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It is well-known in the field of lossless data compression that probabilistic next-symbol prediction can be used to compress sequences of symbols. Deep neural networks are able to capture rich dependencies in data, offering a powerful means…
With some regularity conditions maximum likelihood estimators (MLEs) always produce asymptotically optimal (in the sense of consistency, efficiency, sufficiency, and unbiasedness) estimators. But in general, the MLEs lead to non-robust…
We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…
We consider deep multivariate models for heterogeneous collections of random variables. In the context of computer vision, such collections may e.g. consist of images, segmentations, image attributes, and latent variables. When developing…
This paper considers the problem of channel coding with a given (possibly suboptimal) maximum-metric decoding rule. A cost-constrained random-coding ensemble with multiple auxiliary costs is introduced, and is shown to achieve error…
At high levels, the asymptotic distribution of a stationary, regularly varying Markov chain is conveniently given by its tail process. The latter takes the form of a geometric random walk, the increment distribution depending on the sign of…
Estimates are constructed for the deviation of the concentration functions of sums of independent random variables with finite variances from the folded normal distribution function without any assumptions concerning the existence of the…
Several Artificial Intelligence schemes for reasoning under uncertainty explore either explicitly or implicitly asymmetries among probabilities of various states of their uncertain domain models. Even though the correct working of these…
Prediction sets provide a means of quantifying the uncertainty in predictive tasks. Using held out calibration data, conformal prediction and risk control can produce prediction sets that exhibit statistically valid error control in a…
Computers are deterministic dynamical systems (CHAOS 19:033124, 2009). Among other things, that implies that one should be able to use deterministic forecast rules to predict their behavior. That statement is sometimes-but not always-true.…
Probabilistic programming languages (PPLs) are a powerful modeling tool, able to represent any computable probability distribution. Unfortunately, probabilistic program inference is often intractable, and existing PPLs mostly rely on…
A major impediment towards the industrial adoption of decentralized distributed systems comes from the difficulty to theoretically prove that these systems exhibit the required behavior. In this paper, we use probability theory to analyze a…
This paper proposes a model predictive controller for discrete-time linear systems with additive, possibly unbounded, stochastic disturbances and subject to chance constraints. By computing a polytopic probabilistic positively invariant set…
This paper develops upper and lower bounds for the probability of Boolean functions by treating multiple occurrences of variables as independent and assigning them new individual probabilities. We call this approach dissociation and give an…
Morgan and McIver's weakest pre-expectation framework is one of the most well-established methods for deductive verification of probabilistic programs. Roughly, the idea is to generalize binary state assertions to real-valued expectations,…
Distributed Principal Component Analysis (PCA) has been studied to deal with the case when data are stored across multiple machines and communication cost or privacy concerns prohibit the computation of PCA in a central location. However,…
Many problems in computational science and engineering become one-to-many after coarse graining, partial observation, or inverse reconstruction: a resolved state may not determine a unique subgrid forcing, a structural descriptor may not…
Running machine learning algorithms on large and rapidly growing volumes of data is often computationally expensive, one common trick to reduce the size of a data set, and thus reduce the computational cost of machine learning algorithms,…
We study efficient algorithms for linear regression and covariance estimation in the absence of Gaussian assumptions on the underlying distributions of samples, making assumptions instead about only finitely-many moments. We focus on how…
We propose an analytical approach to the computation of tail probabilities of compound distributions whose individual components have heavy tails. Our approach is based on the contour integration method, and gives rise to a representation…