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We introduce a framework for statistical estimation that leverages knowledge of how samples are collected but makes no distributional assumptions on the data values. Specifically, we consider a population of elements $[n]={1,\ldots,n}$ with…
We consider a binary unsupervised classification problem where each observation is associated with an unobserved label that we want to retrieve. More precisely, we assume that there are two groups of observation: normal and abnormal. The…
Over the past decades, researchers and ML practitioners have come up with better and better ways to build, understand and improve the quality of ML models, but mostly under the key assumption that the training data is distributed…
In this paper, we develop connections between two seemingly disparate, but central, models in robust statistics: Huber's epsilon-contamination model and the heavy-tailed noise model. We provide conditions under which this connection…
Estimating the number of unseen species is an important problem in many scientific endeavors. Its most popular formulation, introduced by Fisher, uses $n$ samples to predict the number $U$ of hitherto unseen species that would be observed…
Method of moment estimators exhibit appealing statistical properties, such as asymptotic unbiasedness, for nonconvex problems. However, they typically require a large number of samples and are extremely sensitive to model misspecification.…
This pedagogical review examines the use of machine learning methods in finite-population inference for survey sampling, with an emphasis on design-based validity and statistical inference. While flexible prediction tools offer substantial…
During the past few decades, missing-data problems have been studied extensively, with a focus on the ignorable missing case, where the missing probability depends only on observable quantities. By contrast, research into non-ignorable…
We consider the famous Rasch model, which is applied to psychometric surveys when n persons under test answer m questions. The score is given by a realization of a random binary (n,m)-matrix. Its (j,k)th component indicates whether or not…
We consider three problems in high-dimensional Gaussian linear mixed models. Without any assumptions on the design for the fixed effects, we construct an asymptotic $F$-statistic for testing whether a collection of random effects is zero,…
Health data are generally complex in type and small in sample size. Such domain-specific challenges make it difficult to capture information reliably and contribute further to the issue of generalization. To assist the analytics of…
We consider the situation where the observed sample contains some observations whose class of origin is known (that is, they are classified with respect to the g underlying classes of interest), and where the remaining observations in the…
This work proposes a non-iterative strategy for missing value imputations which is guided by similarity between observations, but instead of explicitly determining distances or nearest neighbors, it assigns observations to overlapping…
Finite mixture models are statistical models which appear in many problems in statistics and machine learning. In such models it is assumed that data are drawn from random probability measures, called mixture components, which are…
Scientific observations may consist of a large number of variables (features). Identifying a subset of meaningful features is often ignored in unsupervised learning, despite its potential for unraveling clear patterns hidden in the ambient…
Large-scale population-level datasets, such as the UK Biobank and the All of Us Research Program, often lack covariates needed for a specific analysis, such as genetic or lifestyle measures, while related studies measure them. This creates…
We consider the fundamental problem of matching a template to a signal. We do so by M-estimation, which encompasses procedures that are robust to gross errors (i.e., outliers). Using standard results from empirical process theory, we derive…
In a smooth semiparametric model, the marginal posterior distribution of the finite dimensional parameter of interest is expected to be asymptotically equivalent to the sampling distribution of frequentist's efficient estimators. This is…
We propose a methodology for modeling and comparing probability distributions within a Bayesian nonparametric framework. Building on dependent normalized random measures, we consider a prior distribution for a collection of discrete random…
Estimating the underlying distribution from \textit{iid} samples is a classical and important problem in statistics. When the alphabet size is large compared to number of samples, a portion of the distribution is highly likely to be…