Related papers: Stochastic filtering via L2 projection on mixture …
A novel approximate Bayesian filter based on backward stochastic differential equations is introduced. It uses a nonlinear Feynman--Kac representation of the filtering problem and the approximation of an unnormalized filtering density using…
We consider a non-linear filtering problem, whereby the signal obeys the stochastic Navier-Stokes equations and is observed through a linear mapping with additive noise. The setup is relevant to data assimilation for numerical weather…
Solving large-scale systems of nonlinear equations/inequalities is a fundamental problem in computing and optimization. In this paper, we propose a generic successive projection (SP) framework for this problem. The SP sequentially projects…
For finite-dimensional problems, stochastic approximation methods have long been used to solve stochastic optimization problems. Their application to infinite-dimensional problems is less understood, particularly for nonconvex objectives.…
In this paper, we provide a multiscale perspective on the problem of maximum marginal likelihood estimation. We consider and analyse a diffusion-based maximum marginal likelihood estimation scheme using ideas from multiscale dynamics. Our…
We consider stochastic algorithms derived from methods for solving deterministic optimization problems, especially comparison-based algorithms derived from stochastic approximation algorithms with a constant step-size. We develop a…
We study the problem of learning policy of an infinite-horizon, discounted cost, Markov decision process (MDP) with a large number of states. We compute the actions of a policy that is nearly as good as a policy chosen by a suitable oracle…
In this paper, a scalable iterative projection-type algorithm for solving non-stationary systems of linear inequalities is considered. A non-stationary system is understood as a large-scale system of inequalities in which coefficients and…
We study stochastic projection-free methods for constrained optimization of smooth functions on Riemannian manifolds, i.e., with additional constraints beyond the parameter domain being a manifold. Specifically, we introduce stochastic…
Particle filtering is a popular method for inferring latent states in stochastic dynamical systems, whose theoretical properties have been well studied in machine learning and statistics communities. In many control problems, e.g.,…
Predictive recursion is an accurate and computationally efficient algorithm for nonparametric estimation of mixing densities in mixture models. In semiparametric mixture models, however, the algorithm fails to account for any uncertainty in…
We obtain a class of higher-degree stochastic integration filters (SIF) for nonlinear filtering applications. SIF are based on stochastic spherical-radial integration rules that achieve asymptotically exact evaluations of Gaussian weighted…
Filtering in spatially-extended dynamical systems is a challenging problem with significant practical applications such as numerical weather prediction. Particle filters allow asymptotically consistent inference but require infeasibly large…
A numerical method is developed for solving a system of partial differential equations modeling the flow of a nematic liquid crystal fluid with stretching effect, which takes into account the geometrical shape of its molecules. This system…
We consider the problem of high-dimensional filtering of state-space models (SSMs) at discrete times. This problem is particularly challenging as analytical solutions are typically not available and many numerical approximation methods can…
The joint bilateral filter, which enables feature-preserving signal smoothing according to the structural information from a guidance, has been applied for various tasks in geometry processing. Existing methods either rely on a static…
In this paper, we propose a novel primal-dual inexact gradient projection method for nonlinear optimization problems with convex-set constraint. This method only needs inexact computation of the projections onto the convex set for each…
Gaussian mixture models form a flexible and expressive parametric family of distributions that has found applications in a wide variety of applications. Unfortunately, fitting these models to data is a notoriously hard problem from a…
$L^1$ based optimization is widely used in image denoising, machine learning and related applications. One of the main features of such approach is that it naturally provide a sparse structure in the numerical solutions. In this paper, we…
In this work we are interested in stochastic particle methods for multi-objective optimization. The problem is formulated using parametrized, single-objective sub-problems which are solved simultaneously. To this end a consensus based…