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The Shannon entropy, and related quantities such as mutual information, can be used to quantify uncertainty and relevance. However, in practice, it can be difficult to compute these quantities for arbitrary probability distributions,…

In this paper, we consider the problem of partitioning a small data sample drawn from a mixture of $k$ product distributions. We are interested in the case that individual features are of low average quality $\gamma$, and we want to use as…

Nonprobability (convenience) samples are increasingly sought to stabilize estimations for one or more population variables of interest that are performed using a randomized survey (reference) sample by increasing the effective sample size.…

Spectral clustering refers to a family of unsupervised learning algorithms that compute a spectral embedding of the original data based on the eigenvectors of a similarity graph. This non-linear transformation of the data is both the key of…

Nowadays, parallel computing is ubiquitous in several application fields, both in engineering and science. The computations rely on the floating-point arithmetic specified by the IEEE754 Standard. In this context, an elementary brick of…

Many modern statistical applications involve inference for complex stochastic models, where it is easy to simulate from the models, but impossible to calculate likelihoods. Approximate Bayesian computation (ABC) is a method of inference for…

Approximate Bayesian Computation (ABC) is a powerful method for carrying out Bayesian inference when the likelihood is computationally intractable. However, a drawback of ABC is that it is an approximate method that induces a systematic…

For better learning, large datasets are often split into small batches and fed sequentially to the predictive model. In this paper, we study such batch decompositions from a probabilistic perspective. We assume that data points (possibly…

We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…

Variational inference approximates the posterior distribution of a probabilistic model with a parameterized density by maximizing a lower bound for the model evidence. Modern solutions fit a flexible approximation with stochastic gradient…

Data privacy has increasingly become a daunting challenge because it limits data availability, which is essential in estimating statistical models such as generalized linear mixed models. Access to personal data often involves considerable…

Given a large dataset and an estimation task, it is common to pre-process the data by reducing them to a set of sufficient statistics. This step is often regarded as straightforward and advantageous (in that it simplifies statistical…

Compressed sensing allows perfect recovery of sparse signals (or signals sparse in some basis) using only a small number of random measurements. Existing results in compressed sensing literature have focused on characterizing the achievable…

With the increasing penetration of high-frequency sensors across a number of biological and physical systems, the abundance of the resulting observations offers opportunities for higher statistical accuracy of down-stream estimates, but…

Classifying sequential data as early and as accurately as possible is a challenging yet critical problem, especially when a sampling cost is high. One algorithm that achieves this goal is the sequential probability ratio test (SPRT), which…

This paper studies the sample complexity of searching over multiple populations. We consider a large number of populations, each corresponding to either distribution P0 or P1. The goal of the search problem studied here is to find one…

Given a linear dynamical system, we consider the problem of constructing an approximate system using only a subset of the sensors out of the total set such that the observability Gramian of the new system is approximately equal to that of…

Spectral clustering is a popular and versatile clustering method based on a relaxation of the normalised graph cut objective. Despite its popularity, however, there is no single agreed upon method for tuning the important scaling parameter,…

Econometricians have usefully separated study of estimation into identification and statistical components. Identification analysis, which assumes knowledge of the probability distribution generating observable data, places an upper bound…

Rapid advancements in data science require us to have fundamentally new frameworks to tackle prevalent but highly non-trivial "irregular" inference problems, to which the large sample central limit theorem does not apply. Typical examples…