[ENH] Implement outlier detection based on probabilistic regressors

[arnavk23]

Reference Issues/PRs

Fixes #390

What does this implement/fix? Explain your changes.

It introduces three reduction strategies from probabilistic regression to outlier/anomaly detection with a PyOD-compatible interface:

1. QuantileOutlierDetector - Detects outliers based on predictive quantile extremity. Samples falling outside the expected quantile range (configurable via alpha parameter) are flagged as outliers. The outlier score is computed as the distance from the nearest quantile bound, normalized by the quantile range.

2. DensityOutlierDetector - Detects outliers based on probability density (negative log-likelihood). Samples with low probability density under the predictive distribution are flagged as outliers. Supports both log-likelihood and raw likelihood scoring via the use_log parameter.

3. LossOutlierDetector - Detects outliers based on predictive loss. Supports multiple loss functions:

   • log_loss: negative log-likelihood (equivalent to density-based)
   • crps: Continuous Ranked Probability Score
   • interval_score: interval score with configurable coverage
   • Custom loss functions via callable

Key features:

• PyOD-compatible interface with fit(), predict(), and decision_function() methods
• Works with any skpro probabilistic regressor
• Configurable contamination parameter for automatic threshold determination
• Can be used with both conditional and unconditional distribution estimates

Implementation details:

• Base class BaseOutlierDetector provides common functionality
• All detectors compute outlier scores during training and use percentile-based thresholds

Does your contribution introduce a new dependency? If yes, which one?

No, this implementation uses only existing dependencies (numpy, pandas, scipy - already required by skpro).

What should a reviewer concentrate their feedback on?

• Does the PyOD-compatible interface make sense for skpro users?
• Are the outlier scoring methods mathematically sound and properly implemented?
• Particularly in _quantile.py and _loss.py where we handle array reshaping and multi-output cases
• The CRPS implementation in _loss.py uses a Normal distribution approximation - is this adequate or should we use quantile-based approximation instead?
• Are the docstrings clear and comprehensive enough?

Did you add any tests for the change?

Yes, comprehensive test suite added in skpro/outlier/tests/test_outliers.py:

• Tests for fitting all three detector types
• Tests for prediction and decision_function methods
• Tests for different loss functions (log_loss, CRPS, interval_score)
• Tests for custom loss functions
• Tests for error handling (missing y values)
• Integration test verifying all detectors work with the same interface
• Tests use @run_test_for_class decorator for proper test discovery

Example Output

The implementation includes a comprehensive example that demonstrates all three detector types on synthetic data with known outliers.
The visualization shows:

• Outlier scores from QuantileOutlierDetector and DensityOutlierDetector
• Detected outliers in feature space
• Performance comparison (precision/recall) across different methods

Any other comments?

• The implementation is designed to be extensible - users can easily create custom detectors by subclassing BaseOutlierDetector and implementing _compute_decision_scores().

PR checklist

For all contributions

• I've added myself to the list of contributors with any new badges I've earned :-)
• The PR title starts with either [ENH], [MNT], [DOC], or [BUG]. (Title: [ENH] Implement outlier detection based on probabilistic regressors)

For new estimators

• I've added the estimator to the API reference - in docs/source/api_reference/taskname.rst, follow the pattern.
• I've added one or more illustrative usage examples to the docstring, in a pydocstyle compliant Examples section.
• If the estimator relies on a soft dependency, I've set the python_dependencies tag and ensured dependency isolation (N/A - no new soft dependencies)

[arnavk23]

@fkiraly @marrov Could you please review this pr? I think this is entirely done here.

[marrov]

@arnavk23 - Pretty large PR, nothing jumps at me after a quick scan. I'll trigger the LLM review and come back to it when I have some bandwidth (maybe next week).

[Copilot]

Pull request overview

Adds a new skpro.outlier module that implements outlier/anomaly detection by “reducing” the task to probabilistic regression, exposing a PyOD-like interface (fit, decision_function, predict).

Changes:

• Introduces BaseOutlierDetector plus three detector implementations: quantile-, density-, and loss-based.
• Adds documentation/API reference entries and a runnable example script.
• Adds a new test suite covering detectors’ core interface and key options.

Reviewed changes

Copilot reviewed 11 out of 11 changed files in this pull request and generated 13 comments.

Show a summary per file

File	Description
skpro/outlier/base.py	Adds shared PyOD-like base class and thresholding logic.
skpro/outlier/_quantile.py	Implements quantile-interval based scoring logic.
skpro/outlier/_density.py	Implements likelihood / negative-log-likelihood based scoring.
skpro/outlier/_loss.py	Implements loss-based scoring incl. log-loss, CRPS, interval score, custom loss.
skpro/outlier/__init__.py	Exposes new detectors via package exports.
skpro/outlier/tests/test_outliers.py	Adds unit/integration tests for the new detectors.
skpro/outlier/tests/__init__.py	Initializes tests package.
docs/source/api_reference/outlier.rst	Documents new outlier module and classes in API reference.
docs/source/api_reference.rst	Links outlier API reference into master index.
examples/outlier_detection_example.py	Adds end-to-end usage example + optional visualization.
.all-contributorsrc	Adds contributor entry for the PR author.

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[Copilot]

Pull request overview

Copilot reviewed 11 out of 11 changed files in this pull request and generated 7 comments.

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Pull request overview

Copilot reviewed 11 out of 11 changed files in this pull request and generated 6 comments.

Comments suppressed due to low confidence (1)

docs/source/api_reference.rst:24

• The toctree lists api_reference/tags twice. This can lead to duplicate entries / Sphinx warnings and is likely unintended; remove the duplicate (keep a single api_reference/tags entry).

.. toctree::
    :maxdepth: 1

    api_reference/tags
    api_reference/regression
    api_reference/survival
    api_reference/outlier
    api_reference/distributions
    api_reference/metrics
    api_reference/tags
    api_reference/base

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