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Given an infinitesimal perturbation of a discrete-time finite Markov chain, we seek the states that are stable despite the perturbation, \textit{i.e.} the states whose weights in the stationary distributions can be bounded away from $0$ as…

Discrete Mathematics · Computer Science 2016-02-15 Volker Betz , Stephane Le Roux

Clustering algorithms frequently require the number of clusters to be chosen in advance, but it is usually not clear how to do this. To tackle this challenge when clustering within sequential data, we present a method for estimating the…

Machine Learning · Statistics 2024-07-29 Thomas van Vuren , Thomas Cronk , Jaron Sanders

We exhibit an efficient procedure for testing, based on a single long state sequence, whether an unknown Markov chain is identical to or $\varepsilon$-far from a given reference chain. We obtain nearly matching (up to logarithmic factors)…

Machine Learning · Statistics 2019-09-26 Geoffrey Wolfer , Aryeh Kontorovich

We study the problem of learning the Markov order in categorical sequences that represent paths in a network, i.e. sequences of variable lengths where transitions between states are constrained to a known graph. Such data pose challenges…

Machine Learning · Computer Science 2020-07-07 Luka V. Petrović , Ingo Scholtes

We present a novel approach to detecting and utilizing symmetries in probabilistic graphical models with two main contributions. First, we present a scalable approach to computing generating sets of permutation groups representing the…

Artificial Intelligence · Computer Science 2014-08-12 Mathias Niepert

We present a novel approach to detecting and utilizing symmetries in probabilistic graphical models with two main contributions. First, we present a scalable approach to computing generating sets of permutation groups representing the…

Artificial Intelligence · Computer Science 2012-06-29 Mathias Niepert

We consider continuous-space, discrete-time Markov chains on $\mathbb{R}^d$, that admit a finite number $N$ of metastable states. Our main motivation for investigating these processes is to analyse random Poincar\'e maps, which describe…

Probability · Mathematics 2025-08-19 Nils Berglund

Exponential stability of the nonlinear filtering equation is revisited, when the signal is a finite state Markov chain. An asymptotic upper bound for the filtering error due to incorrect initial condition is derived in the case of slowly…

Probability · Mathematics 2007-05-23 P. Chigansky

In this paper we study possibilities of using hierarchical reasoning, symbol elimination and model generation for the verification of parametric systems, where the parameters can be constants or functions. Our goal is to automatically…

Logic in Computer Science · Computer Science 2019-10-14 Viorica Sofronie-Stokkermans

We introduce the problem of formally verifying properties of Markov processes where the parameters are given by the output of machine learning models. For a broad class of machine learning models, including linear models, tree-based models,…

Machine Learning · Computer Science 2025-05-13 Muhammad Maaz , Timothy C. Y. Chan

We study and provide efficient algorithms for multi-objective model checking problems for Markov Decision Processes (MDPs). Given an MDP, M, and given multiple linear-time (\omega -regular or LTL) properties \varphi\_i, and probabilities…

Logic in Computer Science · Computer Science 2015-07-01 Kousha Etessami , Marta Kwiatkowska , Moshe Y. Vardi , Mihalis Yannakakis

We study the problem of sequentially testing whether a given stochastic process is generated by a known Markov chain. Formally, given access to a stream of random variables, we want to quickly determine whether this sequence is a trajectory…

Applications · Statistics 2025-01-24 Greg Fields , Tara Javidi , Shubhanshu Shekhar

Recently, Brand, Ganian and Simonov introduced a parameterized refinement of the classical PAC-learning sample complexity framework. A crucial outcome of their investigation is that for a very wide range of learning problems, there is a…

Data Structures and Algorithms · Computer Science 2023-08-23 Robert Ganian , Liana Khazaliya , Kirill Simonov

In statistical modeling of computer experiments sometimes prior information is available about the underlying function. For example, the physical system simulated by the computer code may be known to be monotone with respect to some or all…

Methodology · Statistics 2014-06-17 Shirin Golchi , Derek R. Bingham , Hugh Chipman , David A. Campbell

We consider the problem of approximating the reachability probabilities in Markov decision processes (MDP) with uncountable (continuous) state and action spaces. While there are algorithms that, for special classes of such MDP, provide a…

Systems and Control · Electrical Eng. & Systems 2022-07-13 Kush Grover , Jan Křetínský , Tobias Meggendorfer , Maximilian Weininger

An algorithm for estimating quasi-stationary distribution of finite state space Markov chains has been proven in a previous paper. Now this paper proves a similar algorithm that works for general state space Markov chains under very general…

Probability · Mathematics 2015-03-04 Jose H. Blanchet , Peter Glynn , Shuheng Zheng

We describe an exact test of the null hypothesis that a Markov chain is nth order versus the alternate hypothesis that it is $(n+1)$-th order. The procedure does not rely on asymptotic properties, but instead builds up the test statistic…

Data Analysis, Statistics and Probability · Physics 2013-02-07 Shawn D. Pethel , Daniel W. Hahs

A labelled Markov decision process is a labelled Markov chain with nondeterminism, i.e., together with a strategy a labelled MDP induces a labelled Markov chain. The model is related to interval Markov chains. Motivated by applications of…

Formal Languages and Automata Theory · Computer Science 2020-09-25 Stefan Kiefer , Qiyi Tang

A statistical test is presented to decide whether data are adequately described by probabilistic functions of finite state Markov chains (''hidden Markov models'') as applied in the analysis of ion channel data. Particularly, the test can…

chao-dyn · Physics 2009-10-30 J. Timmer , S. Klein

Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer $k$-th order Markov chains, for arbitrary $k$, from finite data by applying Bayesian methods to both…

Statistics Theory · Mathematics 2009-11-13 Christopher C. Strelioff , James P. Crutchfield , Alfred W. Hubler