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This article considers exponential families of truncated multivariate normal distributions with one-sided truncation for some or all coordinates. We observe that if all components are one-sided truncated then this family is not full. The…
We consider the minimax estimation problem of a discrete distribution with support size $k$ under locally differential privacy constraints. A privatization scheme is applied to each raw sample independently, and we need to estimate the…
The explosion of large-scale data in fields such as finance, e-commerce, and social media has outstripped the processing capabilities of single-machine systems, driving the need for distributed statistical inference methods. Traditional…
We study the pricing query complexity of revenue maximization for a single buyer whose private valuation is drawn from an unknown distribution. In this setting, the seller must learn the optimal monopoly price by posting prices and…
In certain privacy-sensitive scenarios within fields such as clinical trial simulations, federated learning, and distributed learning, researchers often face the challenge of estimating correlations between variables without access to…
The $p$-tensor Ising model is a one-parameter discrete exponential family for modeling dependent binary data, where the sufficient statistic is a multi-linear form of degree $p \geq 2$. This is a natural generalization of the matrix Ising…
Distributed statistical inference has recently attracted immense attention. The asymptotic efficiency of the maximum likelihood estimator (MLE), the one-step MLE, and the aggregated estimating equation estimator are established for…
Microscopy research often requires recovering particle-size distributions in three dimensions from only a few (10 - 200) profile measurements in the section. This problem is especially relevant for petrographic and mineralogical studies,…
We study and compare three estimators of a discrete monotone distribution: (a) the (raw) empirical estimator; (b) the "method of rearrangements" estimator; and (c) the maximum likelihood estimator. We show that the maximum likelihood…
Every student in statistics or data science learns early on that when the sample size largely exceeds the number of variables, fitting a logistic model produces estimates that are approximately unbiased. Every student also learns that there…
We consider the parameter estimation problem of a probabilistic generative model prescribed using a natural exponential family of distributions. For this problem, the typical maximum likelihood estimator usually overfits under limited…
After decades of research in Direction of Arrival (DoA) estimation, today Maximum Likelihood (ML) algorithms still provide the best performance in terms of resolution capabilities. At the cost of a multidimensional search, ML algorithms…
The hardcore model on a graph $G$ with parameter $\lambda>0$ is a probability measure on the collection of all independent sets of $G$, that assigns to each independent set $I$ a probability proportional to $\lambda^{|I|}$. In this paper we…
This work makes two advances in the study of the (approximate) nonparametric maximum likelihood estimator (NPMLE) for exponential family mixture models. First, we develop a data-compression strategy that reduces the cost of repeated…
We investigate Learning from Label Proportions (LLP), a partial information setting where examples in a training set are grouped into bags, and only aggregate label values in each bag are available. Despite the partial observability, the…
Determining the number of clusters in a dataset is a fundamental issue in data clustering. Many methods have been proposed to solve the problem of selecting the number of clusters, considering it to be a problem with regard to model…
Distribution learning finds probability density functions from a set of data samples, whereas clustering aims to group similar data points to form clusters. Although there are deep clustering methods that employ distribution learning…
We consider an expected-value ranking and selection (R&S) problem where all k solutions' simulation outputs depend on a common parameter whose uncertainty can be modeled by a distribution. We define the most probable best (MPB) to be the…
Since its introduction, the skew-$t$ distribution has received much attention in the literature both for the study of theoretical properties and as a model for data fitting in empirical work. A major motivation for this interest is the high…
Estimating statistical models within sensor networks requires distributed algorithms, in which both data and computation are distributed across the nodes of the network. We propose a general approach for distributed learning based on…