_mode(root_mean_square)`, the raw score is the root mean square of the per-attribute modified Z-scores. With `score_mode(any_feature_extreme)`, the raw score is the maximum absolute per-attribute modified Z-score.

The `baseline_class_values/1` option declares which dataset class labels are admissible for fitting the baseline medians and median absolute deviations. The `baseline_selection_policy/1` option then controls what happens when other labels are present in the training data. The default `reject` policy raises a `domain_error(baseline_only_training_data, Dataset)` exception when any non-baseline example is found. The `filter` policy removes non-baseline examples before fitting.

Attributes with zero observed median absolute deviation are assigned a fallback scale of `1.0`. This keeps the detector well-defined for singleton datasets or constant columns while still yielding zero score for matching values and positive scores for deviating values.

The root-mean-square aggregation keeps the default threshold stable as the number of observed dimensions grows and avoids penalizing partially observed queries solely for having fewer known attributes.

Use `score_mode(any_feature_extreme)` when a single extreme feature should be sufficient to flag an anomaly in high-dimensional data.