# `ewma_anomaly_detector`

EWMA (Exponentially Weighted Moving Average) anomaly detector for continuous sequence-like datasets. It is a statistical anomaly-detection method based on a two-sided EWMA control chart: for each known step value `x_t`, it computes a standardized deviation, updates the EWMA statistic `E_t`, and uses the maximum normalized excursion `|E_t| / (L*c_t)` as the raw anomaly score, so a score of `1.0` corresponds exactly to reaching the chosen EWMA control limit.

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. Declared continuous attributes are interpreted as ordered monitoring steps in a sequence. See the `ewma_anomaly_detector/tests.lgt` file for example datasets.

## API documentation

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

## Loading

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

    | ?- logtalk_load(ewma_anomaly_detector(loader)).

## Testing

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

    | ?- logtalk_load(ewma_anomaly_detector(tester)).

## Features

- Statistical method: implements anomaly detection based on a two-sided EWMA control chart, using learned per-step population means and standard deviations for continuous attributes.

- Ordered sequence interpretation: declared continuous attributes are treated as ordered monitoring steps. For each known step value `x_t`, the library computes `z_t = (x_t - mu_t) / sigma_t` and updates the EWMA recurrence `E_t = lambda*z_t + (1 - lambda)*E_(t-1)` with `E_0 = 0`.

- EWMA control limits: the raw anomaly score is the maximum normalized excursion `|E_t| / (L*c_t)`, where `L` is the learn-time `control_limit_multiplier/1` option and `c_t = sqrt(lambda/(2-lambda) * (1 - (1-lambda)^(2*t)))` is the classical EWMA control-limit factor after `t` EWMA updates. The learned detector stores a precomputed attribute schema so that query values can be reordered efficiently during scoring.

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

- 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 any non-baseline training example is found. The `filter` policy removes non-baseline examples before fitting the baseline statistics.

- Missing-value tolerant: ignores missing values when fitting per-step statistics. During scoring, missing step values do not update the EWMA state or advance the EWMA update count. Queries must still provide at least one known value.

- Bounded scoring: maps the raw EWMA excursion to `[0.0, 1.0)` using `Score = Raw / (1 + Raw)`.

- EWMA control parameters: supports learn-time `control_limit_multiplier/1` and `smoothing_factor/1` options. The default `control_limit_multiplier(3.0)` and `smoothing_factor(0.2)` correspond to a common EWMA monitoring setup.

- Default threshold: the default `anomaly_threshold(0.5)` corresponds to the chosen EWMA control limit after score normalization. Because the raw score is already normalized by the learned control limit, this threshold remains the same for any learned `control_limit_multiplier/1` value.

- Learn-time control parameters: `control_limit_multiplier/1` and `smoothing_factor/1` are recorded in the learned detector and reused for subsequent scoring and prediction. Passing them to `predict/4` does not override the learned values. Only `anomaly_threshold/1` can be overridden at predict time.

- All-missing queries rejected: scoring and prediction throw a `domain_error(non_empty_known_values, AttributeNames)` exception when every declared step 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: `0.5`)

- `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 `reject` and `filter` (default: `reject`)

- `control_limit_multiplier(ControlLimitMultiplier)`: Learn-time EWMA control-limit multiplier `L` (default: `3.0`)

- `smoothing_factor(SmoothingFactor)`: Learn-time EWMA smoothing factor `lambda` (default: `0.2`)

## Detector representation

The learned detector is represented by default as:

    ewma_detector(TrainingDataset, AttributeSchema, Encoders, Diagnostics)

Where:

- `TrainingDataset`: training dataset object identifier

- `AttributeSchema`: precomputed attribute ordering metadata used to validate and reorder query step values efficiently during scoring

- `Encoders`: list of `ewma_encoder(Attribute, Mean, Scale)` records

- `Diagnostics`: learned metadata terms including `model/1`, `training_dataset/1`, `attribute_names/1`, `feature_count/1`, `example_count/1`, and `options/1`. The `example_count/1` value is the effective number of training examples after applying the selected baseline selection policy.

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 standardized deviation `z_t = (x_t - mu_t) / sigma_t` for each known monitoring step. Second, those deviations are processed sequentially using the EWMA recurrence `E_t = lambda*z_t + (1 - lambda)*E_(t-1)` with the learned `smoothing_factor/1` value. Third, the maximum normalized excursion `|E_t| / (L*c_t)` is mapped to the interval `[0.0, 1.0)` using `Score = Raw / (1 + Raw)`.

The control-limit factor `c_t` is computed from the number of actual EWMA updates, not from the declared attribute position. Accordingly, leading or intermediate missing step values neither update the EWMA state nor widen the control limits.

The `smoothing_factor/1` option changes the EWMA update rule itself. Smaller values make the detector retain longer-term history while larger values react more strongly to recent deviations. The `control_limit_multiplier/1` option scales the control limits directly in the score path. Larger values therefore make the detector less sensitive by requiring larger EWMA excursions before the raw score reaches `1.0`.

The `baseline_class_values/1` option declares which dataset class labels are admissible for baseline fitting. 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 and raises a `domain_error(non_empty_baseline_training_data, Dataset)` exception if no training examples remain after filtering.

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