Learning Deep Kernels for Non-Parametric Two-Sample Tests

By Feng Liu, Wenkai Xu, Jie Lu, Guangquan Zhang, Arthur Gretton, Danica J. Sutherland. 2020

225 citations recorded by the source corpus.

We propose a class of kernel-based two-sample tests, which aim to determine whether two sets of samples are drawn from the same distribution. Our tests are constructed from kernels parameterized by deep neural nets, trained to maximize test power. These tests adapt to variations in distribution smoothness and shape over space, and are especially suited to high dimensions and complex data. By contrast, the simpler kernels used in prior kernel testing work are spatially homogeneous, and adaptive only in lengthscale. We explain how this scheme includes popular classifier-based two-sample tests as a special case, but improves on them in general. We provide the first proof of consistency for the proposed adaptation method, which applies both to kernels on deep features and to simpler radial basis kernels or multiple kernel learning. In experiments, we establish the superior performance of our deep kernels in hypothesis testing on benchmark and real-world data. The code of our deep-kernel-based two sample tests is available at this https URL.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Yunchao Wei
2. Zhen Fang
3. Yi Yang
4. Guoliang Kang
5. Gan Sun
6. Jie Lu
7. Xiao Wang
8. Yang Cong

In Computer Vision and Pattern Recognition

1. Yunchao Wei
2. Yi Yang
3. Guoliang Kang
4. Ming-Hsuan Yang
5. Luc Van Gool
6. Jiashi Feng
7. Dacheng Tao
8. Feng Liu

Citations in the corpus

• Federated Class-Incremental Learning (2022, background): “Different from existing knowledge distillation strategies [1, 3, 8, 17, 26] that only ensure old classes’ semantic consistency among Θ t − 1 l and Θ r,tl , we consider inter-class relations between old and new classes simultaneously via optimizing L RD .”
• Learning Bounds for Open-Set Learning (2021, background): “The kernel bandwidth selection also impacts the overall performance (Liu et al., 2020).”
• Where and How to Transfer: Knowledge Aggregation-Induced Transferability Perception for Unsupervised Domain Adaptation (2021, background): “[26] proposes a bidirectional learning including the visual appearance translation and semantic feature adaptation to bridge the distribution shift across domains [28].”
• Domain Consensus Clustering for Universal Domain Adaptation (2021, methodology): “Some methods minimize the discrepancy in the feature space directly [40, 39, 56, 59, 42, 61, 30, 16].”