Interpretable Distribution Features with Maximum Testing Power

By Wittawat Jitkrittum, Zoltán Szabó, Kacper P. Chwialkowski, Arthur Gretton. 2016

148 citations recorded by the source corpus.

Two semimetrics on probability distributions are proposed, given as the sum of differences of expectations of analytic functions evaluated at spatial or frequency locations (i.e, features). The features are chosen so as to maximize the distinguishability of the distributions, by optimizing a lower bound on test power for a statistical test using these features. The result is a parsimonious and interpretable indication of how and where two distributions differ locally. An empirical estimate of the test power criterion converges with increasing sample size, ensuring the quality of the returned features. In real-world benchmarks on high-dimensional text and image data, linear-time tests using the proposed semimetrics achieve comparable performance to the state-of-the-art quadratic-time maximum mean discrepancy test, while returning human-interpretable features that explain the test results.

Subfields: Statistics and Probability, Safety, Robustness & Interpretability

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Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, background): “Based on the work of Chwialkowski et al. (2015), Jitkrittum et al. (2016) proposes test statistics as a difference of mean embeddings evaluated at locations chosen to maximize the test power lower bound.”
Revisiting Classifier Two-Sample Tests (2016, methodology): “Distinguishing between facial expressions Finally, we apply C2ST-NN to the problem of distinguishing between positive (happy, neutral, surprised) and negative (afraid, angry, disgusted) facial expressions from the Karolinska Directed Emotional Faces dataset, as discussed in (Jitkrittum et al., 2016)”
Learning Deep Kernels for Non-Parametric Two-Sample Tests (2020, methodology): “There are also several closely related methods, including tests based on checking for differences in mean embeddings evaluated at specific locations (Chwialkowski et al., 2015; Jitkrittum et al., 2016) and kernel Fisher discriminant analysis (Harchaoui et al.”
Transferable Representation Learning with Deep Adaptation Networks (2019, background): “Examples include Maximum Mean Discrepancy (MMD) [13], [45] and Mean Embedding Test (ME) [14], [46].”