Data-Driven Representations for Testing Independence: Modeling, Analysis and Connection with Mutual Information Estimation
This work addresses testing the independence of two continuous and finite-dimensional random variables from the design of a data-driven partition. The empirical log-likelihood statistic is adopted to approximate the sufficient statistics of an oracle test against independence (that knows the two hypotheses). It is shown that approximating the sufficient statistics of the oracle test offers a learning criterion for designing a data-driven partition that connects with the problem of mutual information estimation. Applying these ideas in the context of a data-dependent tree-structured partition (TSP), we derive conditions on the TSP's parameters to achieve a strongly consistent distribution-free test of independence over the family of probabilities equipped with a density. Complementing this result, we present finite-length results that show our TSP scheme's capacity to detect the scenario of independence structurally with the data-driven partition as well as new sampling complexity bounds for this detection. Finally, some experimental analyses provide evidence regarding our scheme's advantage for testing independence compared with some strategies that do not use data-driven representations.
Code (0)
등록된 구현이 없습니다.
Tasks
Mutual Information EstimationMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Toward Scalable and Valid Conditional Independence Testing with Spectral Representations
Conditional independence (CI) is central to causal inference, feature selection, and graphical modeling, yet it is untestable in many settings without additional assumptions. Existing CI tests often rely on restrictive s…
Representation LearningCausal InferenceEdge-preserving Image Denoising via Multi-scale Adaptive Statistical Independence Testing
Edge detection is crucial in image processing, but existing methods often produce overly detailed edge maps, affecting clarity. Fixed-window statistical testing faces issues like scale mismatch and computational redundan…
DenoisingEdge DetectionImage Denoisingstatistical independence testingScore-based Generative Modeling for Conditional Independence Testing
Determining conditional independence (CI) relationships between random variables is a fundamental yet challenging task in machine learning and statistics, especially in high-dimensional settings. Existing generative mode…
Large-Scale Kernel Methods for Independence Testing
Representations of probability measures in reproducing kernel Hilbert spaces provide a flexible framework for fully nonparametric hypothesis tests of independence, which can capture any type of departure from independenc…
Computational EfficiencyConditional Independence Testing via Latent Representation Learning
Detecting conditional independencies plays a key role in several statistical and machine learning tasks, especially in causal discovery algorithms. In this study, we introduce LCIT (Latent representation based Conditiona…
Causal DiscoveryRepresentation Learning