Spectral radius of Markov averaging operator on graphs
The definition of Markov operator which I am familiar with: For a graph $ G=(V,E)$ , Markov’s operator upon a function $ \varphi:V\rightarrow\mathbb{C}$ , $ \varphi\in L^2(G,\nu)$ ($ \nu(v):=\deg(v)$...
View ArticleMarkov inequality: More precise bound?
Given a random variable X, we know that $ P[X\geq A] = 1$ . By Markov inequality, we obtain that $ E[X]\geq A$ . Or, in other words, $ E[X] = A + \lambda,\,\,\lambda\geq 0$ . Is there any way I can...
View ArticleStationary Distribution of a Markov Process defined on the space of permutations
Let $ S$ be the set of $ n!$ permutations of the first $ n$ integers. Let $ p\in(0,1)$ . Consider the Markov Process defined on the elements of $ S$ . Let $ x\in S$ . Choose two distinct integers $...
View ArticleBuild Vorticity Matrix for Markov chain
I have a markov chain with $ Q(u,v)$ as transition probability matrix and $ \pi(u)$ as stationary distribution. The dimension of matrix $ Q$ is $ nxn$ and vector $ \pi$ is $ 1xn$ . I need to build a...
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information theory, find entropy given Markov chain
There is an information source on the information source alphabet $ A = \{a, b, c\}$ represented by the state transition diagram below: a) The random variable representing the $ i$ -th output from...
View ArticleIn Markov Decision Processes, why does R0 get skipped?
I’m in the process of learning the MDP, and a pretty small thing is bugging me. Everywhere I look, I see the order of things go in this order: $ S_{0}, A_{0}, R_{1}, S_{1}, A_{1}, R_{2}, \ldots,...
View ArticleIs there any toolbox for Markov Random Field Structure Learning?
I need a toolbox or software that takes a dataset as input, detect independencies among its random variables and produces the relative Markov Random Field graphical structure from that. Can anyone...
View ArticleGeneralization of a Markov random field and a Bayesian network?
I am seeking a graphical model that is a generalization of both a Markov random field (MRF) and a Bayesian network (BN). From the Markov random field wiki page: A Markov network or MRF is similar to a...
View ArticleHidden Markov Models for Hand Gestures
I am completing a final year project for hand gesture recognition using Hidden Markov Models I have a fair understanding of Hidden Markov Models and how they work using simple examples such as the...
View ArticleHow to add the weights to the transition graph of a Markov chain?
The following working program uses Graph and Markov Chain P = {{1/2, 1/2, 0, 0}, {1/2, 1/2, 0, 0}, {1/4, 1/4, 1/4, 1/4}, {0, 0, 0, 1}}; proc = DiscreteMarkovProcess[3, P]; Graph[proc, GraphStyle ->...
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