Related papers: A closed-form filter for binary time series
In this article, an overview of Bayesian methods for sequential simulation from posterior distributions of nonlinear and non-Gaussian dynamic systems is presented. The focus is mainly laid on sequential Monte Carlo methods, which are based…
Computing smoothing distributions, the distributions of one or more states conditional on past, present, and future observations is a recurring problem when operating on general hidden Markov models. The aim of this paper is to provide a…
Filtering is a general name for inferring the states of a dynamical system given observations. The most common filtering approach is Gaussian Filtering (GF) where the distribution of the inferred states is a Gaussian whose mean is an affine…
We propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the…
We study the filtering and smoothing problem for continuous-time linear Gaussian systems. While classical approaches such as the Kalman-Bucy filter and the Rauch-Tung-Striebel (RTS) smoother provide recursive formulas for the conditional…
We introduce state-space models where the functionals of the observational and the evolutionary equations are unknown, and treated as random functions evolving with time. Thus, our model is nonparametric and generalizes the traditional…
Exact inference for hidden Markov models requires the evaluation of all distributions of interest - filtering, prediction, smoothing and likelihood - with a finite computational effort. This article provides sufficient conditions for exact…
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…
Practical Bayes filters often assume the state distribution of each time step to be Gaussian for computational tractability, resulting in the so-called Gaussian filters. When facing nonlinear systems, Gaussian filters such as extended…
Statistical arbitrage strategies, such as pairs trading and its generalizations, rely on the construction of mean-reverting spreads enjoying a certain degree of predictability. Gaussian linear state-space processes have recently been…
In science and engineering, we often work with models designed for accurate prediction of variables of interest. Recognizing that these models are approximations of reality, it becomes desirable to apply multiple models to the same data and…
This paper focuses on Sequential Monte Carlo approximations of smoothing distributions in conditionally linear and Gaussian state spaces. To reduce Monte Carlo variance of smoothers, it is typical in these models to use…
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…
We examine an analytic variational inference scheme for the Gaussian Process State Space Model (GPSSM) - a probabilistic model for system identification and time-series modelling. Our approach performs variational inference over both the…
This article discusses a partially adapted particle filter for estimating the likelihood of a nonlinear structural econometric state space models whose state transition density cannot be expressed in closed form. The filter generates the…
Classical discriminant analysis assumes identically distributed training data, yet in many applications observations are collected over time and the class-conditional distributions drift. This population drift renders stationary classifiers…
A prevalent problem in general state space models is the approximation of the smoothing distribution of a state conditional on the observations from the past, the present, and the future. The aim of this paper is to provide a rigorous…
State-space models provide an important body of techniques for analyzing time-series, but their use requires estimating unobserved states. The optimal estimate of the state is its conditional expectation given the observation histories, and…
The Bayesian smoothing equations are generally intractable for systems described by nonlinear stochastic differential equations and discrete-time measurements. Gaussian approximations are a computationally efficient way to approximate the…
Graph neural networks are often used to model interacting dynamical systems since they gracefully scale to systems with a varying and high number of agents. While there has been much progress made for deterministic interacting systems,…