Summary  
This chapter covers how to compute the Mahalanobis distance in code by estimating and inverting the covariance matrix and applying linear algebra operations to measure multivariate distances.  

General domain of usage  
Anomaly detection

import unittest
import numpy as np
import re

def _dynamic_test(tc, cond, ok, fail):
    if cond:
        tc._testMethodName = ok
        tc.assertTrue(True, ok)
    else:
        tc._testMethodName = fail
        tc.fail(fail)

class TestUserCode(unittest.TestCase):
    """Checks structure and correctness of Mahalanobis distance implementation."""

    def test_variables_declared(self):
        import user_code
        required = ["X", "mean_vec", "cov", "cov_inv", "distances", "outliers"]
        cond = all(hasattr(user_code, v) for v in required)
        _dynamic_test(self, cond,
            "All required variables are declared.",
            f"Expected {required} variables to be declared."
        )

    def test_covariance_and_inverse_exist(self):
        import user_code
        cond = isinstance(user_code.cov, np.ndarray) and isinstance(user_code.cov_inv, np.ndarray)
        _dynamic_test(self, cond,
            "`cov` and `cov_inv` are numpy arrays.",
            "Expected both `cov` and `cov_inv` to be NumPy arrays."
        )

    def test_distance_computed(self):
        import user_code
        cond = isinstance(user_code.distances, np.ndarray)
        _dynamic_test(self, cond,
            "`distances` array is computed.",
            "Expected Mahalanobis distance array `distances` to exist."
        )

    def test_outlier_mask(self):
        import user_code
        cond = isinstance(user_code.outliers, np.ndarray) or isinstance(user_code.outliers, (list, np.generic))
        _dynamic_test(self, cond,
            "Outlier mask `outliers` is computed.",
            "Expected variable `outliers` to be computed as boolean mask."
        )

    def test_no_for_loops_in_code(self):
        with open("user_code.py", "r") as f:
            src = f.read()
        cond = "for " not in src
        _dynamic_test(self, cond,
            "Vectorized NumPy operations used (no explicit loops).",
            "Detected manual loops; expected vectorized NumPy operations."
        )

if __name__ == "__main__":
    unittest.main()


test_code.py

A comprehensive, hands-on course exploring the theory, intuition, and practical implementation of outlier and novelty detection algorithms in Python. Learn to identify anomalies using statistical, isolation, density, and kernel-based methods, interpret results, and compare approaches for real-world applications.

Establish core concepts, terminology, and visualization techniques for anomaly detection.

Explore classical statistical and distance-based approaches for anomaly detection.

Delve into tree-based anomaly detection using Isolation Forest.

Investigate density-based anomaly detection with Local Outlier Factor.

Explore boundary-based novelty detection using One-Class SVM.

Compare algorithms, metrics, and trade-offs for real-world anomaly detection.

Challenge: Mahalanobis Distance in Practice

解答