Related papers: Using Markov Models and Statistics to Learn, Extra…

This paper investigates optimal portfolio strategies in a market where the drift is driven by an unobserved Markov chain. Information on the state of this chain is obtained from stock prices and expert opinions in the form of signals at…

We describe a simple method that can be used to sample the rare fluctuations of discrete-time Markov chains. We focus on the case of Markov chains with well-defined steady-state measures, and derive expressions for the large-deviation rate…

This chapter presents an introduction to Markovian modeling for the analysis of sequence data. Contrary to the deterministic approach seen in the previous sequence analysis chapters, Markovian models are probabilistic models, focusing on…

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…

Data-driven, model-free analytics are natural choices for discovery and forecasting of complex, nonlinear systems. Methods that operate in the system state-space require either an explicit multidimensional state-space, or, one approximated…

Forecasting tasks using large datasets gathering thousands of heterogeneous time series is a crucial statistical problem in numerous sectors. The main challenge is to model a rich variety of time series, leverage any available external…

To understand the long-run behavior of Markov population models, the computation of the stationary distribution is often a crucial part. We propose a truncation-based approximation that employs a state-space lumping scheme, aggregating…

We study classical stochastic systems with discrete states, coupled to switching external environments. For fast environmental processes we derive reduced dynamics for the system itself, focusing on corrections to the adiabatic limit of…

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…

Given a data set of numerical values which are sampled from some unknown probability distribution, we will show how to check if the data set exhibits the Markov property and we will show how to use the Markov property to predict future…

This article presents several results establishing connections be- tween Markov chains and dynamical systems, from the point of view of open systems in physics. We show how all Markov chains can be understood as the information on one…

Complex and nonlinear dynamical systems often involve parameters that change with time, accurate tracking of which is essential to tasks such as state estimation, prediction, and control. Existing machine-learning methods require full state…

The slow processes of metastable stochastic dynamical systems are difficult to access by direct numerical simulation due the sampling problem. Here, we suggest an approach for modeling the slow parts of Markov processes by approximating the…

We propose a computational method for large deviation statistics of time-averaged quantities in general Markov processes. In our proposed method, we repeat a response measurement against external forces, where the forces are determined by…

Skewed parton distributions contain new non-perturbative information about hadronic states. Thus, their extraction from experimental data is an important goal. Properties and models for skewed parton distributions as well as their…

When dealing with datasets containing a billion instances or with simulations that require a supercomputer to execute, computational resources become part of the equation. We can improve the efficiency of learning and inference by…

The past decade has seen a revived interest in the unavoidable or intrinsic noise in biochemical and genetic networks arising from the finite copy number of the participating species. That is, rather than modeling regulatory networks in…

In this paper, we propose a class of efficient, accurate, and general methods for solving state-estimation problems with equality and inequality constraints. The methods are based on recent developments in variable splitting and partially…

This paper describes a data reduction technique in case of a markov chain of specified order. Instead of observing all the transitions in a markov chain we record only a few of them and treat the remaining part as missing. The decision…

Invariant measures encode the long-time behaviour of a dynamical system. In this work, we propose an optimization-based method to discover invariant measures directly from data gathered from a system. Our method does not require an explicit…