Related papers: Markov chain models for inspecting response dynami…

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…

The ability to predict future events or patterns based on previous experience is crucial for many applications such as traffic control, weather forecasting, or supply chain management. While modern supervised Machine Learning approaches…

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…

We introduce the Conditional Mutual Information (CMI) for the estimation of the Markov chain order. For a Markov chain of $K$ symbols, we define CMI of order $m$, $I_c(m)$, as the mutual information of two variables in the chain being $m$…

Markov models lie at the interface between statistical independence in a probability distribution and graph separation properties. We review model selection and estimation in directed and undirected Markov models with Gaussian…

The first motivation of this paper is to study stationarity and ergodic properties for a general class of time series models defined conditional on an exogenous covariates process. The dynamic of these models is given by an autoregressive…

Data of sequential nature arise in many application domains in forms of, e.g. textual data, DNA sequences, and software execution traces. Different research disciplines have developed methods to learn sequence models from such datasets: (i)…

These lecture notes aim at a post-Bachelor audience with a background at an introductory level in Applied Mathematics and Applied Statistics. They discuss the logic and methodology of the Bayes-Laplace approach to inductive statistical…

Hidden Markov models (HMMs) have been used increasingly to understand how movement patterns of animals arise from behavioural states. An animal is assumed to transition between behavioural states through time, as described by transition…

Motivated by techniques developed in recent progress on lower bounds for sublinear time algorithms (Behnezhad, Roghani and Rubinstein, STOC 2023, FOCS 2023, and STOC 2024) we introduce and study a new class of randomized algorithmic…

Systems of interacting continuous-time Markov chains are a powerful model class, but inference is typically intractable in high dimensional settings. Auxiliary information, such as noisy observations, is typically only available at discrete…

We derive some key extremal features for $k$th order Markov chains that can be used to understand how the process moves between an extreme state and the body of the process. The chains are studied given that there is an exceedance of a…

Various and ubiquitous information systems are being used in monitoring, exchanging, and collecting information. These systems are generating massive amount of event sequence logs that may help us understand underlying phenomenon. By…

Stochastic models in which agents interact with their neighborhood according to a network topology are a powerful modeling framework to study the emergence of complex dynamic patterns in real-world systems. Stochastic simulations are often…

Measuring conditional dependencies among the variables of a network is of great interest to many disciplines. This paper studies some shortcomings of the existing dependency measures in detecting direct causal influences or their lack of…

Prediction models are used amongst others to inform medical decisions on interventions. Typically, individuals with high risks of adverse outcomes are advised to undergo an intervention while those at low risk are advised to refrain from…

Markov decision processes are typically used for sequential decision making under uncertainty. For many aspects however, ranging from constrained or safe specifications to various kinds of temporal (non-Markovian) dependencies in task and…

Immune events such as infection, vaccination, and a combination of the two result in distinct time-dependent antibody responses in affected individuals. These responses and event prevalences combine non-trivially to govern antibody levels…

Constraint-based methods are one of the main approaches for causal structure learning that are particularly valued as they are asymptotically guaranteed to find a structure that is Markov equivalent to the causal graph of the system. On the…

We consider a Markovian single server queue in which customers are preemptively scheduled by exogenously assigned priority levels. The novelty in our model is that the priority levels are randomly assigned from a continuous probability…