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Several types of graphs with different conditional independence interpretations --- also known as Markov properties --- have been proposed and used in graphical models. In this paper we unify these Markov properties by introducing a class…

Statistics Theory · Mathematics 2017-07-12 Steffen Lauritzen , Kayvan Sadeghi

Conditional independence and Markov properties are powerful tools allowing expression of multidimensional probability distributions by means of low-dimensional ones. As multidimensional possibilistic models have been studied for several…

Artificial Intelligence · Computer Science 2013-01-18 Jirina Vejnarova

Shared information is a measure of mutual dependence among multiple jointly distributed random variables with finite alphabets. For a Markov chain on a tree with a given joint distribution, we give a new proof of an explicit…

Information Theory · Computer Science 2024-01-23 Sagnik Bhattacharya , Prakash Narayan

In this note we re-visit the fundamental question of the strong law of large numbers and central limit theorem for processes in continuous time with conditional stationary and independent increments. For convenience we refer to them as…

Probability · Mathematics 2026-02-05 Andreas E. Kyprianou , Victor Rivero

Continuous Markovian Logic (CML) is a multimodal logic that expresses quantitative and qualitative properties of continuous-time labelled Markov processes with arbitrary (analytic) state-spaces, henceforth called continuous Markov processes…

Logic in Computer Science · Computer Science 2015-07-01 Radu Mardare , Luca Cardelli , Kim G. Larsen

We consider iterated function systems (finite or countable), together with linear and continuous operators on Hilbert spaces, which enable us to construct Markov-type operators. Under suitable conditions, these Markov-type operators have…

Classical Analysis and ODEs · Mathematics 2017-01-30 Ion Chiţescu , Loredana Ioana , Radu Miculescu , Lucian Niţă

Model checking properties are often described by means of finite automata. Any particular such automaton divides the set of infinite trees into finitely many classes, according to which state has an infinite run. Building the full type…

Logic in Computer Science · Computer Science 2015-07-01 Klaus Aehlig

We show that the complexity of the Markov bases of multidimensional tables stabilizes eventually if a single table dimension is allowed to vary. In particular, if this table dimension is beyond a computable bound, the Markov bases consist…

Combinatorics · Mathematics 2008-04-18 Serkan Hosten , Seth Sullivant

We study the limiting object of a sequence of Markov chains analogous to the limits of graphs, hypergraphs, and other objects which have been studied. Following a suggestion of Aldous, we assign to a sequence of finite Markov chains with…

Logic · Mathematics 2015-03-13 Henry Towsner

We establish an equivalence-singularity dichotomy for a large class of one-dimensional Markov measures. Our approach is new in that we deal with one-sided and two-sided chains simultaneously, and in that we do not appeal to any 0-1 law. In…

Probability · Mathematics 2022-12-07 Nachi Avraham-Re'em

Recent work has proposed the use of a composite hypothesis Hoeffding test for statistical anomaly detection. Setting an appropriate threshold for the test given a desired false alarm probability involves approximating the false alarm…

Information Theory · Computer Science 2016-09-19 Jing Zhang , Ioannis Ch. Paschalidis

The present contribution derives an explicit expression for (a version of) every uni- and multi-variate conditional distribution (i.e., Markov kernel) of Archimedean copulas and uses this representation to generalize a recently established…

Statistics Theory · Mathematics 2022-11-07 Thimo Maria Kasper

Without prior knowledge, distinguishing different languages may be a hard task, especially when their borders are permeable. We develop an extension of spectral clustering -- a powerful unsupervised classification toolbox -- that is shown…

Computation and Language · Computer Science 2008-10-08 Richard Nock , Pascal Vaillant , Frank Nielsen , Claudia Henry

Many proofs in discrete mathematics and theoretical computer science are based on the probabilistic method. To prove the existence of a good object, we pick a random object and show that it is bad with low probability. This method is…

Information Theory · Computer Science 2017-08-01 Pat Morin , Wolfgang Mulzer , Tommy Reddad

In this paper we consider the statistics of repeated measurements on the output of a quantum Markov chain. We establish a large deviations result analogous to Sanov's theorem for the empirical measure associated to finite sequences of…

Quantum Physics · Physics 2015-06-22 Merlijn van Horssen , Madalin Guta

One open problem in source coding is to characterize the limits of representing losslessly a non-identity discrete function of the data encoded independently by the encoders of several correlated sources with memory. This paper investigates…

Information Theory · Computer Science 2013-06-26 Sheng Huang , Mikael Skoglund

The successive discrete structures generated by a sequential algorithm from random input constitute a Markov chain that may exhibit long term dependence on its first few input values. Using examples from random graph theory and search…

Probability · Mathematics 2023-06-22 Rudolf Grübel

The optimal causal coding of a partially observed Markov process is studied, where the cost to be minimized is a bounded, non-negative, additive, measurable single-letter function of the source and the receiver output. A structural result…

Information Theory · Computer Science 2012-08-24 Serdar Yüksel

This paper introduces an objective function that seeks to minimise the average total number of bits required to encode the joint state of all of the layers of a Markov source. This type of encoder may be applied to the problem of optimising…

Neural and Evolutionary Computing · Computer Science 2007-05-23 Stephen Luttrell

We present a unifying framework for type systems for process calculi. The core of the system provides an accurate correspondence between essentially functional processes and linear logic proofs; fragments of this system correspond to…

Logic in Computer Science · Computer Science 2015-05-29 Emmanuel Beffara