# Questions tagged [bayesian-network]

For questions related to Bayesian networks, the generic example of a directed probabilistic graphical model. Includes dynamic Bayesian networks, e.g. Hidden Markov Models (HMMs) and Kalman Filters. For applications of Bayesian networks in any field, e.g. machine learning. NOT for general questions about Bayes' theorem, Bayesian statistics, conditional probabilities, networks, or graph theory.

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### When does maximum of the Bethe energy function corresponds to true marginals?

I have a question and I would be quite grateful if you could answer. It is known that Belief propagation converges to stationary points of Bethe energy function. Is it known that the maximum of the ...
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### Deriving hyperparameter updates in Online Interactive Collaborative Filtering

I've been going through "Online Interactive Collaborative Filtering Using Multi-Armed Bandit with Dependent Arms" by Wang et al. and am unable to understand how the update equations for the ...
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### Bayesian Network Enumeration

I want to calculate P(L) for the given Bayesian Network. The solution that I am presented with by the lecturer is 0.170 My calculation path is as following. Since we know that in a Bayesian network ...
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### Unintuitive result while working with a temporal Bayesian Network

I am working on a temporal Bayesian Network toy problem using BayesFusion GeNIe Software. I have a node (Case_24 in the figure) that models the state (0 or 1) of a time-dependent variable. At every ...
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### Algebraic proof of conditional independence in a Bayesian network

I have a Bayesian network shown as $a \to b \to c \leftarrow d \leftarrow e$. I want to prove $a \perp e$. It's easy to show $b \perp d$ since $$P(b,c,d)=P(c|b,d)P(b)P(d)=P(c|b,d)P(b|d)P(d).$$ So ...
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### Understanding normalization in Bayes net

I can't seem to wrap my mind around the concept of normalization. I am hoping these examples will clarify my understanding. If I have a variable A (which has 3 values eg something like A = Sunny, ...
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### How to solve Bayes' probabilistic network problem?

Given the following Bayesian Probabilistic Network, let's say I am trying to find the probability of P(!FO|HB). I understand basic Bayes theorem, but not sure how to use it here.
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### Graphoid axioms properties doesn't make sense to me.

I am studying some concepts about d-separation through the book , however, I am not understanding the intuition behind the axiomatization of graphoids. If anyone can help me with a little ...
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### How to calculate the probability of L from this Bayesian Network

This is a follow up to a previous question posted. I am now working on calculating P(~B|~F). The Bayesian Network: So far, I have: ...
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### Bayesian network probability truth table

I am working on a bayesian network problem and have been given the following table of data: ...
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### Probability and Bayesian Networks: Set of nodes reachable from X via trails active in G, given Z

I am self studying the book Probabilistic Graphical Models. In a question I am asked to prove: The algorithm Reachable(G, X,Z) returns the set of all nodes ...
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### Calculating Joint Probability Distribution from Bayesian Network

Apologies in advance if this is considered an easy topic. I am absolutely mired and feel so defeated. I am working with the following Bayesian Network: I am being asked to compute the following: <...
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### inference by enumeration on Bayes graph

a graph with known conditional prob between nodes, i.e. P(P2 | P1), P(P2 | ¬P1) are all known: ...
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### conditional independence on Bayes graph

I am confusing on conditional independence on Bayes graph. a graph: P6 ↓ P1 → P3 → P4 → P5 ↓ P7 Please kindly let me know if ...
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### D-Separation in a Bayesian Network

I am working with the graph below: I know the three cases of d-separation are below (taken from here): I need to find ALL pairs of nodes separated by {A} and <...
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### What really the message means in the Belief propagation

I am trying to understand the Belief propagation, and I have question about the message: the message is: $m_{ij}(x_j)$ to reresent the message from node i to node j Does $x_j$ mean the attribute ...
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### Got stuck at trying to figure out what the single shot at inference for Variational Autoencoder should be

Let's say you have an already trained Variational Autoencoder where the parameters are $\phi, \theta$ for the recognition and generative models respectively. Let's also assume you have the following ...
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### Probabilities in simplified Bayesian (?) network

I have the following simple network (sorry for the link, I cannot insert pictures yet) with nodes and conditional probabilities attached to the edges, and I am looking for an algorithm to efficiently ...
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### How to prove d-separation implies conditional independence?

All of the materials I see online just state it as fact. I don't see it as obvious at all. I use this definition of a Belief network. And this is the definition of d-seperation from the textbook:
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### In probability, what “prior knowledge” means??

So i have this equation, that is a Bayesian Score Metric: In this context, what "prior knowledge" means?
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### Help with Cooper and Herskovits (1992) Bayesian Score Metric

Im studying the Chickering (1996) "Learning Bayesian Networks is NP-Complete", available in this link: http://maxchickering.com/publications/lns96.pdf And i have some questions about the following ...