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A way of constructing a nonlinear filter close to the optimal Kolmogorov - Wiener filter is proposed within the framework of the statistical approach to inverse problems. Quasi-optimal filtering, which has no Bayesian assumptions, produces…

Mathematical Physics · Physics 2009-11-10 V. Yu. Terebizh

In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…

Analysis of PDEs · Mathematics 2020-09-04 Prakash Kumar Das , M. M. Panja

A new learning algorithm proposed by Brandt and Lin for neural network [1], [2] has been shown to be mathematically equivalent to the conventional back-propagation learning algorithm, but has several advantages over the backpropagation…

Neural and Evolutionary Computing · Computer Science 2022-02-28 Feng Lin

The aim of this paper is to provide a variational interpretation of the nonlinear filter in continuous time. A time-stepping procedure is introduced, consisting of successive minimization problems in the space of probability densities. The…

Optimization and Control · Mathematics 2014-12-19 Richard S. Laugesen , Prashant G. Mehta , Sean P. Meyn , Maxim Raginsky

Inference for partially observed Markov process models has been a longstanding methodological challenge with many scientific and engineering applications. Iterated filtering algorithms maximize the likelihood function for partially observed…

Statistics Theory · Mathematics 2012-11-26 Edward L. Ionides , Anindya Bhadra , Yves Atchadé , Aaron King

Reservoir computing is a recently introduced brain-inspired machine learning paradigm capable of excellent performances in the processing of empirical data. We focus in a particular kind of time-delay based reservoir computers that have…

Dynamical Systems · Mathematics 2014-11-11 Lyudmila Grigoryeva , Julie Henriques , Laurent Larger , Juan-Pablo Ortega

The nonlinear filtering problem is concerned with finding the conditional probability distribution (posterior) of the state of a stochastic dynamical system, given a history of partial and noisy observations. This paper presents a…

Optimization and Control · Mathematics 2024-03-26 Mohammad Al-Jarrah , Bamdad Hosseini , Amirhossein Taghvaei

Modern applications require methods that are computationally feasible on large datasets but also preserve statistical efficiency. Frequently, these two concerns are seen as contradictory: approximation methods that enable computation are…

Methodology · Statistics 2021-06-11 Darren Homrighausen , Daniel J. McDonald

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…

Computation · Statistics 2010-05-04 M. G. B. Blum , O. Francois

We introduce the first direct policy search algorithm which provably converges to the globally optimal $\textit{dynamic}$ filter for the classical problem of predicting the outputs of a linear dynamical system, given noisy, partial…

Optimization and Control · Mathematics 2022-03-01 Jack Umenberger , Max Simchowitz , Juan C. Perdomo , Kaiqing Zhang , Russ Tedrake

This article proposes a general optimization framework for solving hand-eye calibration problem. Unlike traditional methods, an iterative algorithm based on Lie algebra that achieves approximately global optimal solutions is developed.…

Robotics · Computer Science 2026-05-07 Yanjia Chen , Xiangfei Li , Huan Zhao , Yiyuan Hong , Guanxiao Xia , Jiexin Zhang , Han Ding

This paper presents convergence analysis of a novel data-driven feedback control algorithm designed for generating online controls based on partial noisy observational data. The algorithm comprises a particle filter-enabled state estimation…

Optimization and Control · Mathematics 2024-05-31 Siming Liang , Hui Sun , Richard Archibald , Feng Bao

The solution of the continuous time filtering problem can be represented as a ratio of two expectations of certain functionals of the signal process that are parametrized by the observation path. We introduce a new time discretisation of…

Probability · Mathematics 2014-08-26 Dan Crisan , Salvador Ortiz-Latorre

In this letter, a new filtering technique to solve a nonlinear state estimation problem has been developed. It is well known that for a nonlinear system, the prior and posterior probability density functions (pdf) are non-Gaussian in…

Signal Processing · Electrical Eng. & Systems 2019-12-03 Kundan Kumar , Shovan Bhaumik

This paper introduces the {\it particle swarm filter} (not to be confused with particle swarm optimization): a recursive and embarrassingly parallel algorithm that targets an approximation to the sequence of posterior predictive…

Methodology · Statistics 2021-02-16 Taylor R. Brown

A new formulation of the particle filter for nonlinear filtering is presented, based on concepts from optimal control, and from the mean-field game theory. The optimal control is chosen so that the posterior distribution of a particle…

Numerical Analysis · Mathematics 2013-02-27 Tao Yang , Prashant G. Mehta , Sean P. Meyn

In order to interact intelligently with objects in the world, animals must first transform neural population responses into estimates of the dynamic, unknown stimuli which caused them. The Bayesian solution to this problem is known as a…

Machine Learning · Computer Science 2025-07-30 Sacha Sokoloski

We provide a method for approximating Bayesian inference using rejection sampling. We not only make the process efficient, but also dramatically reduce the memory required relative to conventional methods by combining rejection sampling…

Machine Learning · Computer Science 2015-12-04 Nathan Wiebe , Christopher Granade , Ashish Kapoor , Krysta M Svore

Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…

Optimization and Control · Mathematics 2019-10-29 Sulaiman A. Alghunaim , Kun Yuan , Ali H. Sayed

By using stochastic analysis, two probability versions of Li-Yau type inequalities are established for diffusion semigroups on a manifold possibly with (non-convex) boundary. The inequalities are explicitly given by the Bakry-Emery…

Probability · Mathematics 2024-11-07 Feng-Yu Wang , Li-Juan Cheng