Related papers: A modern approach to transition analysis and proce…

We consider deep multivariate models for heterogeneous collections of random variables. In the context of computer vision, such collections may e.g. consist of images, segmentations, image attributes, and latent variables. When developing…

In this paper, we propose a data-driven robust safety verification framework for stochastic dynamical systems modeled as Markov decision processes with time-varying and uncertain transition probabilities. Rather than assuming access to the…

Car-following behavior is fundamental to traffic flow theory, yet traditional models often fail to capture the stochasticity of naturalistic driving. This paper introduces a new car-following modeling category called the empirical…

Stochastic (Markovian) process algebra extend classical process algebra with probabilistic exponentially distributed time durations denoted by rates (the parameter of the exponential distribution). Defining a semantics for such an algebra,…

We use Markov categories to generalize the basic theory of Markov chains and hidden Markov models to an abstract setting. This comprises characterizations of hidden Markov models in terms of conditional independences and algorithms for…

Many ion channels spontaneously switch between different levels of activity. Although this behaviour known as modal gating has been observed for a long time it is currently not well understood. Despite the fact that appropriately…

Time series and sequential data have gained significant attention recently since many real-world processes in various domains such as finance, education, biology, and engineering can be modeled as time series. Although many algorithms and…

We present a short introduction into the framework of piecewise deterministic Markov processes. We illustrate the abstract mathematical setting with a series of examples related to dispersal of biological systems, cell cycle models, gene…

Experiments, in particular on biological systems, typically probe lower-dimensional observables which are projections of high-dimensional dynamics. In order to infer consistent models capturing the relevant dynamics of the system, it is…

Mixture models are a fundamental tool in applied statistics and machine learning for treating data taken from multiple subpopulations. The current practice for estimating the parameters of such models relies on local search heuristics…

We develop a semi-parametric state-space model for time-series data with latent regime transitions. Classical Markov-switching models use fixed parametric transition functions, such as logistic or probit links, which restrict flexibility…

A very common way to estimate the parameters of a hidden Markov model (HMM) is the relatively straightforward computation of maximum likelihood (ML) estimates. For this task, most users rely on user-friendly implementation of the estimation…

These lecture notes present some new concentration inequalities for Feynman-Kac particle processes. We analyze different types of stochastic particle models, including particle profile occupation measures, genealogical tree based evolution…

Mixture models are probabilistic models aimed at uncovering and representing latent subgroups within a population. In the realm of network data analysis, the latent subgroups of nodes are typically identified by their connectivity…

In this paper, we develop methods of nonlinear filtering and prediction of an unobservable Markov chain with a finite set of states. This Markov chain controls coefficients of AR(p) model. Using observations generated by AR(p) model we have…

A rigorous and largely self-contained account of (a) the bread-and-butter concepts and techniques in Markov chain theory and (b) the long-term behaviour of chains. As much as possible, the treatment is probabilistic instead of analytical (I…

Traditional methods for unsupervised learning of finite mixture models require to evaluate the likelihood of all components of the mixture. This becomes computationally prohibitive when the number of components is large, as it is, for…

The impact of randomness on model training is poorly understood. How do differences in data order and initialization actually manifest in the model, such that some training runs outperform others or converge faster? Furthermore, how can we…

Predicting relative risk (RR) of spatial clusters is a complex task in public health that can be achieved through various statistical and machine-learning methods for different time intervals. However, high-resolution longitudinal data is…

It is well established that gene expression can be modeled as a Markovian stochastic process and hence proper observables might be subjected to large fluctuations and rare events. Since dynamics is often more than statics, one can work with…