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Discrete automated processes in industrial and cyber-physical systems often exhibit a repetitive structure in which successive repetitions follow a common trajectory while differing in duration, amplitude, and fine-scale dynamics. Such…

We introduce Generalized Discrete Diffusion from Snapshots (GDDS), a unified framework for discrete diffusion modeling that supports arbitrary noising processes over large discrete state spaces. Our formulation encompasses all existing…

Despite the proliferation of generative models, achieving fast sampling during inference without compromising sample diversity and quality remains challenging. Existing models such as Denoising Diffusion Probabilistic Models (DDPM) deliver…

The Gaussian process latent variable model (GP-LVM) provides a flexible approach for non-linear dimensionality reduction that has been widely applied. However, the current approach for training GP-LVMs is based on maximum likelihood, where…

Stochastic models of biochemical reaction networks are widely used to capture intrinsic noise in cellular systems. The typical formulation of these models are based on Markov processes for which there is extensive research on efficient…

In this paper we introduce a novel online time series forecasting model we refer to as the pM-GP filter. We show that our model is equivalent to Gaussian process regression, with the advantage that both online forecasting and online…

We propose a latent topic model with a Markovian transition for process data, which consist of time-stamped events recorded in a log file. Such data are becoming more widely available in computer-based educational assessment with complex…

Understanding molecular structure, dynamics, and reactivity requires bridging processes that occur across widely separated time scales. Conventional molecular dynamics simulations provide atomistic resolution, but their femtosecond time…

We identify a new variational inference scheme for dynamical systems whose transition function is modelled by a Gaussian process. Inference in this setting has either employed computationally intensive MCMC methods, or relied on…

We develop a method for reconstructing regulatory interconnection networks between variables evolving according to a linear dynamical system. The work is motivated by the problem of gene regulatory network inference, that is, finding causal…

This paper develops the theory and methods for modeling a stationary count time series via Gaussian transformations. The techniques use a latent Gaussian process and a distributional transformation to construct stationary series with very…

We consider two-state Non-Homogeneous Hidden Markov Models (NHHMMs) for forecasting univariate time series. Given a set of predictors, the time series are modeled via predictive regressions with state dependent coefficients and time-varying…

Many of the data, particularly in medicine and disease mapping are count. Indeed, the under or overdispersion problem in count data distrusts the performance of the classical Poisson model. For taking into account this problem, in this…

We introduce generative models for accelerating simulations of complex systems through learning and evolving their effective dynamics. In the proposed Generative Learning of Effective Dynamics (G-LED), instances of high dimensional data are…

We propose a hidden Markov model for univariate proportion time series taking values in (0,1), where regime switching captures latent structural changes and the emission distribution belongs to the Beta family. In each latent state, the…

The deployment of autonomous systems that operate in unstructured environments necessitates algorithms to verify their safety. This can be challenging due to, e.g., black-box components in the control software, or undermodelled dynamics…

A beta-negative binomial (BNB) process is proposed, leading to a beta-gamma-Poisson process, which may be viewed as a "multi-scoop" generalization of the beta-Bernoulli process. The BNB process is augmented into a beta-gamma-gamma-Poisson…

Structured distributions, i.e. distributions over combinatorial spaces, are commonly used to learn latent probabilistic representations from observed data. However, scaling these models is bottlenecked by the high computational and memory…

Stochastic kinetic models describe systems across biology, chemistry, and physics where discrete events and small populations render deterministic approximations inadequate. Parameter inference and inverse design in these systems require…

Markov jump processes and continuous time Bayesian networks are important classes of continuous time dynamical systems. In this paper, we tackle the problem of inferring unobserved paths in these models by introducing a fast auxiliary…