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Markov Population Models are a widespread formalism used to model the dynamics of complex systems, with applications in Systems Biology and many other fields. The associated Markov stochastic process in continuous time is often analyzed by…

Behavioural and neural time series are often correlated with the past. This history-dependence may represent a fundamental property of the measured variables, or may arise from how confounding variables change over time. Here we argue that…

As a model for an on-line classification setting we consider a stochastic process $(X_{-n},Y_{-n})_{n}$, the present time-point being denoted by 0, with observables $ \ldots,X_{-n},X_{-n+1},\ldots, X_{-1}, X_0$ from which the pattern $Y_0$…

This paper provides insight into when, why, and how forecast strategies fail when they are applied to complicated time series. We conjecture that the inherent complexity of real-world time-series data---which results from the dimension,…

Fitting generative models to sequential data typically involves two recursive computations through time, one forward and one backward. The latter could be a computation of the loss gradient (as in backpropagation through time), or an…

When is keeping a memory of observations worthwhile? We use hidden Markov models to look at phase transitions that emerge when comparing state estimates in systems with discrete states and noisy observations. We infer the underlying state…

We present a new algorithm for discovering patterns in time series and other sequential data. We exhibit a reliable procedure for building the minimal set of hidden, Markovian states that is statistically capable of producing the behavior…

We address tracking and prediction of multiple moving objects in visual data streams as inference and sampling in a disentangled latent state-space model. By encoding objects separately and including explicit position information in the…

The probabilistic description of the time evolution of a physical system can take two conceptually distinct forms: a trajectory of probabilities, which specifies how probabilities evolve over time, and a probability on trajectories, which…

The study of belief change has been an active area in philosophy and AI. In recent years two special cases of belief change, belief revision and belief update, have been studied in detail. Roughly, revision treats a surprising observation…

Biological systems need to react to stimuli over a broad spectrum of timescales. If and how this ability can emerge without external fine-tuning is a puzzle. We consider here this problem in discrete Markovian systems, where we can leverage…

We consider a pair of correlated processes {Z_n} and {S_n} (two sided), where the former is observable and the later is hidden. The uncertainty in the estimation of Z_n upon its finite past history is H(Z_n|Z_0^{n-1}), and for estimation of…

Time series prediction is a widespread and well studied problem with applications in many domains (medical, geoscience, network analysis, finance, econometry etc.). In the case of multivariate time series, the key to good performances is to…

The investigation of the phenomenon of dephasing assisted quantum transport, which happens when the presence of dephasing benefits the efficiency of this process, has been mainly focused on Markovian scenarios associated with constant and…

We observe n possibly dependent random variables, the distribution of which is presumed to be stationary even though this might not be true, and we aim at estimating the stationary distribution. We establish a non-asymptotic deviation bound…

We introduce the minimal maximally predictive models ({\epsilon}-machines) of processes generated by certain hidden semi-Markov models. Their causal states are either hybrid discrete-continuous or continuous random variables and…

The mixing time of a Markov chain determines how fast the iterates of the Markov chain converge to the stationary distribution; however, it does not control the dependencies between samples along the Markov chain. In this paper, we study…

When the initial and transition probabilities of a finite Markov chain in discrete time are not well known, we should perform a sensitivity analysis. This can be done by considering as basic uncertainty models the so-called credal sets that…

Optimal designs minimize the number of experimental runs (samples) needed to accurately estimate model parameters, resulting in algorithms that, for instance, efficiently minimize parameter estimate variance. Governed by knowledge of past…

In Bayesian persuasion, an informed sender strategically discloses information to a receiver so as to persuade them to undertake desirable actions. Recently, a growing attention has been devoted to settings in which sender and receivers…