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Stochastic Rounding is a probabilistic rounding mode that is surprisingly effective in large-scale computations and low-precision arithmetic. Its random nature promotes error cancellation rather than error accumulation, resulting in slower…

Wasserstein barycenters provide a geometrically meaningful way to aggregate probability distributions, built on the theory of optimal transport. They are difficult to compute in practice, however, leading previous work to restrict their…

Adversarial examples pose a security threat to many critical systems built on neural networks. Given that deterministic robustness often comes with significantly reduced accuracy, probabilistic robustness (i.e., the probability of having…

It is becoming increasingly apparent that probabilistic approaches can overcome conservatism and computational complexity of the classical worst-case deterministic framework and may lead to designs that are actually safer. In this paper we…

We present an extension of local sensitivity analysis, also referred to as the perturbation approach for uncertainty quantification, to Bayesian inverse problems. More precisely, we show how moments of random variables with respect to the…

In this paper, we introduce a method for approximating the solution to inference and optimization tasks in uncertain and deterministic reasoning. Such tasks are in general intractable for exact algorithms because of the large number of…

An algorithm of searching a zero of an unknown undimensional function is considered, measured at a point x with some error. The step sizes are random positive values and are calculated according to the rule: if two consecutive iterations…

In this paper, we study the accuracy of values aggregated over classes predicted by a classification algorithm. The problem is that the resulting aggregates (e.g., sums of a variable) are known to be biased. The bias can be large even for…

We investigate the statistical properties of cut sizes generated by heuristic algorithms which solve approximately the graph bisection problem. On an ensemble of sparse random graphs, we find empirically that the distribution of the cut…

We consider the task of performing probabilistic inference with probabilistic logical models. Many algorithms for approximate inference with such models are based on sampling. From a logic programming perspective, sampling boils down to…

The widely recommended procedure of Bayesian model averaging is flawed in the M-open setting in which the true data-generating process is not one of the candidate models being fit. We take the idea of stacking from the point estimation…

We present a stochastic variance-reduced heavy ball power iteration algorithm for solving PCA and provide a convergence analysis for it. The algorithm is an extension of heavy ball power iteration, incorporating a step size so that progress…

In real-world Bayesian inference applications, prior assumptions regarding the parameters of interest may be unrepresentative of their actual values for a given dataset. In particular, if the likelihood is concentrated far out in the wings…

Conformal prediction has emerged as a popular technique for facilitating valid predictive inference across a spectrum of machine learning models, under minimal assumption of exchangeability. Recently, Hoff (2023) showed that full conformal…

Approximate Bayesian computation (ABC) has gained popularity in recent years owing to its easy implementation, nice interpretation and good performance. Its advantages are more visible when one encounters complex models where maximum…

Also known as likelihood-free methods, approximate Bayesian computational (ABC) methods have appeared in the past ten years as the most satisfactory approach to untractable likelihood problems, first in genetics then in a broader spectrum…

Large sectors of the recent optimization literature focused in the last decade on the development of optimal stochastic first order schemes for constrained convex models under progressively relaxed assumptions. Stochastic proximal point is…

We address an optimization problem where the cost function is the expectation of a random mapping. To tackle the problem two approaches based on the approximation of the objective function by consensus-based particle optimization methods on…

In this paper, we propose a proximal stochasitc gradient algorithm (PSGA) for solving composite optimization problems by incorporating variance reduction techniques and an adaptive step-size strategy. In the PSGA method, the objective…

Gradient boosting is a prediction method that iteratively combines weak learners to produce a complex and accurate model. From an optimization point of view, the learning procedure of gradient boosting mimics a gradient descent on a…