Variable Selection for Kernel Two-Sample Tests

• URL: http://arxiv.org/abs/2302.07415v3
• Date: Thu, 12 Oct 2023 14:08:18 GMT
• Title: Variable Selection for Kernel Two-Sample Tests
• Authors: Jie Wang and Santanu S. Dey and Yao Xie
• Abstract summary: We propose a framework based on the kernel maximum mean discrepancy (MMD) We present mixed-integer programming formulations and develop exact and approximation algorithms with performance guarantees. Experiment results on synthetic and real datasets demonstrate the superior performance of our approach.
• Score: 10.768155884359777
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the variable selection problem for two-sample tests, aiming to select the most informative variables to distinguish samples from two groups. To solve this problem, we propose a framework based on the kernel maximum mean discrepancy (MMD). Our approach seeks a group of variables with a pre-specified size that maximizes the variance-regularized MMD statistics. This formulation also corresponds to the minimization of asymptotic type-II error while controlling type-I error, as studied in the literature. We present mixed-integer programming formulations and develop exact and approximation algorithms with performance guarantees for different choices of kernel functions. Furthermore, we provide a statistical testing power analysis of our proposed framework. Experiment results on synthetic and real datasets demonstrate the superior performance of our approach.

Related papers

• 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)
• Best Arm Identification with Fixed Budget: A Large Deviation Perspective [54.305323903582845]
  We present sred, a truly adaptive algorithm that can reject arms in it any round based on the observed empirical gaps between the rewards of various arms. In particular, we present sred, a truly adaptive algorithm that can reject arms in it any round based on the observed empirical gaps between the rewards of various arms.
  arXiv  Detail & Related papers  (2023-12-19T13:17:43Z)
• Variable Selection in Maximum Mean Discrepancy for Interpretable Distribution Comparison [9.12501922682336]
  Two-sample testing decides whether two datasets are generated from the same distribution. This paper studies variable selection for two-sample testing, the task being to identify the variables responsible for the discrepancies between the two distributions.
  arXiv  Detail & Related papers  (2023-11-02T18:38:39Z)
• MMD-FUSE: Learning and Combining Kernels for Two-Sample Testing Without Data Splitting [28.59390881834003]
  We propose novel statistics which maximise the power of a two-sample test based on the Maximum Mean Discrepancy (MMD) We show how these kernels can be chosen in a data-dependent but permutation-independent way, in a well-calibrated test, avoiding data splitting. We highlight the applicability of our MMD-FUSE test on both synthetic low-dimensional and real-world high-dimensional data, and compare its performance in terms of power against current state-of-the-art kernel tests.
  arXiv  Detail & Related papers  (2023-06-14T23:13:03Z)
• 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)
• Sharp Variance-Dependent Bounds in Reinforcement Learning: Best of Both Worlds in Stochastic and Deterministic Environments [48.96971760679639]
  We study variance-dependent regret bounds for Markov decision processes (MDPs) We propose two new environment norms to characterize the fine-grained variance properties of the environment. For model-based methods, we design a variant of the MVP algorithm. In particular, this bound is simultaneously minimax optimal for both and deterministic MDPs.
  arXiv  Detail & Related papers  (2023-01-31T06:54:06Z)
• Spectral Regularized Kernel Two-Sample Tests [7.915420897195129]
  We show the popular MMD (maximum mean discrepancy) two-sample test to be not optimal in terms of the separation boundary measured in Hellinger distance. We propose a modification to the MMD test based on spectral regularization and prove the proposed test to be minimax optimal with a smaller separation boundary than that achieved by the MMD test. Our results hold for the permutation variant of the test where the test threshold is chosen elegantly through the permutation of the samples.
  arXiv  Detail & Related papers  (2022-12-19T00:42:21Z)
• A Lagrangian Duality Approach to Active Learning [119.36233726867992]
  We consider the batch active learning problem, where only a subset of the training data is labeled. We formulate the learning problem using constrained optimization, where each constraint bounds the performance of the model on labeled samples. We show, via numerical experiments, that our proposed approach performs similarly to or better than state-of-the-art active learning methods.
  arXiv  Detail & Related papers  (2022-02-08T19:18:49Z)
• Learning MDPs from Features: Predict-Then-Optimize for Sequential Decision Problems by Reinforcement Learning [52.74071439183113]
  We study the predict-then-optimize framework in the context of sequential decision problems (formulated as MDPs) solved via reinforcement learning. Two significant computational challenges arise in applying decision-focused learning to MDPs.
  arXiv  Detail & Related papers  (2021-06-06T23:53:31Z)
• Greedy Search Algorithms for Unsupervised Variable Selection: A Comparative Study [3.4888132404740797]
  This paper focuses on unsupervised variable selection based dimensionality reduction. We present a critical evaluation of seven unsupervised greedy variable selection algorithms. We introduce and evaluate for the first time, a lazy implementation of the variance explained based forward selection component analysis (FSCA) algorithm.
  arXiv  Detail & Related papers  (2021-03-03T21:10:26Z)
• Distributed Averaging Methods for Randomized Second Order Optimization [54.51566432934556]
  We consider distributed optimization problems where forming the Hessian is computationally challenging and communication is a bottleneck. We develop unbiased parameter averaging methods for randomized second order optimization that employ sampling and sketching of the Hessian. We also extend the framework of second order averaging methods to introduce an unbiased distributed optimization framework for heterogeneous computing systems.
  arXiv  Detail & Related papers  (2020-02-16T09:01:18Z)

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.