Related papers: Efficient Transition Probability Computation for C…

In parameter estimation problems one computes a posterior distribution over uncertain parameters defined jointly by a prior distribution, a model, and noisy data. Markov Chain Monte Carlo (MCMC) is often used for the numerical solution of…

Computing the stationary distributions of a continuous-time Markov chain (CTMC) involves solving a set of linear equations. In most cases of interest, the number of equations is infinite or too large, and the equations cannot be solved…

Probabilistic inference is a fundamental task in modern machine learning. Recent advances in tensor network (TN) contraction algorithms have enabled the development of better exact inference methods. However, many common inference tasks in…

Methods for inference and simulation of linearly constrained Gaussian Markov Random Fields (GMRF) are computationally prohibitive when the number of constraints is large. In some cases, such as for intrinsic GMRFs, they may even be…

Markov chains are a common framework for individual-based state and time discrete models in ecology and evolution. Their use, however, is largely limited to systems with a low number of states, since the transition matrices involved pose…

The computer simulation of many molecular processes is complicated by long time scales caused by rare transitions between long-lived states. Here, we propose a new approach to simulate such rare events, which combines transition path…

We present an approach for testing for the existence of continuous generators of discrete stochastic transition matrices. Typically, the known approaches to ascertain the existence of continuous Markov processes are based in the assumption…

Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while…

Predictive models for binary data are fundamental in various fields, and the growing complexity of modern applications has motivated several flexible specifications for modeling the relationship between the observed predictors and the…

Many generative models can be expressed as a differentiable function of random inputs drawn from some simple probability density. This framework includes both deep generative architectures such as Variational Autoencoders and a large class…

Labeled continuous-time Markov chains (CTMCs) describe processes subject to random timing and partial observability. In applications such as runtime monitoring, we must incorporate past observations. The timing of these observations matters…

Tensor-network techniques have enjoyed outstanding success in physics, and have recently attracted attention in machine learning, both as a tool for the formulation of new learning algorithms and for enhancing the mathematical understanding…

In this work, we present a general method to establish properties of multi-dimensional continuous-time Markov chains representing stochastic reaction networks. This method consists of grouping states together (via a partition of the state…

Probabilistic models based on continuous latent spaces, such as variational autoencoders, can be understood as uncountable mixture models where components depend continuously on the latent code. They have proven to be expressive tools for…

Markov Chain Monte Carlo (MCMC) methods are algorithms for sampling probability distributions, commonly applied to the Boltzmann distribution in physical and chemical models such as protein folding and the Ising model. These methods enable…

We revisit the Bayesian Context Trees (BCT) modelling framework for discrete time series, which was recently found to be very effective in numerous tasks including model selection, estimation and prediction. A novel representation of the…

Non-Markovian models have great expressive power, at the cost of complex analysis of the stochastic process. The method of Stochastic State Classes (SSCs) derives closed-form analytical expressions for the joint Probability Density…

For rare events described in terms of Markov processes, truly unbiased estimation of the rare event probability generally requires the avoidance of numerical approximations of the Markov process. Recent work in the exact and…

The discrete class algorithm presented in this paper is an efficient simulation tool for stochastic processes governed by a reasonably small set of transition rates. The algorithm is presented, its performance compared to prevailing methods…

We consider the down/up crossing property of weighted Markov branching processes. The joint probability distribution of multi crossing numbers of such processes are obtained. In particular, for Markov branching processes, the probability…