Related papers: Stochastic Gradient MCMC for Nonlinear State Space…

Stochastic gradient Markov Chain Monte Carlo (SGMCMC) is considered the gold standard for Bayesian inference in large-scale models, such as Bayesian neural networks. Since practitioners face speed versus accuracy tradeoffs in these models,…

State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference \emph{and learning} (i.e. state estimation and system…

In this paper, we explore the class of the Hidden Semi-Markov Model (HSMM), a flexible extension of the popular Hidden Markov Model (HMM) that allows the underlying stochastic process to be a semi-Markov chain. HSMMs are typically used less…

State-space models (SSMs) are commonly used to model time series data where the observations depend on an unobserved latent process. However, inference on the model parameters of an SSM can be challenging, especially when the likelihood of…

Being the most classical generative model for serial data, state-space models (SSM) are fundamental in AI and statistical machine learning. In SSM, any form of parameter learning or latent state inference typically involves the computation…

State space models (SSMs) have emerged as a powerful framework for modelling long-range dependencies in sequence data. Unlike traditional recurrent neural networks (RNNs) and convolutional neural networks (CNNs), SSMs offer a structured and…

Hidden semi-Markov Models (HSMM's) - while broadly in use - are restricted to a discrete and uniform time grid. They are thus not well suited to explain often irregularly spaced discrete event data from continuous-time phenomena. We show…

Fitting stochastic kinetic models represented by Markov jump processes within the Bayesian paradigm is complicated by the intractability of the observed data likelihood. There has therefore been considerable attention given to the design of…

Sequential state estimation in non-linear and non-Gaussian state spaces has a wide range of applications in statistics and signal processing. One of the most effective non-linear filtering approaches, particle filtering, suffers from weight…

In this article we consider Bayesian parameter inference associated to partially-observed stochastic processes that start from a set B0 and are stopped or killed at the first hitting time of a known set A. Such processes occur naturally…

Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is…

Inference for spatial generalized linear mixed models (SGLMMs) for high-dimensional non-Gaussian spatial data is computationally intensive. The computational challenge is due to the high-dimensional random effects and because Markov chain…

We consider state and parameter estimation for a dynamical system having both time-varying and time-invariant parameters. It has been shown that the robustness of the Markov Chain Monte Carlo (MCMC) algorithm for estimating time-invariant…

Bayesian methods hold significant promise for improving the uncertainty quantification ability and robustness of deep neural network models. Recent research has seen the investigation of a number of approximate Bayesian inference methods…

Understanding stochastic gradient descent (SGD) and its variants is essential for machine learning. However, most of the preceding analyses are conducted under amenable conditions such as unbiased gradient estimator and bounded objective…

Nonlinear non-Gaussian state-space models arise in numerous applications in statistics and signal processing. In this context, one of the most successful and popular approximation techniques is the Sequential Monte Carlo (SMC) algorithm,…

Markov chain Monte Carlo (MCMC) algorithms are generally regarded as the gold standard technique for Bayesian inference. They are theoretically well-understood and conceptually simple to apply in practice. The drawback of MCMC is that in…

We consider Bayesian inference in sequential latent variable models in general, and in nonlinear state space models in particular (i.e., state smoothing). We work with sequential Monte Carlo (SMC) algorithms, which provide a powerful…

In the case of a linear state space model, we implement an MCMC sampler with two phases. In the learning phase, a self-tuning sampler is used to learn the parameter mean and covariance structure. In the estimation phase, the parameter mean…

In this paper we consider fully Bayesian inference in general state space models. Existing particle Markov chain Monte Carlo (MCMC) algorithms use an augmented model that takes into account all the variable sampled in a sequential Monte…