相关论文: Optimal Projection Filters

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 [ABF19] the authors define three projections of Rd-valued stochastic differential equations (SDEs) onto submanifolds: the Stratonovich, Ito-vector and Ito-jet projections. In this paper, after a brief survey of SDEs on manifolds, we…

We examine some differential geometric approaches to finding approximate solutions to the continuous time nonlinear filtering problem. Our primary focus is a new projection method for the optimal filter infinite dimensional Stochastic…

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…

This work extends the previous quantum projection filtering scheme in [Gao Q., Zhang G., & Petersen I. R. (2019). An exponential quantum projection filter for open quantum systems. \emph{Automatica}, 99, 59-68.], by adding an optimality…

Two nonlinear stochastic complimentary filters are developed on SO(3). They guarantee that errors in the Rodriguez vector and estimates are semi-globally uniformly ultimately bounded in mean square, and they converge to a small neighborhood…

We introduce and analyse a new nonparametric estimator of a multi-dimensional density. Our smooth projection estimator (SPE) is defined by a least squares projection of the sample onto an infinite dimensional mixture class via an…

Stochastic differential equations projected onto manifolds occur in physics, chemistry, biology, engineering, nanotechnology and optimization, with interdisciplinary applications. Intrinsic coordinate stochastic equations on the manifold…

This work proposes a nonlinear stochastic filter evolved on the Special Orthogonal Group SO(3) as a solution to the attitude filtering problem. One of the most common potential functions for nonlinear deterministic attitude observers is…

In this paper, we establish explicit convergence rates for the stochastic smooth approximations of infimal convolutions introduced and developed in \cite{MR4581306,MR4923371}. In particular, we quantify the convergence of the associated…

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.…

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…

In this paper, we study a family of non-convex and possibly non-smooth inf-projection minimization problems, where the target objective function is equal to minimization of a joint function over another variable. This problem include…

This paper introduces a new way to calculate distance-based statistics, particularly when the data are multivariate. The main idea is to pre-calculate the optimal projection directions given the variable dimension, and to project…

This work presents the first projection-free algorithm to solve stochastic bi-level optimization problems, where the objective function depends on the solution of another stochastic optimization problem. The proposed $\textbf{S}$tochastic…

Enforcing exact macroscopic conservation laws, such as mass and energy, in neural partial differential equation (PDE) solvers is computationally challenging in high dimensions. Traditional discrete projections rely on deterministic…

Stochastic bilevel optimization, which captures the inherent nested structure of machine learning problems, is gaining popularity in many recent applications. Existing works on bilevel optimization mostly consider either unconstrained…

Orthogonality constrained optimization is widely used in applications from science and engineering. Due to the nonconvex orthogonality constraints, many numerical algorithms often can hardly achieve the global optimality. We aim at…

Stochastic differential equations (SDE) are widely used in modeling stochastic dynamics in literature. However, SDE alone is not enough to determine a unique process. A specified interpretation for stochastic integration is needed.…

We consider stochastic variational inequalities with monotone operators defined as the expected value of a random operator. We assume the feasible set is the intersection of a large family of convex sets. We propose a method that combines…