Related papers: MCMC for State Space models
Sampling from the conditional (or posterior) probability distribution of the latent states of a Hidden Markov Model, given the realization of the observed process, is a non-trivial problem in the context of Markov Chain Monte Carlo. To do…
Learning accurate predictive models of real-world dynamic phenomena (e.g., climate, biological) remains a challenging task. One key issue is that the data generated by both natural and artificial processes often comprise time series that…
We develop a semi-parametric state-space model for time-series data with latent regime transitions. Classical Markov-switching models use fixed parametric transition functions, such as logistic or probit links, which restrict flexibility…
This paper addresses the problem of sampling from binary distributions with constraints. In particular, it proposes an MCMC method to draw samples from a distribution of the set of all states at a specified distance from some reference…
I introduce a Markov chain Monte Carlo (MCMC) scheme in which sampling from a distribution with density pi(x) is done using updates operating on an "ensemble" of states. The current state x is first stochastically mapped to an ensemble,…
We introduce a new version of particle filter in which the number of "children" of a particle at a given time has a Poisson distribution. As a result, the number of particles is random and varies with time. An advantage of this scheme is…
Generative modeling, which learns joint probability distribution from data and generates samples according to it, is an important task in machine learning and artificial intelligence. Inspired by probabilistic interpretation of quantum…
We propose a unified mixture sampler (UMS) that provides a universal estimation framework for nonlinear state-space models with "exp-exp" likelihood kernels. Unlike existing methods that require deriving new mixture approximations for each…
Models for open quantum systems, which play important roles in electron transport problems and quantum computing, must take into account the interaction of the quantum system with the surrounding environment. Although such models can be…
Many problems arising in applications result in the need to probe a probability distribution for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion processes. Standard MCMC algorithms typically become…
State-space models are dynamical systems defined by a latent and an observed process. In ecology, stochastic state-space models in discrete time are most often used to describe the imperfectly observed dynamics of population sizes or animal…
We develop an approach for Bayesian learning of spatiotemporal dynamical mechanistic models. Such learning consists of statistical emulation of the mechanistic system that can efficiently interpolate the output of the system from arbitrary…
Markov chain Monte Carlo (MCMC) methods are widely used in machine learning. One of the major problems with MCMC is the question of how to design chains that mix fast over the whole state space; in particular, how to select the parameters…
Motivated by the problem of exploring discrete but very complex state spaces in Bayesian models, we propose a novel Markov Chain Monte Carlo search algorithm: the taxicab sampler. We describe the construction of this sampler and discuss how…
Randomised measurements can efficiently characterise many-body quantum states by learning the expectation values of observables with low Pauli weights. In this paper, we generalise the theoretical tools of classical shadow tomography to the…
State-space models are commonly used to describe different forms of ecological data. We consider the case of count data with observation errors. For such data the system process is typically multi-dimensional consisting of coupled Markov…
We introduce a new version of deep state-space models (DSSMs) that combines a recurrent neural network with a state-space framework to forecast time series data. The model estimates the observed series as functions of latent variables that…
This paper presents a new filter for state-space models based on Bellman's dynamic-programming principle, allowing for nonlinearity, non-Gaussianity and degeneracy in the observation and/or state-transition equations. The resulting Bellman…
This article addresses the problem of efficient Bayesian inference in dynamic systems using particle methods and makes a number of contributions. First, we develop a correlated pseudo-marginal (CPM) approach for Bayesian inference in state…
Deep state-space models (Deep SSMs) are becoming popular as effective approaches to model sequence data. They have also been shown to be capable of in-context learning, much like transformers. However, a complete picture of how SSMs might…