Statistical Inference for Persistence Diagrams via Landmark Embeddings: Minimax Theory and Finite Approximation
本文通过地标嵌入方法解决持久图的统计推断问题，利用Hilbert空间理论开发了一种针对人群平均嵌入的推断框架。
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Continuity-Free Near-Minimax Leading-Order Regret for CVaR-UCBVI
本文解决了CVaR强化学习中的遗憾界问题，通过Bernstein CVaR-UCBVI算法，在无需连续性假设下达到近似最优的遗憾率。
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Minimax Quantile Bounds via Information Measures
本文通过信息度量方法，构建了一个统一的信息论框架来解决最小最大分位数的下界问题，并针对不同恢复标准使用了多种信息度量方法。
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How Many Samples Are Needed to Determine Causal Direction? Sharp Minimax Bounds for Bivariate LiNGAM
This study addresses the sample complexity of causal identification in bivariate linear non-Gaussian models by integrating non-Gaussian independent component analysis with minimax theory. It establishes, for the first time, sharp local minimax bounds that depend on edge strength, non-Gaussianity, and scale uncertainty. The derived exact sample size formula elucidates identification mechanisms under weak-effect or near-Gaussian regimes and characterizes critical conditions distinguishing non-Gaussianity-dominated from covariance-dominated identification. By providing rigorous theoretical support and quantitative criteria, this work significantly advances the understanding of statistical limits in determining causal directionality within linear non-Gaussian frameworks.
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Sharp Minimax Theory for Randomized Experiments
This study addresses the minimax optimal design problem for estimating the sample average treatment effect with binary outcomes in finite-population randomized experiments. By reformulating risk equivalence as a two-parameter estimation task, we derive an exact second-order asymptotic expansion involving Airy functions. We propose a novel framework combining Bernoulli randomization with nonlinear shrinkage estimation, obtaining explicit second-order risk constants and establishing its minimax optimality. Our results demonstrate that while the traditional difference-in-means estimator achieves only first-order optimality, the proposed estimator significantly outperforms standard procedures at the second order. These findings elucidate the limitations of existing methods and underscore the practical significance of second-order refinements in experimental design.
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Statistical Inference for Persistence Diagrams via Landmark Embeddings: Minimax Theory and Finite Approximation
本文通过地标嵌入方法解决持久图的统计推断问题，利用Hilbert空间理论开发了一种针对人群平均嵌入的推断框架。
0 citationsRead paper
Continuity-Free Near-Minimax Leading-Order Regret for CVaR-UCBVI
本文解决了CVaR强化学习中的遗憾界问题，通过Bernstein CVaR-UCBVI算法，在无需连续性假设下达到近似最优的遗憾率。
0 citationsRead paper
Minimax Quantile Bounds via Information Measures
本文通过信息度量方法，构建了一个统一的信息论框架来解决最小最大分位数的下界问题，并针对不同恢复标准使用了多种信息度量方法。
0 citationsRead paper
How Many Samples Are Needed to Determine Causal Direction? Sharp Minimax Bounds for Bivariate LiNGAM
This study addresses the sample complexity of causal identification in bivariate linear non-Gaussian models by integrating non-Gaussian independent component analysis with minimax theory. It establishes, for the first time, sharp local minimax bounds that depend on edge strength, non-Gaussianity, and scale uncertainty. The derived exact sample size formula elucidates identification mechanisms under weak-effect or near-Gaussian regimes and characterizes critical conditions distinguishing non-Gaussianity-dominated from covariance-dominated identification. By providing rigorous theoretical support and quantitative criteria, this work significantly advances the understanding of statistical limits in determining causal directionality within linear non-Gaussian frameworks.
0 citationsRead paper
Sharp Minimax Theory for Randomized Experiments
This study addresses the minimax optimal design problem for estimating the sample average treatment effect with binary outcomes in finite-population randomized experiments. By reformulating risk equivalence as a two-parameter estimation task, we derive an exact second-order asymptotic expansion involving Airy functions. We propose a novel framework combining Bernoulli randomization with nonlinear shrinkage estimation, obtaining explicit second-order risk constants and establishing its minimax optimality. Our results demonstrate that while the traditional difference-in-means estimator achieves only first-order optimality, the proposed estimator significantly outperforms standard procedures at the second order. These findings elucidate the limitations of existing methods and underscore the practical significance of second-order refinements in experimental design.
0 citationsRead paper