# Questions tagged [markov-chains]

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45 questions
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-...
2answers
209 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 ...
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2answers
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### 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 ...
1answer
34 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 ...
1answer
438 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 ...
1answer
107 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. ...
1answer
161 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 ...
0answers
150 views

### Multicommodity flows with minimum congestion: NP-hard?

I have a question related to a paper of Chen, Lovasz and Pak . The paper concerns the construction of the Markov chain with optimal mixing time on an arbitrary graph. They prove the optimal bound (...
3answers
397 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 ...
1answer
90 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 ...
2answers
90 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 ...
1answer
260 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....
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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73 views

1answer
617 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 ...
1answer
75 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 ...
1answer
277 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 ...
0answers
52 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'...
0answers
103 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 ...
0answers
52 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 ...
0answers
86 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: ...
0answers
166 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 ...
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 ...
0answers
362 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 ...
1answer
29 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....
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15 views

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### 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?
0answers
155 views

### What's the relationship of max-flow-min-cut and Markov Random Fields?

I am trying to follow this paper . 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,...
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 ...
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 ...