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Infinite random sequences of letters can be viewed as stochastic chains or as strings produced by a source, in the sense of information theory. The relationship between Variable Length Markov Chains (VLMC) and probabilistic dynamical…

Probability · Mathematics 2010-07-20 Peggy Cénac , Brigitte Chauvin , Frédéric Paccaut , Nicolas Pouyanne

Let $X_1,X_2,...$ be a sequence of random variables satisfying the distributional recursion $X_1=0$ and $X_n= X_{n-I_n}+1$ for $n=2,3,...$, where $I_n$ is a random variable with values in $\{1,...,n-1\}$ which is independent of…

Probability · Mathematics 2007-11-01 Alex Iksanov , Martin Möhle

We consider uniform random permutations in classes having a finite combinatorial specification for the substitution decomposition. These classes include (but are not limited to) all permutation classes with a finite number of simple…

Strong typicality and the Markov lemma have been used in the proofs of several multiterminal source coding theorems. Since these two tools can be applied to finite alphabets only, the results proved by them are subject to the same…

Information Theory · Computer Science 2010-06-03 Siu-Wai Ho

We consider Markov processes in continuous time with state space $\posint^N$ and provide two sufficient conditions and one necessary condition for the existence of moments $E(\|X(t)\|^r)$ of all orders $r \in \nat$ for all $t \geq 0$. The…

Probability · Mathematics 2015-02-02 Muruhan Rathinam

Redundancy is related to the amount of functionality that the structure can sustain in the worst-case scenario of structural degradation. This paper proposes a widely-applicable concept of redundancy optimization of finite-dimensional…

Optimization and Control · Mathematics 2017-08-22 Yoshihiro Kanno

Using a martingale concentration inequality, concentration bounds `from time $n_0$ on' are derived for stochastic approximation algorithms with contractive maps and both martingale difference and Markov noises. These are applied to…

Machine Learning · Computer Science 2022-06-14 Siddharth Chandak , Vivek S. Borkar , Parth Dodhia

Consideration is given to the three different analytical methods for the computation of upper bounds for the rate of convergence to the limiting regime of one specific class of (in)homogeneous continuous-time Markov chains. This class is…

We derive sublinear regret bounds for undiscounted reinforcement learning in continuous state space. The proposed algorithm combines state aggregation with the use of upper confidence bounds for implementing optimism in the face of…

Machine Learning · Computer Science 2013-02-12 Ronald Ortner , Daniil Ryabko

We present a new approach to convergence rate results for variational regularization. Avoiding Bregman distances and using image space approximation rates as source conditions we prove a nearly minimax theorem showing that the modulus of…

Numerical Analysis · Mathematics 2021-07-07 Philip Miller

This paper deals with unconstrained discounted continuous-time Markov decision processes in Borel state and action spaces. Under some conditions imposed on the primitives, allowing unbounded transition rates and unbounded (from both above…

Optimization and Control · Mathematics 2011-03-02 Alexey Piunovskiy , Yi Zhang

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

We study the Markov chain $x_{n+1}=ax_n+b_n$ on a finite field $\mathbb{F}_p$, where $a \in \mathbb{F}_p$ is fixed and $b_n$ are independent and identically distributed random variables in $\mathbb{F}_p$. Conditionally on the Riemann…

Probability · Mathematics 2022-08-25 Emmanuel Breuillard , Péter P. Varjú

The problem of joint universal source coding and identification is considered in the setting of fixed-rate lossy coding of continuous-alphabet memoryless sources. For a wide class of bounded distortion measures, it is shown that any…

Information Theory · Computer Science 2007-07-13 Maxim Raginsky

Association rules are among the most widely employed data analysis methods in the field of Data Mining. An association rule is a form of partial implication between two sets of binary variables. In the most common approach, association…

Logic in Computer Science · Computer Science 2019-03-14 Jose L. Balcazar

This paper characterizes the second-order coding rates for lossy source coding with side information available at both the encoder and the decoder. We first provide non-asymptotic bounds for this problem and then specialize the…

Information Theory · Computer Science 2014-10-13 Sy-Quoc Le , Vincent Y. F. Tan , Mehul Motani

Let $X=(X_t, t\geq 0)$ be a self-similar Markov process taking values in $\mathbb{R}$ such that the state 0 is a trap. In this paper, we present a necessary and sufficient condition for the existence of a self-similar recurrent extension of…

Probability · Mathematics 2019-06-10 Henry Pantí , Juan Carlos Pardo , Víctor Manuel Rivero

This article extends the concept of compressed sensing to signals that are not sparse in an orthonormal basis but rather in a redundant dictionary. It is shown that a matrix, which is a composition of a random matrix of certain type and a…

Probability · Mathematics 2010-11-10 Holger Rauhut , Karin Schnass , Pierre Vandergheynst

This paper presents prefix codes which minimize various criteria constructed as a convex combination of maximum codeword length and average codeword length or maximum redundancy and average redundancy, including a convex combination of the…

Information Theory · Computer Science 2011-02-11 Charalambos D. Charalambous , Themistoklis Charalambous , Farzad Rezaei

We consider a joint source-channel coding problem on a finite-field multiway relay channel, and we give closed-form lower and upper bounds on the optimal source-channel rate. These bounds are shown to be tight for all discrete memoryless…

Information Theory · Computer Science 2016-06-01 Lawrence Ong , Roy Timo