Related papers: Stochastic filtering via L2 projection on mixture …
In this paper we introduce a projection method for the space of probability distributions based on the differential geometric approach to statistics. This method is based on a direct L2 metric as opposed to the usual Hellinger distance and…
We present the two new notions of projection of a stochastic differential equation (SDE) onto a submanifold, as developed in Armstrong, Brigo e Rossi Ferrucci (2019, 2018): the Ito-vector and Ito-jet projections. This allows one to…
Stochastic filtering is defined as the estimation of a partially observed dynamical system. A massive scientific and computational effort is dedicated to the development of numerical methods for approximating the solution of the filtering…
The projection filter is a technique for approximating the solutions of optimal filtering problems. In projection filters, the Kushner--Stratonovich stochastic partial differential equation that governs the propagation of the optimal…
We define two new notions of projection of a stochastic differential equation (SDE) onto a submanifold: the Ito-vector and Ito-jet projections. This allows one to systematically develop low dimensional approximations to high dimensional…
In this article, we study the continuous-discrete projection filter for exponential-family manifolds with conjugate likelihoods. We first derive the local projection error of the prediction step of the continuous-discrete projection filter.…
A series of novel filters for probabilistic inference that propose an alternative way of performing Bayesian updates, called particle flow filters, have been attracting recent interest. These filters provide approximate solutions to…
We consider the numerical solution of parameterized linear systems where the system matrix, the solution, and the right-hand side are parameterized by a set of uncertain input parameters. We explore spectral methods in which the solutions…
This paper presents a new approach for filter design based on stochastic distances and tests between distributions. A window is defined around each pixel, overlapping samples are compared and only those which pass a goodness-of-fit test are…
This paper studies Galerkin approximations applied to the Zakai equation of stochastic filtering. The basic idea of this approach is to project the infinite-dimensional Zakai equation onto some finite-dimensional subspace generated by…
We develop algorithms for computing expectations of the laws of models associated to stochastic differential equations (SDEs) driven by pure L\'evy processes. We consider filtering such processes and well as pricing of path dependent…
We propose a novel projection-based particle method for solving the McKean-Vlasov stochastic differential equations. Our approach is based on a projection-type estimation of the marginal density of the solution in each time step. The…
Both in classical and quantum stochastic control theory a major role is played by the filtering equation, which recursively updates the information state of the system under observation. Unfortunately, the theory is plagued by…
Nonlinear Kalman Filters are powerful and widely-used techniques when trying to estimate the hidden state of a stochastic nonlinear dynamic system. In this paper, we extend the Smart Sampling Kalman Filter (S2KF) with a new point symmetric…
We study maximum likelihood estimation for spatial generalized linear mixed models with Gaussian process approximations using a stochastic Newton-Raphson algorithm. We consider two Gaussian Process approximations in this context: spectral…
The subject of this work is a new stochastic Galerkin method for second-order elliptic partial differential equations with random diffusion coefficients. It combines operator compression in the stochastic variables with tree-based spline…
We consider the problem of approximating optimal in the Minimum Mean Squared Error (MMSE) sense nonlinear filters in a discrete time setting, exploiting properties of stochastically convergent state process approximations. More…
This paper presents a structure-preserving model reduction framework for linear systems, in which the $\mathcal{H}_2$ optimization is incorporated with the Petrov-Galerkin projection to preserve structural features of interest, including…
We consider the problem of learning the optimal policy for infinite-horizon Markov decision processes (MDPs). For this purpose, some variant of Stochastic Mirror Descent is proposed for convex programming problems with Lipschitz-continuous…
We look at a stochastic time-varying optimization problem and we formulate online algorithms to find and track its optimizers in expectation. The algorithms are derived from the intuition that standard prediction and correction steps can be…