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Alteration Detection of Tensor Dependence Structure via Sparsity-Exploited Reranking Algorithm
Methodology · Submitted 13 Oct 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We demonstrate the efficacy of the proposed method through intensive simulations and two scientific applications.
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The abstract, sentence by sentence
Tensor-valued data arise frequently from a wide variety of scientific applications, and many among them can be translated into an alteration detection problem of tensor dependence structures. In this article, we formulate the problem under the popularly adopted tensor-normal distributions and aim at two-sample correlation/partial correlation comparisons of tensor-valued observations. Through decorrelation and centralization, a separable covariance structure is employed to pool sample information from different tensor modes to enhance the power of the test. Additionally, we propose a novel Sparsity-Exploited Reranking Algorithm (SERA) to further improve the multiple testing efficiency. The algorithm is approached through reranking of the p-values derived from the primary test statistics, by incorporating a carefully constructed auxiliary tensor sequence. Besides the tensor framework, SERA is also generally applicable to a wide range of two-sample large-scale inference problems with sparsity structures, and is of independent interest. The asymptotic properties of the proposed test are derived and the algorithm is shown to control the false discovery at the pre-specified level. We demonstrate the efficacy of the proposed method through intensive simulations and two scientific applications.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Tensor-valued data arise frequently from a wide variety of scientific applications, and many among them can be translated into an alteration detection problem of tensor dependence structures. | background 1.00 | 0.05 | 0.03 | asserted 0.94 |
| s1 | In this article, we formulate the problem under the popularly adopted tensor-normal distributions and aim at two-sample correlation/partial correlation comparisons of tensor-valued observations. | contribution 0.66 | 0.84 | 0.04 | asserted 0.92 |
| s2 | Through decorrelation and centralization, a separable covariance structure is employed to pool sample information from different tensor modes to enhance the power of the test. | method 0.99 | 0.86 | 0.04 | asserted 1.00 |
| s3 | Additionally, we propose a novel Sparsity-Exploited Reranking Algorithm (SERA) to further improve the multiple testing efficiency. | contribution 0.87 | 0.95 | 0.10 | asserted 1.00 |
| s4 | The algorithm is approached through reranking of the p-values derived from the primary test statistics, by incorporating a carefully constructed auxiliary tensor sequence. | method 0.99 | 0.91 | 0.06 | asserted 1.00 |
| s5 | Besides the tensor framework, SERA is also generally applicable to a wide range of two-sample large-scale inference problems with sparsity structures, and is of independent interest. | contribution 0.78 | 0.54 | 0.11 | asserted 1.00 |
| s6 | The asymptotic properties of the proposed test are derived and the algorithm is shown to control the false discovery at the pre-specified level. | result 0.92 | 0.95 | 0.27 | asserted 1.00 |
| s7 | We demonstrate the efficacy of the proposed method through intensive simulations and two scientific applications. | result 0.49 | 0.96 | 0.28 | asserted 1.00 |
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Original abstract
Tensor-valued data arise frequently from a wide variety of scientific applications, and many among them can be translated into an alteration detection problem of tensor dependence structures. In this article, we formulate the problem under the popularly adopted tensor-normal distributions and aim at two-sample correlation/partial correlation comparisons of tensor-valued observations. Through decorrelation and centralization, a separable covariance structure is employed to pool sample information from different tensor modes to enhance the power of the test. Additionally, we propose a novel Sparsity-Exploited Reranking Algorithm (SERA) to further improve the multiple testing efficiency. The algorithm is approached through reranking of the p-values derived from the primary test statistics, by incorporating a carefully constructed auxiliary tensor sequence. Besides the tensor framework, SERA is also generally applicable to a wide range of two-sample large-scale inference problems with sparsity structures, and is of independent interest. The asymptotic properties of the proposed test are derived and the algorithm is shown to control the false discovery at the pre-specified level. We demonstrate the efficacy of the proposed method through intensive simulations and two scientific applications.
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What it cites · 3 sentences without a confident label
Uses the method or tool of 1 paper
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Since $π(U_i,j)$ is unknown, the first step of SERA estimates $π(U_i,j)$ by $π̂^τ(U_i,j)$ using a kernel-based approach following similar ideas in [ref] and [ref] , where $τ$ is a pre-specified screening parameter; see Equation [ref] in Algorithm [ref].
NAPA: Neighborhood-Assisted and Posterior-Adjusted Two-sample Inference · Step 3: A Power Enhanced Procedure SERA · 0.97
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In comparison to the existing multiple testing methods with auxiliary covariates [ref] , the proposed SERA explores the underlying sparsity structure in a continuous fashion, and enjoys power superiority, dependency robustness and computation efficiency in the meantime; see the detailed explanations and numerical comparisons in Section [ref].
Incorporation of Sparsity Information in Large-scale Multiple Two-sample $t$ Tests · Related Works and Our Contributions · 0.94
Cites as support 1 paper
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Condition [ref] can be easily satisfied by many common dependence structures as shown in [ref] .
NAPA: Neighborhood-Assisted and Posterior-Adjusted Two-sample Inference · Estimation Consistency of the Posterior Sparsity Level · 0.98
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