Related papers: Estimating the Probability that a Function Observe…

Through the Bayesian lens of data assimilation, uncertainty on model parameters is traditionally quantified through the posterior covariance matrix. However, in modern settings involving high-dimensional and computationally expensive…

Monte Carlo methods have become increasingly relevant for control of non-differentiable systems, approximate dynamics models and learning from data. These methods scale to high-dimensional spaces and are effective at the non-convex…

Bayesian parameter inference for complex stochastic simulators is challenging due to intractable likelihood functions. Existing simulation-based inference methods often require large number of simulations and become costly to use in…

Constraints can be interpreted in a broad sense as any kind of explicit restriction over the parameters. While some constraints are defined directly on the parameter space, when they are instead defined by known behaviour on the model,…

Inferring unknown conic sections on the basis of noisy data is a challenging problem with applications in computer vision. A major limitation of the currently available methods for conic sections is that estimation methods rely on the…

In this paper, we develop convergence analysis of a modified line search method for objective functions whose value is computed with noise and whose gradient estimates are inexact and possibly random. The noise is assumed to be bounded in…

Score based approaches to sampling have shown much success as a generative algorithm to produce new samples from a target density given a pool of initial samples. In this work, we consider if we have no initial samples from the target…

In this work we detail the application of a fast convolution algorithm computing high dimensional integrals to the context of multiplicative noise stochastic processes. The algorithm provides a numerical solution to the problem of…

We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters. If the system dynamics is expensive to compute, standard sampling…

We present an algorithm to approximate the solutions to variational problems where set of admissible functions consists of convex functions. The main motivator behind this numerical method is estimating solutions to Adverse Selection…

There is currently a gap in theory for point patterns that lie on the surface of objects, with researchers focusing on patterns that lie in a Euclidean space, typically planar and spatial data. Methodology for planar and spatial data thus…

We focus on the problem of estimating and quantifying uncertainties on the excursion set of a function under a limited evaluation budget. We adopt a Bayesian approach where the objective function is assumed to be a realization of a Gaussian…

Tuning of measurement models is challenging in real-world applications of sequential Monte Carlo methods. Recent advances in differentiable particle filters have led to various efforts to learn measurement models through neural networks.…

Monte Carlo simulations are based on the manipulation of random numbers to evaluate probable outcomes, with applicability in a variety of different fields. By assigning probabilities, which can be determined a priori, to various events, it…

Rejection Sampling is a fundamental Monte-Carlo method. It is used to sample from distributions admitting a probability density function which can be evaluated exactly at any given point, albeit at a high computational cost. However,…

We propose a new type of Monte Carlo approach in numerical studies of quantum systems. Introducing a probability function which determines whether a state in the vector space survives or not, we can evaluate expectation values of powers of…

We revisit random search for stochastic optimization, where only noisy function evaluations are available. We show that the method works under weaker smoothness assumptions than previously considered, and that stronger assumptions enable…

The problem of estimating the probability p=P(g(X<0) is considered when X represents a multivariate stochastic input of a monotone function g. First, a heuristic method to bound p is formally described, involving a specialized design of…

The generation of decision-theoretic Bayesian optimal designs is complicated by the significant computational challenge of minimising an analytically intractable expected loss function over a, potentially, high-dimensional design space. A…

Estimation and prediction in high dimensional multivariate factor stochastic volatility models is an important and active research area because such models allow a parsimonious representation of multivariate stochastic volatility. Bayesian…