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1. A simple permutation‐based test of intermodal correspondence

   https://doi.org/10.1002/hbm.25577  

   Weinstein, Sarah M. ; Vandekar, Simon N. ; Adebimpe, Azeez ; Tapera, Tinashe M. ; Robert‐Fitzgerald, Timothy ; Gur, Ruben C. ; Gur, Raquel E. ; Raznahan, Armin ; Satterthwaite, Theodore D. ; Alexander‐Bloch, Aaron F. ; et al ( September 2021 , Human Brain Mapping)

   Many key findings in neuroimaging studies involve similarities between brain maps, but statistical methods used to measure these findings have varied. Current state‐of‐the‐art methods involve comparing observed group‐level brain maps (after averaging intensities at each image location across multiple subjects) against spatial null models of these group‐level maps. However, these methods typically make strong and potentially unrealistic statistical assumptions, such as covariance stationarity. To address these issues, in this article we propose using subject‐level data and a classical permutation testing framework to test and assess similarities between brain maps. Our method is comparable to traditional permutation tests in that it involves randomly permuting subjects to generate a null distribution of intermodal correspondence statistics, which we compare to an observed statistic to estimate ap‐value. We apply and compare our method in simulated and real neuroimaging data from the Philadelphia Neurodevelopmental Cohort. We show that our method performs well for detecting relationships between modalities known to be strongly related (cortical thickness and sulcal depth), and it is conservative when an association would not be expected (cortical thickness and activation on then‐back working memory task). Notably, our method is the most flexible and reliable for localizing intermodal relationships within subregions of the brain and allows for generalizable statistical inference.

    

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2. InfoFair: Information-Theoretic Intersectional Fairness

   https://doi.org/10.1109/BigData55660.2022.10020588  

   Kang, Jian ; Xie, Tiankai ; Wu, Xintao ; Maciejewski, Ross ; Tong, Hanghang ( December 2022 , 2022 IEEE International Conference on Big Data (Big Data))

   Algorithmic fairness is becoming increasingly important in data mining and machine learning. Among others, a foundational notation is group fairness. The vast majority of the existing works on group fairness, with a few exceptions, primarily focus on debiasing with respect to a single sensitive attribute, despite the fact that the co-existence of multiple sensitive attributes (e.g., gender, race, marital status, etc.) in the real-world is commonplace. As such, methods that can ensure a fair learning outcome with respect to all sensitive attributes of concern simultaneously need to be developed. In this paper, we study the problem of information-theoretic intersectional fairness (InfoFair), where statistical parity, a representative group fairness measure, is guaranteed among demographic groups formed by multiple sensitive attributes of interest. We formulate it as a mutual information minimization problem and propose a generic end-to-end algorithmic framework to solve it. The key idea is to leverage a variational representation of mutual information, which considers the variational distribution between learning outcomes and sensitive attributes, as well as the density ratio between the variational and the original distributions. Our proposed framework is generalizable to many different settings, including other statistical notions of fairness, and could handle any type of learning task equipped with a gradientbased optimizer. Empirical evaluations in the fair classification task on three real-world datasets demonstrate that our proposed framework can effectively debias the classification results with minimal impact to the classification accuracy. 

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3. Measuring Group Advantage: A Comparative Study of Fair Ranking Metrics

   https://doi.org/10.1145/3461702.3462588  

   Kuhlman, Caitlin ; Gerych, Walter ; Rundensteiner, Elke ( May 2021 , Proceedings of the 2021 AAAI/ACM Conference on AI, Ethics, and Society (AIES ’21))

   null (Ed.)

   Ranking evaluation metrics play an important role in information retrieval, providing optimization objectives during development and means of assessment of deployed performance. Recently, fairness of rankings has been recognized as crucial, especially as automated systems are increasingly used for high impact decisions. While numerous fairness metrics have been proposed, a comparative analysis to understand their interrelationships is lacking. Even for fundamental statistical parity metrics which measure group advantage, it remains unclear whether metrics measure the same phenomena, or when one metric may produce different results than another. To address these open questions, we formulate a conceptual framework for analytical comparison of metrics.We prove that under reasonable assumptions, popular metrics in the literature exhibit the same behavior and that optimizing for one optimizes for all. However, our analysis also shows that the metrics vary in the degree of unfairness measured, in particular when one group has a strong majority. Based on this analysis, we design a practical statistical test to identify whether observed data is likely to exhibit predictable group bias. We provide a set of recommendations for practitioners to guide the choice of an appropriate fairness metric. 

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4. Differentially Private Testing of Identity and Closeness of Discrete Distributions

   Acharya, Jayadev ; Sun, Ziteng ; Zhang, Huanyu ( January 2018 , Advances in Neural Information Processing Systems 31 (NIPS 2018))

   We study the fundamental problems of identity testing (goodness of fit), and closeness testing (two sample test) of distributions over k elements, under differential privacy. While the problems have a long history in statistics, finite sample bounds for these problems have only been established recently. In this work, we derive upper and lower bounds on the sample complexity of both the problems under (epsilon, delta)-differential privacy. We provide sample optimal algorithms for identity testing problem for all parameter ranges, and the first results for closeness testing. Our closeness testing bounds are optimal in the sparse regime where the number of samples is at most k. Our upper bounds are obtained by privatizing non-private estimators for these problems. The non-private estimators are chosen to have small sensitivity. We propose a general framework to establish lower bounds on the sample complexity of statistical tasks under differential privacy. We show a bound on di erentially private algorithms in terms of a coupling between the two hypothesis classes we aim to test. By carefully constructing chosen priors over the hypothesis classes, and using Le Cam’s two point theorem we provide a general mechanism for proving lower bounds. We believe that the framework can be used to obtain strong lower bounds for other statistical tasks under privacy. 

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5. A Statistical Hypothesis Testing Strategy for Adaptively Blending Particle Filters and Ensemble Kalman Filters for Data Assimilation

   https://doi.org/10.1175/MWR-D-22-0108.1  

   Kurosawa, Kenta ; Poterjoy, Jonathan ( January 2023 , Monthly Weather Review)

   Abstract Particle filters avoid parametric estimates for Bayesian posterior densities, which alleviates Gaussian assumptions in nonlinear regimes. These methods, however, are more sensitive to sampling errors than Gaussian-based techniques such as ensemble Kalman filters. A recent study by the authors introduced an iterative strategy for particle filters that match posterior moments—where iterations improve the filter’s ability to draw samples from non-Gaussian posterior densities. The iterations follow from a factorization of particle weights, providing a natural framework for combining particle filters with alternative filters to mitigate the impact of sampling errors. The current study introduces a novel approach to forming an adaptive hybrid data assimilation methodology, exploiting the theoretical strengths of nonparametric and parametric filters. At each data assimilation cycle, the iterative particle filter performs a sequence of updates while the prior sample distribution is non-Gaussian, then an ensemble Kalman filter provides the final adjustment when Gaussian distributions for marginal quantities are detected. The method employs the Shapiro–Wilk test to determine when to make the transition between filter algorithms, which has outstanding power for detecting departures from normality. Experiments using low-dimensional models demonstrate that the approach has a significant value, especially for nonhomogeneous observation networks and unknown model process errors. Moreover, hybrid factors are extended to consider marginals of more than one collocated variables using a test for multivariate normality. Findings from this study motivate the use of the proposed method for geophysical problems characterized by diverse observation networks and various dynamic instabilities, such as numerical weather prediction models. Significance Statement Data assimilation statistically processes observation errors and model forecast errors to provide optimal initial conditions for the forecast, playing a critical role in numerical weather forecasting. The ensemble Kalman filter, which has been widely adopted and developed in many operational centers, assumes Gaussianity of the prior distribution and solves a linear system of equations, leading to bias in strong nonlinear regimes. On the other hand, particle filters avoid many of those assumptions but are sensitive to sampling errors and are computationally expensive. We propose an adaptive hybrid strategy that combines their advantages and minimizes the disadvantages of the two methods. The hybrid particle filter–ensemble Kalman filter is achieved with the Shapiro–Wilk test to detect the Gaussianity of the ensemble members and determine the timing of the transition between these filter updates. Demonstrations in this study show that the proposed method is advantageous when observations are heterogeneous and when the model has an unknown bias. Furthermore, by extending the statistical hypothesis test to the test for multivariate normality, we consider marginals of more than one collocated variable. These results encourage further testing for real geophysical problems characterized by various dynamic instabilities, such as real numerical weather prediction models. 

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