"Explaining k-Nearest Neighbors: Abductive and Counterfactual Explanations"

Transform impossible high-dimensional comparisons into intuitive 2D visualizations.

Making sense of multivariate chaos through elegant half-space depth plots.

This paper introduces a novel way to compare multivariate distributions using half-space depth information, making complex distribution comparisons visually interpretable through 2D plots.

https://arxiv.org/abs/2501.06078

🎯 Original Problem:

→ Comparing multivariate distributions is challenging, especially in high dimensions

→ Existing methods lack visual interpretability and often work only for specific distributions like normal distributions

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🔍 Solution in this Paper:

→ Introduces data-depth discrepancy (DDD) measure using half-space depth information criteria

→ Creates a 2D visualization tool that works regardless of data dimensionality

→ Proposes two test statistics: Kolmogorov-Smirnov and Cramér-von Mises based on DDD

→ Implements bootstrap procedures for computing empirical p-values efficiently

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💡 Key Insights:

→ Half-space depth uniquely characterizes distributions under minimal assumptions

→ The proposed 2D visualization remains effective even for high-dimensional data

→ Test statistics are computationally feasible and robust against heavy-tailed distributions

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📊 Results:

→ Successfully tested on dimensions up to d=60 with sample sizes smaller than dimension

→ Outperforms existing tests for heavy-tailed distributions

→ Validated on real benchmark datasets showing practical applicability

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