DUAL: Learning Diverse Kernels for Aggregated Two-sample and Independence Testing

• URL: http://arxiv.org/abs/2510.11140v1
• Date: Mon, 13 Oct 2025 08:30:42 GMT
• Title: DUAL: Learning Diverse Kernels for Aggregated Two-sample and Independence Testing
• Authors: Zhijian Zhou, Xunye Tian, Liuhua Peng, Chao Lei, Antonin Schrab, Danica J. Sutherland, Feng Liu,
• Abstract summary: We propose an aggregated statistic that explicitly incorporates kernel diversity based on the covariance between different kernels.<n>This motivates a testing framework with selection inference, which leverages information from the training phase to select kernels with strong individual performance.
• Score: 21.083713063070586
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: To adapt kernel two-sample and independence testing to complex structured data, aggregation of multiple kernels is frequently employed to boost testing power compared to single-kernel tests. However, we observe a phenomenon that directly maximizing multiple kernel-based statistics may result in highly similar kernels that capture highly overlapping information, limiting the effectiveness of aggregation. To address this, we propose an aggregated statistic that explicitly incorporates kernel diversity based on the covariance between different kernels. Moreover, we identify a fundamental challenge: a trade-off between the diversity among kernels and the test power of individual kernels, i.e., the selected kernels should be both effective and diverse. This motivates a testing framework with selection inference, which leverages information from the training phase to select kernels with strong individual performance from the learned diverse kernel pool. We provide rigorous theoretical statements and proofs to show the consistency on the test power and control of Type-I error, along with asymptotic analysis of the proposed statistics. Lastly, we conducted extensive empirical experiments demonstrating the superior performance of our proposed approach across various benchmarks for both two-sample and independence testing.

Related papers

• Fusion of classical and quantum kernels enables accurate and robust two-sample tests [0.8178073457017482]
  We propose a novel hybrid testing strategy that fuses classical and quantum kernels.<n>This approach creates a powerful and adaptive test by combining the domain-specific inductive biases of classical kernels with the unique expressive power of quantum kernels.
  arXiv  Detail & Related papers  (2025-11-26T00:25:17Z)
• A Unified View of Optimal Kernel Hypothesis Testing [3.1727619150610837]
  This paper provides a unifying view of optimal kernel hypothesis testing across the MMD two-sample, HSIC independence, and KSD goodness-of-fit frameworks.<n>Minimax optimal separation rates in the kernel and $L2$ metrics are presented, with two adaptive kernel selection methods.
  arXiv  Detail & Related papers  (2025-03-10T09:06:40Z)
• Learning Representations for Independence Testing [13.842061060076004]
  We show how to construct powerful tests with finite-sample validity using variational estimators of mutual information.<n>Second, we establish a close connection between these variational mutual information-based tests and tests based on the Hilbert-Schmidt Independence Criterion (HSIC)<n>Finally, we show how to, rather than selecting a representation to maximize the statistic itself, select a representation which can maximize the power of a test.
  arXiv  Detail & Related papers  (2024-09-10T22:18:07Z)
• Optimal Kernel Choice for Score Function-based Causal Discovery [92.65034439889872]
  We propose a kernel selection method within the generalized score function that automatically selects the optimal kernel that best fits the data. We conduct experiments on both synthetic data and real-world benchmarks, and the results demonstrate that our proposed method outperforms kernel selection methods.
  arXiv  Detail & Related papers  (2024-07-14T09:32:20Z)
• Boosting the Power of Kernel Two-Sample Tests [4.07125466598411]
  A kernel two-sample test based on the maximum mean discrepancy (MMD) is one of the most popular methods for detecting differences between two distributions over general metric spaces. We propose a method to boost the power of the kernel test by combining MMD estimates over multiple kernels using their Mahalanobis distance.
  arXiv  Detail & Related papers  (2023-02-21T14:14:30Z)
• Targeted Separation and Convergence with Kernel Discrepancies [61.973643031360254]
  kernel-based discrepancy measures are required to (i) separate a target P from other probability measures or (ii) control weak convergence to P.<n>In this article we derive new sufficient and necessary conditions to ensure (i) and (ii)<n>For MMDs on separable metric spaces, we characterize those kernels that separate Bochner embeddable measures and introduce simple conditions for separating all measures with unbounded kernels.
  arXiv  Detail & Related papers  (2022-09-26T16:41:16Z)
• Variational Autoencoder Kernel Interpretation and Selection for Classification [59.30734371401315]
  This work proposed kernel selection approaches for probabilistic classifiers based on features produced by the convolutional encoder of a variational autoencoder. In the proposed implementation, each latent variable was sampled from the distribution associated with a single kernel of the last encoder's convolution layer, as an individual distribution was created for each kernel. choosing relevant features on the sampled latent variables makes it possible to perform kernel selection, filtering the uninformative features and kernels.
  arXiv  Detail & Related papers  (2022-09-10T17:22:53Z)
• Federated Doubly Stochastic Kernel Learning for Vertically Partitioned Data [93.76907759950608]
  We propose a doubly kernel learning algorithm for vertically partitioned data. We show that FDSKL is significantly faster than state-of-the-art federated learning methods when dealing with kernels.
  arXiv  Detail & Related papers  (2020-08-14T05:46:56Z)
• Bayesian Sparse Factor Analysis with Kernelized Observations [67.60224656603823]
  Multi-view problems can be faced with latent variable models. High-dimensionality and non-linear issues are traditionally handled by kernel methods. We propose merging both approaches into single model.
  arXiv  Detail & Related papers  (2020-06-01T14:25:38Z)
• Learning Deep Kernels for Non-Parametric Two-Sample Tests [50.92621794426821]
  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.
  arXiv  Detail & Related papers  (2020-02-21T03:54:23Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.