Related papers: Inference on Estimators defined by Mathematical Pr…
We prove that quantum computation is polynomially equivalent to classical probabilistic computation with an oracle for estimating the value of simple sums, quadratically signed weight enumerators. The problem of estimating these sums can be…
The computational burden of probabilistic inference remains a hurdle for applying probabilistic programming languages to practical problems of interest. In this work, we provide a semantic and algorithmic foundation for efficient exact…
In this paper we address the challenging problem of designing globally convergent estimators for the parameters of nonlinear systems containing a non-separable exponential nonlinearity. This class of terms appears in many practical…
Our aim is to explain mathematical programs with equilibrium constraints (MPECs), motivate them through applications, present the main equivalent formulations of equilibrium constraints, and summarize the basic existence theory for optimal…
We propose a methodology, based on machine learning and optimization, for selecting a solver configuration for a given instance. First, we employ a set of solved instances and configurations in order to learn a performance function of the…
The study addresses the problem of precision in floating-point (FP) computations. A method for estimating the errors which affect intermediate and final results is proposed and a summary of many software simulations is discussed. The basic…
We propose a data-driven framework for efficiently solving quadratic programming (QP) problems by reducing the number of variables in high-dimensional QPs using instance-specific projection. A graph neural network-based model is designed to…
In optimization problems, the quality of a candidate solution can be characterized by the optimality gap. For most stochastic optimization problems, this gap must be statistically estimated. We show that for risk-averse problems, standard…
Universal probabilistic programming languages (PPLs) make it relatively easy to encode and automatically solve statistical inference problems. To solve inference problems, PPL implementations often apply Monte Carlo inference algorithms…
In this article, we consider computing expectations w.r.t. probability measures which are subject to discretization error. Examples include partially observed diffusion processes or inverse problems, where one may have to discretize time…
We propose a robust and scalable procedure for general optimization and inference problems on manifolds leveraging the classical idea of `median-of-means' estimation. This is motivated by ubiquitous examples and applications in modern data…
Probabilistic Logic Programming is an effective formalism for encoding problems characterized by uncertainty. Some of these problems may require the optimization of probability values subject to constraints among probability distributions…
The computational cost for inference and prediction of statistical models based on Gaussian processes with Mat\'ern covariance functions scales cubicly with the number of observations, limiting their applicability to large data sets. The…
There has been a recent push in making machine learning models more interpretable so that their performance can be trusted. Although successful, these methods have mostly focused on the deep learning methods while the fundamental…
Missing covariates in regression or classification problems can prohibit the direct use of advanced tools for further analysis. Recent research has realized an increasing trend towards the usage of modern Machine Learning algorithms for…
This manuscript proposes a probabilistic framework for algorithms that iteratively solve unconstrained linear problems $Bx = b$ with positive definite $B$ for $x$. The goal is to replace the point estimates returned by existing methods with…
Programs with floating-point computations are often derived from mathematical models or designed with the semantics of the real numbers in mind. However, for a given input, the computed path with floating-point numbers may differ from the…
We introduce a new approach for the numerical pricing of American options. The main idea is to choose a finite number of suitable excessive functions (randomly) and to find the smallest majorant of the gain function in the span of these…
High-dimensional nonlinear optimization problems subject to nonlinear constraints can appear in several contexts including constrained physical and dynamical systems, statistical estimation, and other numerical models. Feasible optimization…
A risk-aware decision-making problem can be formulated as a chance-constrained linear program in probability measure space. Chance-constrained linear program in probability measure space is intractable, and no numerical method exists to…