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This paper introduces an algorithm for discovering implicit and delayed causal relations between events observed by a robot at arbitrary times, with the objective of improving data-efficiency and interpretability of model-based…

In this paper we explore representations of temporal knowledge based upon the formalism of Causal Probabilistic Networks (CPNs). Two different ?continuous-time? representations are proposed. In the first, the CPN includes variables…

Stochastic resetting can be naturally understood as a renewal process governing the evolution of an underlying stochastic process. In this work, we formally derive well-known results of diffusion with resets from a renewal theory…

This paper describes a method for the online state estimation of systems described by a general class of linear noncausal time-varying difference descriptor equations subject to uncertainties. The method is based on the notions of a linear…

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…

Certain deterministic non-linear systems may show chaotic behaviour. Time series derived from such systems seem stochastic when analyzed with linear techniques. However, uncovering the deterministic structure is important because it allows…

Reinforced processes are known to provide a stochastic representation for the quasi-stationary distribution of a given killed Markov process - describing the killed Markov process at fixed time instants. In this paper we shall adapt the…

Coupled relaxation oscillators, realized via chemical or other means, can exhibit a multiplicity of steady states, characterized by spatial patterns resulting from lateral inhibition. We show that perturbation-initiated transformations…

Time lags are ubiquitous in biophysiological processes and more generally in real-world complex networks. It has been recently proposed to use information-theoretic tools such as transfer entropy to detect and estimate a possible delay in…

Driven-dissipative quantum systems generically do not satisfy simple notions of detailed balance based on the time symmetry of correlation functions. We show that such systems can nonetheless exhibit a hidden time-reversal symmetry which…

Very large state spaces with a sparse reward signal are difficult to explore. The lack of a sophisticated guidance results in a poor performance for numerous reinforcement learning algorithms. In these cases, the commonly used random…

We present a flexible Bayesian semiparametric mixed model for longitudinal data analysis in the presence of potentially high-dimensional categorical covariates. Building on a novel hidden Markov tensor decomposition technique, our proposed…

We consider the problem of computing the set of initial states of a dynamical system such that there exists a control strategy to ensure that the trajectories satisfy a temporal logic specification with probability 1 (almost-surely). We…

This paper generalizes the notion of stochastic order to a relation between probability measures over arbitrary measurable spaces. This generalization is motivated by the observation that for the stochastic ordering of two stationary Markov…

Typically, real-world stochastic processes are not easy to analyze. In this work we study the representation of any stochastic process as a memoryless innovation process triggering a dynamic system. We show that such a representation is…

Our paper illustrates how the theory of Lie systems allows recovering known results and provide new examples of piecewise deterministic processes with phase-type jumps for which the corresponding first-time passage problems may be solved…

Counterfactual estimation using synthetic controls is one of the most successful recent methodological developments in causal inference. Despite its popularity, the current description only considers time series aligned across units and…

When analysing gene expression time series data an often overlooked but crucial aspect of the model is that the regulatory network structure may change over time. Whilst some approaches have addressed this problem previously in the…

Appealing to several multivariate information measures---some familiar, some new here---we analyze the information embedded in discrete-valued stochastic time series. We dissect the uncertainty of a single observation to demonstrate how the…

Temporal causal representation learning is a powerful tool for uncovering complex patterns in observational studies, which are often represented as low-dimensional time series. However, in many real-world applications, data are…