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Questions tagged [bayesian-network]

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Is retrospective inference NP-hard?

Here is a minimal working example of the question: Consider a network with nodes arranged in a pyramid: $1$ node in the first row, $1+d$ nodes in the second, $1+2d$ nodes in the third, and so on, ...
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Is a “stacked”, “local” version of 3-SAT NP-hard?

In this previous question, I learned that if each variable in a string $C \in 3\text{-SAT}$ appears only "locally", then finding a satisfying assignment is no longer NP-hard. My question below builds ...
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Time complexity of a problem in probabilistic inference on a Bayesian network

Suppose we have a simple Bayesian network with two rows of nodes: $x_1, x_2, \ldots, x_n$ and $y_1, y_2, \ldots, y_n$. Each node $x_k$ takes a state of either 0 or 1 with equal probability. Each ...
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How do we prove the time complexity of this simple problem in probabilistic inference on a Bayesian network?

Suppose we have a simple Bayesian network with two rows of nodes: $x_1, x_2, \ldots, x_n$ and $y_1, y_2, \ldots, y_n$. Each node $x_k$ takes a state of either 0 or 1 with equal probability. Each ...
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How to learn Bayesian Network's parameters using KL divergence and stochastic optimization?

I have a problem to resolve: A Bayesian Network structure is given to me, with a dataset of values for each variable. I also have a set of queries, like P(A=1 | B=0) or P(L=0, B=1 | C=1). The goal ...
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Conditional probability in Bayesian network

I have the following Bayesian network: I want to state that P(S|B) = 1 - P(!S|B) In the solution they use "P(S|B) = P(S|B,F) + P(S|B,!F)", which I understand but I don't understand why can't I use ...
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Transforming undirected maximum spanning tree into directed augmented network

I am having trouble transforming a maximum weighted spanning tree into a directed tree such that each node is allowed at most one parent node. Taken from page 141 Friedman et. al (1997), the outline ...
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Does no parents imply variable independence in a Bayesian network?

If A and B don't have parents on a Bayesian network, does that mean we can infer A and B are independent? Whatever the answer is, please explain how you get to it.
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DAGs and Equivalence Class of DAGs

I am learning DAGs and Equivalence Class of DAGs, I am reading the material by Prof. Campos Ibáñez here: https://www.cs.cmu.edu/afs/cs/project/jair/pub/volume18/acid03a-html/node2.html However, I ...
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Examples of difference between Hidden Markov Model and Bayesian Network?

I am trying to more deeply understand the difference between Hidden Markov Models and Bayesian Network? The general idea is that HMMs have a single variable which has probabilities of entering ...