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The focus in this paper is interior-point methods for bound-constrained nonlinear optimization, where the system of nonlinear equations that arise are solved with Newton's method. There is a trade-off between solving Newton systems…
We consider chance-constrained binary knapsack problems, where the weights of items are independent random variables with the means and standard deviations known. The chance constraint can be reformulated as a second-order cone constraint…
The DUCK-calculus presented here is a recent approach to cope with probabilistic uncertainty in a sound and efficient way. Uncertain rules with bounds for probabilities and explicit conditional independences can be maintained incrementally.…
Regression methods are fundamental for scientific and technological applications. However, fitted models can be highly unreliable outside of their training domain, and hence the quantification of their uncertainty is crucial in many of…
While the theory of operator approximation with any given accuracy is well elaborated, the theory of {best constrained} constructive operator approximation is still not so well developed. Despite increasing demands from applications this…
Convex sample approximations of chance-constrained optimization problems are considered, in which chance constraints are replaced by sets of sampled constraints. We propose a randomized sample selection strategy that allows tight bounds to…
In this paper an approach to automated deduction under uncertainty,based on possibilistic logic, is proposed ; for that purpose we deal with clauses weighted by a degree which is a lower bound of a necessity or a possibility measure,…
Recent advances in uncertainty quantification increasingly emphasise the distinction between aleatory and epistemic uncertainty in machine learning, motivating the need for more unified frameworks. However, despite much progress in…
We introduce a method for using deep neural networks to amortize the cost of inference in models from the family induced by universal probabilistic programming languages, establishing a framework that combines the strengths of probabilistic…
Probabilistic inference procedures are usually coded painstakingly from scratch, for each target model and each inference algorithm. We reduce this effort by generating inference procedures from models automatically. We make this code…
A number of algorithms have been developed to solve probabilistic inference problems on belief networks. These algorithms can be divided into two main groups: exact techniques which exploit the conditional independence revealed when the…
This paper is about minimum cost constrained selection of inputs and outputs for generic arbitrary pole placement. The input-output set is constrained in the sense that the set of states that each input can influence and the set of states…
This paper proposes a robust approximation method for solving chance constrained optimization (CCO) of polynomials. Assume the CCO is defined with an individual chance constraint that is affine in the decision variables. We construct a…
Estimation and inference in dynamic discrete choice models often relies on approximation to lower the computational burden of dynamic programming. Unfortunately, the use of approximation can impart substantial bias in estimation and results…
This paper provides a review of Approximate Bayesian Computation (ABC) methods for carrying out Bayesian posterior inference, through the lens of density estimation. We describe several recent algorithms and make connection with traditional…
In this paper, we present a distributed algorithm for solving convex, constraint-coupled, optimization problems over peer-to-peer networks. We consider a network of processors that aim to cooperatively minimize the sum of local cost…
Results on approximate deduction in the context of the calculus of evidence of Dempster-Shafer and the theory of interval probabilities are reported. Approximate conditional knowledge about the truth of conditional propositions was assumed…
In this paper, we consider contention resolution algorithms that are augmented with predictions about the network. We begin by studying the natural setup in which the algorithm is provided a distribution defined over the possible network…
We consider distributed convex optimization problems that involve a separable objective function and nontrivial functional constraints, such as Linear Matrix Inequalities (LMIs). We propose a decentralized and computationally inexpensive…
In this work, we consider the fundamental problem of deriving quantitative bounds on the probability that a given assertion is violated in a probabilistic program. We provide automated algorithms that obtain both lower and upper bounds on…