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<p>In this article, we address the problem of testing independence between two random variables. We adopt a multiscale approach that examines neighborhoods of varying sizes within the dataset and aggregates the resulting information. To achieve this, we introduce a general multi-scale framework that can utilize an existing association/dependence measure. Building on this framework, we propose a novel test, along with a computationally efficient algorithm for its implementation. We evaluate the performance of the proposed methods through multiple comparisons with existing tests on both simulated and real datasets. The results demonstrate that our tests are particularly effective at detecting associations caused by explicit or implicit functional relationships between variables. Additionally, a visualization method has been proposed for exploring the localization of dependence within datasets.</p>

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A novel multiscale approach to independence testing

  • 期刊论文

  • 发表日期：

    2026年2月18日

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  • Seetharaman Parameswaran,
  • Sagnik Das,
  • Angshuman Roy

摘要

In this article, we address the problem of testing independence between two random variables. We adopt a multiscale approach that examines neighborhoods of varying sizes within the dataset and aggregates the resulting information. To achieve this, we introduce a general multi-scale framework that can utilize an existing association/dependence measure. Building on this framework, we propose a novel test, along with a computationally efficient algorithm for its implementation. We evaluate the performance of the proposed methods through multiple comparisons with existing tests on both simulated and real datasets. The results demonstrate that our tests are particularly effective at detecting associations caused by explicit or implicit functional relationships between variables. Additionally, a visualization method has been proposed for exploring the localization of dependence within datasets.