Questions tagged [markov-chains]
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47
questions
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Vorticity Matrix for Markov chain
I have a markov chain with $Q(u,v)$ as transition probability matrix and $\pi(u)$ as stationary distribution defined on state space $\Omega$. The dimension of matrix $Q$ is $nxn$ and vector $\pi$ is $...
0
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1answer
46 views
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 this ...
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0answers
13 views
Logical inference as Markov decision process?
Are there efforts to consider forward or backward (theorem proving) logical inference process as Markov decision process in which the the action space is: 1) selection of the inference rule (e.g. from ...
1
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1answer
27 views
How to find optimal token set for compression?
By token I mean the smallest element of source data, that the compression algorithm works on. It may be a bit (like in DMC), a letter (like in Huffman or PPM), a word, or variable-length string (like ...
1
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1answer
23 views
Probabilisitc timed automaton
I am kind of new to timed automaton domain. I am trying to understand in which way they are different to Markov Decision Process. First I know there objectives is to solve the non-determinism of a MDP....
3
votes
1answer
37 views
Perturbing a Markov chain to be closer to a target stationary distribution
Suppose we are a given a Markov chain $A_0 \in \mathbb{R}^{n \times n}$ and a desired stationary probability vector $\pi_0 \in \mathbb{R}^n$. I would like to find a Markov chain that is as close as ...
0
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1answer
33 views
Sampling Multiple Times From a Markov Chain
In probability theory, the mixing time of a Markov chain is the time until the Markov chain is "close" to its steady state distribution. Lets fix some $\varepsilon\in (0,1]$ as our closeness parameter....
2
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0answers
36 views
Card Shuffling, Bounding Mixing time using Paths and Flows
I've been struggling with a problem that is very similar to a 2014 question posted here. The question in particular is 3(1) and 3(2).
To paraphrase, we are supposed to use paths and an encoding ...
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0answers
54 views
The relationship between MDP's end component and its induced MC recurrent class
Let's assume that I have an MDP $M$ which has a number of maximal end components. I also have a random policy (scheduler) $\pi$ that can convert the MDP $M$ into a Markov chain $m$. Can I argue that ...
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0answers
57 views
Game with Random Digits (Markov Chain / Coupling)
I've been self-studying Markov Chains and came across a problem online here: http://websites.math.leidenuniv.nl/probability/lecturenotes/CouplingLectures.pdf
I'm not asking for anything too formal (I'...
3
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1answer
519 views
How many possible policies in a Markov Decision Process?
If a policy yields an action for a state, how come a 3-state MDP with 2 possible actions, i.e. $S = \{Hot, Mild, Cold\}$, $A = \{East, West\}$, has 8 possible policies? Isn't it 6 if there are 2 ...
1
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1answer
272 views
Why in simulated annealing, thermal equilibrium need to be meet for each temperature throughout the iterations?
I have read in this book, simulated annealing, on page 40-41, if temperature $t$ tend to $0$, then the stationary distribution will be distributed among optimal solutions. What i can not understand ...
2
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3answers
421 views
Why do we need Gibbs sampling (and MCMC)?
I just learned about Gibbs Sampling which is an MCMC method. Given a distribution $\pi$, we want to sample an item according to $\pi$.
Maybe my alternative suggestion would sound somewhat naive (even ...
1
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0answers
106 views
Second-order Markov text generation?
Looking at this video starting at 1:45, the author claims to be using a second-order approximation for a Markov text generation. He has one letter which he outputs followed by another letter which ...
1
vote
1answer
51 views
Maximize entrywise 1-norm of matrix product
I have $8$ sets $E_1, \ldots, E_8$, each one of size $256$, whose elements are $4\times 4$ matrices of (nonnegative) integers. I'd like to design an algorithm to find:
$$\underset{M_1 \in E_1, \...
2
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0answers
76 views
Solving the following recurrence relation derived from a Markov chain
I have the following system of recursive relations on $y_{i,j}$ that are derived from a Markov chain and that I am having difficulty in solving. For $i\ge 1$ and $j \ge 1$, we have
$$y_{i,j} \times (...
1
vote
1answer
698 views
Absorbing Markov Chains: An efficient algorithmic approach
Following this procedure I have successfully written a program to calculate the probability of ending in a given absorbing state given the initial state. The procedure is as follows:
Given the ...
2
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0answers
60 views
Form of conditional observation probabilities in a POMDP
Consider a partially observable Markov decision process (POMDP), see here for a complete definition.
My question is in relation to the conditional observation probabilities (denoted by $O(o|s',a)$ in ...
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0answers
91 views
Calculate expected values of “Craps Game” with the help of Prism Model Checker
I have modelled the craps game (https://en.wikipedia.org/wiki/Craps#Rules_of_play) as a dtmc with the prism model checker:
...
0
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0answers
167 views
probability matrix from digraph adjacency matrix
All I have in hand is a adjacency matrix of a digraph with equal weight on every edge, is there a very simple way to convert this to a state change probability matrix?
2
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1answer
277 views
Convergence of Markov model
I was learning Hidden Markov model, and encountered this theory about convergence of Markov model.
For example, consider a weather model, where on a first-day probability of weather being sunny was 0....
2
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0answers
49 views
Calssifying the Partitions of the problem Cycle Decomposition of Markov Chains
The book Cycle Representations of Markov Processes
solves the problem of Mapping Stochastic Matrices induced from a Markov Chain into Partitions using a $\lambda$-preserving ($\lambda$ is a Lebesgue ...
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0answers
176 views
How the conditional random fields algorithm work? [closed]
Im searching about conditional random fields for a long time and cant understand the concepts of this algorithm.
I understood markov chains, and understood that conditional random field is a more ...
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0answers
165 views
What's the relationship of max-flow-min-cut and Markov Random Fields?
I am trying to follow this paper [1]. There is a relationship between Markov Random Fields (MRF) to max-flow-min-cut. An MRF can be represented as an undirected graph, and you can find flow through it,...
3
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2answers
414 views
The transition function in a Markov decision process
A Markov decision process is typically described as a tuple $\langle A,U,T,R \rangle $ where
$A$ is the state space
$U$ is the action space
$T: A \times U \times A \mapsto [0,\infty) $ is the state ...
2
votes
1answer
92 views
Orderability of Belief States in a POMDP?
Consider a POMDP with integer states $1,2,\ldots,N$, where $N$ is finite. We thus have a complete order over the states.
It seems reasonable to think that belief states for this POMDP may be ...
1
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1answer
416 views
Markov Chain Mixing Time of the Complete Graph
I'm having a hard time understanding mixing time for Markov Chains on Complete Graphs (Kn).
We can define the probability matrix for Kn where Pi,j=probability of going from i to j (technically 1/...
5
votes
1answer
102 views
Clarification of the definition of a POMDP
From what I understand, a $MDP=(G, A, P, R)$ (markov decision process) is represented as:
A complete directed graph $G=(V, E)$
A set of actions $A_u$ for each vertex $u \in V$
A reward function $R$ ...
2
votes
0answers
151 views
Cheeger constant of a graph versus conductance of a Markov chain
Given some graph $G$ with vertices $V$ and edges $E$, its Cheeger constant $h(G)$ is well defined as
$$ h(G) = \min_{S\subset V,0<|S|\leq|V|}\frac{|\partial S|}{|S|}. $$
Given some doubly-...
7
votes
0answers
243 views
Can the solution to a POMDP be found using linear programming?
It is known that Markov decision processes (MDPs) can be solved using linear programming (see page 24 of Carlos Guestrin's PhD dissertation). The linear program is:
$$min_{V(x)} \sum_x \alpha(x)V(x)\\...
3
votes
0answers
156 views
Multicommodity flows with minimum congestion: NP-hard?
I have a question related to a paper of Chen, Lovasz and Pak [1].
The paper concerns the construction of the Markov chain with optimal mixing time on an arbitrary graph.
They prove the optimal bound (...
1
vote
1answer
76 views
Simulating continuous time semi-Markov state machine and changing transition probability on the fly
The problem that I'm trying to solve (well, I think that I almost did, but need a review from someone more experienced) is about changing probability of the transition for semi-Markov state machine ...
2
votes
2answers
91 views
How to sample random game input that looks similar to human control?
What I would like to do is improve upon projects like 'RNG plays pokemon'. There, a computer produces a random sequence of inputs that are transmitted to an emulator and played in-game. Though this ...
2
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0answers
45 views
Calibrating a Markov Chain with little data
I am trying to calibrate a Markov Chain. Usually you would have the amount that "moves" from one state to the other and then the resulting value, with data at any given time with the following ...
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0answers
30 views
Mixing time of three particle systems
Is there anything known about mixing time of Markov chains for three particle systems?
It is proved here
http://www.ams.org/journals/tran/2005-357-08/S0002-9947-05-03610-X/S0002-9947-05-03610-X.pdf
...
4
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1answer
119 views
Average vs Worst-Case Hitting Time
Consider a simple random walk on an undirected graph and let $H_{ij}$ be the hitting time from $i$ to $j$. How much bigger can
$$ H_{\rm max} = \max_{i,j} H_{ij}, $$ be compared to
$$ H_{\rm ave} = \...
3
votes
1answer
110 views
Seemingly non sequitur in proof
I'm trying to understand a small proof in an article about computing lumpability on Markov chains. There is a small detail that I cannot understand, i.e. I don't think it follows from the argument.
...
2
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0answers
90 views
What is the meaning of the output weights of a Conditional Random Field (CRF) model?
Problem
When train my linear chain CRF with annotated observations, I feed it with a number of sequences containing observation values and a "ground-truth" label for each observation. I'm currently ...
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0answers
49 views
Graph Centrality: spectral techniques
What is the difference between:
normalizing the row of an adjacency matrix and taking the right eigenvector
normalizing the row of an adjacency matrix and taking the left eigenvector
normalizing the ...
9
votes
2answers
3k views
What are Markov chains?
I'm currently reading some papers about Markov chain lumping and I'm failing to see the difference between a Markov chain and a plain directed weighted graph.
For example in the article Optimal state-...
1
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1answer
288 views
Markov Chain w/ non-stochastic matrix
I've come across a problem which at first appeared to be a markov process however the transition matrix of the graph is non-stochastic. That is, the probabilities among edges leaving a node do not sum ...
7
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2answers
212 views
Why are HMMs appropriate for speech recognition when the problem doesn't seem to satisfy the Markov property
I'm learning about HMMs and their applications and trying to understand their usages. My knowledge is a bit spotty, so please correct any incorrect assumptions I'm making. The specific example I'm ...
0
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1answer
2k views
Algorithm for finding best combination of elements
Say I have a very large, arbitrary number of variables, each of which I can assign to be type A, B, or C.
The types come with expenses: Type A's are the least expensive, and C's are the most ...
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0answers
363 views
PageRank and EigenTrust: How small should epsilon be?
For probabilistic algorithms such as PageRank and EigenTrust, the stopping case is given as $|R_{t+1} - R_{t}| < \epsilon$ (i.e. convergence is assumed). Neither the papers on EigenTrust or ...
1
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1answer
428 views
How are Bayesian Nets, Hidden Markov Chains, Conditional Random Fields and Neural Nets related?
I am having an AI exam in two weeks, and I am still figuring out certain concepts and ideas, related to Bayesian Nets, Hidden Markov Chains, Conditional Random Fields and Neural Nets (yes it is all ...
3
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1answer
167 views
Improve Markov Chain results
Apologies for another Markov Chain question but this one is best given its own question to avoid confusion. I am using a Markov Chain to get the 10 best search results from the union of 3 different ...
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4answers
3k views
What are the uses of Markov Chains in CS? [closed]
We all know that Markov Chains can be used for generating real-looking text (or real-sounding music). I've also heard that Markov Chains has some applications in the image processing, is that true? ...
