# Questions tagged [bayesian-network]

A Bayesian network is a probabilistic directed acyclic graph. Nodes represent random variables in the Bayesian sense (observable or unobservable); edges represent conditional dependencies between nodes.

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### Why a undirected graph is Markov equivalent to a directed graph iff it is decomposable?

Claim 1. A undirected graph is Markov equivalent to a directed graph iff the undirected graph is decomposable. I am trying to prove Claim 1 and to find a relationship between decomposable and v-...
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### Bayesian Networks vs traditional stats approaches to Causal Inference? [duplicate]

I've been reading the 'book of why' by Judea Pearl and come to understand that Bayesian Networks can be used to establish causality given a directed acyclic graph (DAG) and that the methods are non-...
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### Node that depends on the particular values of it's parents in a Bayesian network?

Consider a Bayesian network containing a binary variable C which denotes whether a certain person has a child or not. There is a second variable B which denotes the birthdate of the person's youngest ...
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### Proof that the Markov Blanket in a Bayesian Network is parents, children, and children's parents

I'm looking for a proof of this fact from wikipedia: The Markov boundary of a node $A$ in a Bayesian network is the set of nodes composed of $A$'s parents, $A$'s children, and $A$'s children's other ...
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### Discrete Bayes Net learning under parameter constraints

What is some relevant research available on estimating the parameters of a Bayes Net (with known structure) when there are known constraints on conditional and marginal probabilities? For example, ...
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### Bayesian hierarchical model inference problem image segmentation

it might be really confusing question. I am working on my thesis and I am stuck at a problem. It's a problem in image segmentation and finding parameters of border lines of continuous region in an ...
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### Calculating conditional probability on bayesian network

In one of my lectures the Bayesian Network below sprung up and I am puzzled because there's no explanation on how did we calculate the denominator of first and second fractions. I already know how to ...
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### mutual information and edge weights in a bayesian network

The mutual information between two random variables X and Y can be stated formally as follows: I(X ; Y) = H(X) – H(X | Y) Where I(X ; Y) is the mutual information for X and Y, H(X) is the entropy for ...
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### When and why converting a Bayesian network into a Markov Random Field?

I found many slides and tutorials (e.g., [1,2]) on the probabilistic graphical model introducing the procedure of "converting a Bayesian network (BN) into a Markov random field (MRF) by ...
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### Neural network regression not learning due to non-uniform data distribution?

I am working on a non-linear multi-output regression problem. I have created a simple neural network. The net is supposed to be a point estimator of $\hat{\theta}_{MAP}$, where $\theta$ are the ...
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### How to calculate $P(A|B,C)$ from Bayesian Network?

Say I have a bayesian network B <- A -> C. I need to calculate $P(A|B,C)$. How can I do that? I tried doing: $P(A|B,C)=\frac{P(A,B,C)}{P(B,C)}$ I also tried various other combinations of ...
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### Specifying conditional distribution in a Bayesian network

I am trying to learn about Bayesian networks and am really having a hard time to figure out how to setup some simple models. Say, I have a model as: ...
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### Can we ignore graphs for inference in linear/Gaussian settings?

Assume I have a linear Bayesian network/graph like the following: where i can derive a joint pdf $$p(\mathbf{x})=p(x_1,x_2,x_3,x_4,x_5)=p(x_1)p(x_2|x_1)p(x_3|x_2)p(x_4|x_3)p(x_5|x_4)$$ Assuming that ...
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### How to orient the undirected edges in the CPDAGs learned by some Bayesian Network structure learning algorithms?

Some Bayesian Network (BN) structure learning algorithms (such as the PC algorithm) learns a CPDAG as the output, which contains both directed and undirected edges. One common evaluation metric for BN ...
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### Bayesian Network: tools for simulation to create a sample set from reference Bayesian Networks?

There are some commonly used reference Bayesian networks, which can be found in the Bayesian Network Repository, and I want to simulate a data set from such a reference graph. Are there any tools that ...
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### Laplace distribution as an Exponential Distribution and Minimizitaion of KL Divergence

In the context of Expectation Propagation [Minka's thesis-2001], I would like to approximate an unknown distribution with a Laplace distribution. This can be solved by minimizing KL-Divergence. In ...
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### the variational family used to approximate the weight posterior of a BNN

Why the variational family used to approximate the weight posterior of a BNN is often chosen to be Gaussian?
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### Why Assumed Density Filtering is also called Moment Matching?

I am learning about Assumed Density Filtering (ADF) and Expectation Propagation in the context of bayesian deep neural networks. I have seen in some textbooks and papers that ADF is also called moment ...
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### Moment Matching for a Laplace Distribution

I have this derivative It belongs to this paper. In the paper, they are trying to model a lightweight bayesian deep neural network by having the distributions on only the activation functions. They ...
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### What are Large Scale and Complicated Priors?

We use priors in Bayesian networks to include prior knowledge in our models. In this context, what are these two terms: -complicated prior -large scale prior I have seen priors like Laplace, zero-mean ...
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### How to eliminate graph cycles?

I checked Why do Bayesian Networks use acyclicity assumption and read two books on Bayesian probability but I haven't found why DAGs (Direct Acyclic Graphs) are must and what would possible be wrong ...
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### How to design a filter to remove the influence of factors on the values of a measurement

Is anybody aware of methods that are appropriate to modify the values of a time series to account for factors that are known to artificially inflate or deflate the measurement. An example of the ...
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### What is the difference between Bayesian Regression and Bayesian Networks

I had actually posted an earlier question about the applications of Bayesian networks, and I received a very good response. I understand that Bayesian networks are usually used to answer probability ...
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### Why using point estimates instead of integrating out the unknown?

I was just wondering why you often use point estimators like MAP and MLE when you have to calculate the posterior distribution for them anyway? Is it because you don't have to calculate the evidence ...