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   https://doi.org/10.1214/19-AOS1887  

   Aragam, B.; Dan, C.; Xing, E.; Ravikumar, P. (April 2020, The annals of statistics)

   Motivated by problems in data clustering, we establish general conditions under which families of nonparametric mixture models are identifiable, by introducing a novel framework involving clustering overfitted parametric (i.e. misspecified) mixture models. These identifiability conditions generalize existing conditions in the literature, and are flexible enough to include for example mixtures of Gaussian mixtures. In contrast to the recent literature on estimating nonparametric mixtures, we allow for general nonparametric mixture components, and instead impose regularity assumptions on the underlying mixing measure. As our primary application, we apply these results to partition-based clustering, generalizing the notion of a Bayes optimal partition from classical parametric model-based clustering to nonparametric settings. Furthermore, this framework is constructive so that it yields a practical algorithm for learning identified mixtures, which is illustrated through several examples on real data. The key conceptual device in the analysis is the convex, metric geometry of probability measures on metric spaces and its connection to the Wasserstein convergence of mixing measures. The result is a flexible framework for nonparametric clustering with formal consistency guarantees. 

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2. Sequential change‐point detection: Computation versus statistical performance

   https://doi.org/10.1002/wics.1628  

   Wang, Haoyun; Xie, Yao (July 2023, WIREs Computational Statistics)

   Abstract Change‐point detection studies the problem of detecting the changes in the underlying distribution of the data stream as soon as possible after the change happens. Modern large‐scale, high‐dimensional, and complex streaming data call for computationally (memory) efficient sequential change‐point detection algorithms that are also statistically powerful. This gives rise to a computation versus statistical power trade‐off, an aspect less emphasized in the past in classic literature. This tutorial takes this new perspective and reviews several sequential change‐point detection procedures, ranging from classic sequential change‐point detection algorithms to more recent non‐parametric procedures that consider computation, memory efficiency, and model robustness in the algorithm design. Our survey also contains classic performance analysis, which provides useful techniques for analyzing new procedures. This article is categorized under:Statistical Models > Time Series ModelsAlgorithms and Computational Methods > AlgorithmsData: Types and Structure > Time Series, Stochastic Processes, and Functional Data 

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3. Counterfactual Sensitivity and Robustness

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   Christensen, Timothy; Connault, Benjamin (January 2023, Econometrica)

   We propose a framework for analyzing the sensitivity of counterfactuals to parametric assumptions about the distribution of latent variables in structural models. In particular, we derive bounds on counterfactuals as the distribution of latent variables spans nonparametric neighborhoods of a given parametric specification while other “structural” features of the model are maintained. Our approach recasts the infinite‐dimensional problem of optimizing the counterfactual with respect to the distribution of latent variables (subject to model constraints) as a finite‐dimensional convex program. We also develop an MPEC version of our method to further simplify computation in models with endogenous parameters (e.g., value functions) defined by equilibrium constraints. We propose plug‐in estimators of the bounds and two methods for inference. We also show that our bounds converge to the sharp nonparametric bounds on counterfactuals as the neighborhood size becomes large. To illustrate the broad applicability of our procedure, we present empirical applications to matching models with transferable utility and dynamic discrete choice models. 

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4. Asymptotically Optimal Sequential Design for Rank Aggregation

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   Chen, Xi; Chen, Yunxiao; Li, Xiaoou (August 2022, Mathematics of Operations Research)

   A sequential design problem for rank aggregation is commonly encountered in psychology, politics, marketing, sports, etc. In this problem, a decision maker is responsible for ranking K items by sequentially collecting noisy pairwise comparisons from judges. The decision maker needs to choose a pair of items for comparison in each step, decide when to stop data collection, and make a final decision after stopping based on a sequential flow of information. Because of the complex ranking structure, existing sequential analysis methods are not suitable. In this paper, we formulate the problem under a Bayesian decision framework and propose sequential procedures that are asymptotically optimal. These procedures achieve asymptotic optimality by seeking a balance between exploration (i.e., finding the most indistinguishable pair of items) and exploitation (i.e., comparing the most indistinguishable pair based on the current information). New analytical tools are developed for proving the asymptotic results, combining advanced change of measure techniques for handling the level crossing of likelihood ratios and classic large deviation results for martingales, which are of separate theoretical interest in solving complex sequential design problems. A mirror-descent algorithm is developed for the computation of the proposed sequential procedures. 

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5. Real-Time Detection and Classification of Power Quality Disturbances

   https://doi.org/10.3390/s22207958  

   Mozaffari, Mahsa; Doshi, Keval; Yilmaz, Yasin (October 2022, Sensors)

   This paper considers the problem of real-time detection and classification of power quality disturbances in power delivery systems. We propose a sequential and multivariate disturbance detection method (aiming for quick and accurate detection). Our proposed detector follows a non-parametric and supervised approach, i.e., it learns nominal and anomalous patterns from training data involving clean and disturbance signals. The multivariate nature of the method enables joint processing of data from multiple meters, facilitating quicker detection as a result of the cooperative analysis. We further extend our supervised sequential detection method to a multi-hypothesis setting, which aims to classify the disturbance events as quickly and accurately as possible in a real-time manner. The multi-hypothesis method requires a training dataset per hypothesis, i.e., per each disturbance type as well as the ’no disturbance’ case. The proposed classification method is demonstrated to quickly and accurately detect and classify power disturbances. 

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