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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Conditional Independence, Bayes Network and d-separation

I have a diagram of a Bayes network as shown below: $$\begin{array}{c}A&&&&B&&&&C\\&\searrow&&\swarrow\\&&D&&&&E\\&&&\...
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Queueing multiple variables beyound Markov Blanket in Bayesian network

Afai understood, the variables beyound Markov Blanket does not influence on the node in Baesian Network. Howewer, if i give some compound query, where 2 or multiple variables are given, and those ...
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Bayesian Network calculations given dependence of variables

I've been given this bayesian network 1 where $P(A) = P(A = t) = 0.2, P(B) = 0.5, P(C) = 0.8.$ $$\require{enclose}\begin{array}{c}\enclose{circle}{~~A~~}&&&&\enclose{circle}{~~B~~}&...
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Bayes Net. How are the values P(G | D,I) calculated?

Example Bayes Net I have been looking into Bayesian Networks but I keep getting hung up on a simple dependence in most example problems which is how are the values in the conditional probability ...
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Influence of conditioning a node in an undirected graph on other nodes

Assume that I have a $D$-variate random variable $\mathbf{X}$, and a $D$-by-$D$ precision matrix denoting the strength of an undirected graph's edges between each of its $D$ univariate nodes (where ...
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Prior in variational autoencoders

I am currently dealing with variational autoencoders where I've read the original paper "An introduction to variational Bayes" from Kingma and Welling. I am currently still a little confused ...
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chain rule ordering

suppose I want to compute the joint probability $P(X,Y,Z)$ with chain rule. Is it true that there will be $3!$ possible factorization ? or is there more ? I got 6 for this example: $P(X|YZ)P(Y|Z)P(Z)$...
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Distributed Hypothesis Testing--reference question

If you don't know the correct keyword, you can still miss a key literature search: I have a problem in distributed Bayesian detection with a serial (or tandem) network topology. The probability ...
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Optimal proposal distribution for Bayesian networks

I was going through chapter 12 of Probabilistic Graphical models by Koller and Friedman. The chapter is on Particle-Based Approximate Inference On page 505, where unnormalised importance sampling is ...
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calculate probability using variable elimination

Consider the following Conditional probability for the Bayesian Network: By using variable elimination, how to calculate the following probability? I am summing all the terms related to $E$, then ...
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Expected Value of Determinant of Wishart Random Variable

In the paper, "Robust Bayesian Clustering" by Cedric Archambeau and Michel Verleysen, the authors have developed a variational Student-T mixture model that is unique because it assumes ...
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Algorithm for computing joint probability distribution from conditional probability table using tensor multiplication in Bayesian Network?

I get stuck on this problem. If in a Bayesian network, how can we do tensor multiplication on the conditional probability table so that it eventually gives the joint probability distribution? If a ...
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How to calculate an intersection in bayesian network

I was trying to solve this question, but i don't know how to proceed from there. And i am not sure how to compute $P(A|X_1,X_2,\neg X_3)$ or $P(A \cap X_1\cap X_2)$. It seems like i don't understand ...
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Bayes Rule combining two sensors

You are programming a demining robot. As the robot drives along, the prior probability of a mine being in its immediate vicinity is 0.001 The robot is equipped with a mine detecting sensor which ...
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Why does the conditional independent rule of INTERSECTION require STRICT POSITIVE DISTRIBUTION?

Recently, I was confused with the proofs of some conditional independent rules (decomposition, weak union, contraction, intersection), particularly the conditional independent rule of INTERSECTION. In ...
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Minimal Bayesian network for a given subset of variables?

Let $G=(V, E)$ be a DAG. Let $\mathrm{dom}$ be a domain for each node in $V$ and $P$ be a joint probabiliy distribution over those domains, that factors as a product of conditional probability ...
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Equivalence of two Bayesian Network Structures

Consider two Bayesian networks with binary random variables, whose directed acyclic graphs are shown in the following figure Define $p_G(A,B,C)$ and $q_{G'}(A,B,C,D,E)$ as the joint probability ...
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Does increasing the number of edges in a Bayesian network improve its perfomance?

Let's assume we have a bayesian net with N number of nodes and M number of edges. If we're somehow able to increase the number of edges while maintaining the same number of nodes will our bayesian net ...
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How do I get $P(A|C,!B)$ with the following probability distributions?

I have the following probability distributions table: I know that $P(B)=0.6$ and that: A may or may not have B Some A have C How do I get $P(A|C,!B)$? I built the following baysiean network: I ...
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How do I find the P(B | D = T) in this bayesina netowrk?

How to find P(B | D = T) in the following Bayesian network?
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Shortest path with jumps (dynamic Bayesian network)?

Suppose I have the following graph structure: It has the following properties: There are four states $\mathcal{S} = {q,s_1,s_2,s_3}$ where $q$ is some origin state where we start from (though it is ...
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How do I find gibbs sampling equations for finding circularly-symmetric Gaussian shaped objects

I have an image D that have some gaussian noise and circularly-symmetric Gaussian shaped object which is defined by $$f(\boldsymbol{x};\boldsymbol{a}) =Ae^{-\frac{((x-X)^2+(y-Y)^2)}{2R^2}}$$ where a={...
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Directed edges in Bayes net could have no effect?

After taking a risk analysis course, I am getting myself familiar with Bayes nets. Currently, I am looking at a common example of whether to take an umbrella on a walk. This is in the context of ...
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True Loss for Bayes Classifier with Two Classes

For a Bayes classifier of two classes (say 0 and 1), I'm not understanding how the largest possible true risk would be 0.5? I'm assuming that we assign a 0 loss for a correct classification and a loss ...
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conditional message passing for a graph

I have the graph below taken from this paper. They said that the conditional density of the latent continuous state sequence $x_{1:T}$ given all other variables, is proportional to $$\prod_{t=1}^{T}\...
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Property between probability spaces

$\textit{Q1:}$ Why the statement below holds? If someone could give the intuition and/or a proof I would appreciate it. (this one is answered already so check $Q2$) Suppose that $\mathcal{I}=(X,\mu)$ ...
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Continuous Parent Variable to a Categorical Child Variable

I am learning about Bayesian Networks for my computational methods for business analytics module. I have a query regarding my assignment: A probit distribution can be used to describe the probability ...
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What is the difference between random process and random field, in view of probabilistic graph model?

Under the normal definition, for a process $X(t,w)$ which $t$ is the time parameter and $w$ stands for samples in population, if $t$ is a single variable then we say $X(t,w)$ is a random process, or ...
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How do I calculate the diagnostic inference for Bayes Net with multiple evidence and hidden variable?

I have a Bayes Net for a tsunami alarm at nuclear power plants that looks like this: Top node is "Tsunami" = (T or F) is the ground truth of whether there is a Tsunami approaching. There is ...
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Computing value of noisy-MAX model

I am having trouble computing the remaining probabilities with the use of an interaction model called the noisy-MAX. The noisy-MAX model is an interaction model which helps a network engineer ...
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Change of Structure in Dynamic Bayesian Networks

I had started reading dynamic bayesian networks recently. I noticed that in general, the base structure remains the same for every time period. I was wondering if it is possible to have different ...
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Peripheralization of Conditional Distributions of head to tail model

If we peripheralize the concurrent probability of the head to tail graphical model for c, we get the following equation. $p(a,b) = p(a)Σ_{c}p(a|c)p(c|b) = p(a)p(b|a)$ The question is, does the ...
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Variable elimination, Bayesian network

I'm self learning the topic variable elimination and try to solve some questions see if I fully understand the concept. But I'm stuck on this problem's second question for hours. Base on my ...
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Multiplication of conditional probability

I was looking up on Bayesian networks and came across this video. In which it states: And I was wondering, how did he get $P(B|A)*P(C|B) = P(B,C|A)$?
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3 votes
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What is the relationship between Probabilistic Graphical Models and Graph Neural Networks?

I would like to learn more about one or both of these. I incline towards Bayesian networks and PGMs but since Battaglia et al, 2018 I have had half an eye on the various kinds of GNN. You seem to be ...
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what is variational over-pruning

I come across this term "variational over-pruning", as I was reading about variational inference. But I didn't understand it, and I couldn't find a proper simplified answer. Can anyone ...
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Prove that non-descendants of C are conditionally independent given C's parents

I'm trying to understand conditional independence and want to show for the following bayesian network: $$p(A,B,C,D,E) = p(A)p(B)(C|A)p(D|B)p(E|D,C)$$ that $C$ is conditionally independent of $B$ or $C$...
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-2 votes
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Conditional probabilities in a Bayesian Network [closed]

The Bayesian Network LMV has three nodes for boolean variables, L, M and V. Bayesian Network LMV$$\require{enclose}\enclose{circle}{L}\lower{2ex}{\searrow\lower{2ex}{\enclose{circle}{V}}\swarrow}\...
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Simple Bayes Net Calculation

I'm reading a paper and I'm trying to understand the Bayes net example they give. Here's the Bayes network in question: Here's the simple calculation they perform using the net above: How do they ...
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calculating conditional probability for bayesian network

My network $$W\lower{2ex}{\searrow\lower{2ex} S\swarrow }U\lower{6ex}{\hspace{-5ex}\searrow\lower{2ex}{Z}\swarrow\raise{2ex}{A\raise{2ex}{\swarrow\raise{2ex}T}}}$$ Here are known probabilities $P(W) = ...
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How can I compute probability P(E|D) from Bayes Net

How can I compute probability P(E|D) from Bayes Net Please refer to the image
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1 vote
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Proving Conditional Independence in a Bayesian Network

$$\require{enclose}\begin{array}{c}\enclose{circle}{X_2}&&&&\enclose{circle}{X_1}\\&\searrow&&&&\searrow\\&&\enclose{circle}{X_3}&&&&\...
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1 vote
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Bayesian network calculations

I'm new to probability theory and Bayesian networks so I really don't understand how to calculate some probabilities based on this network: $$\require{enclose}\boxed{\begin{array}{c|cc}X\backslash Y&...
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4 votes
1 answer
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What is the analogy to logic when denoting independence of random variables as $p\models X\perp Y$?

I'm reading Nir Friedman and Daphne Koller's "Probabilistic Graphical Models: Principles and Techniques". The authors occasionally use the notation $$p\models X\perp Y \mid Z$$ to indicate ...
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Calculating Probabilities in Bayesian Network

The Bayesian network below contains only binary states. The conditional probability for each state is listed. From the Bayesian network, calculate the following probabilities: a) $P(b)$ b) $P(d)$ c)...
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Determining Independence in Bayesian Network

Consider the Bayesian Network Structure Below, decide whether the statements are true or false. b) $G \perp \!\!\! \perp A$ (G is independent of A) c) $E \perp \!\!\! \perp H | \{D,G\}$ (E and H are ...
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$P(A_0 | A_n)$ in a Bayesian network where $A_n → ... → A_0$

I asked a question here about C given A in a Bayesian network where $A→B→C$. According to this answer, $$P(C=1∣A=1)=P(C=1∩B=1∣A=1)+P(C=1∩B=0∣A=1)$$ if A, B, C have a Bernouilli distribution. So in the ...
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C given A in a Bayesian network where $A\to B\to C$?

Let's say I have a Bayesian network with A-->B-->C where A,B,C have a Bernouilli distribution How do I calculate $P(C=1|A=1)$? Is it $P(C=1|B=1∩A=1) + (C=1|...
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2 votes
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Using Bayesian Networks to solve this localization problem?

I'm reading this paper, which I'll summarize here: Let a sensor network (in this case, a network of radio receivers) consist of $N$ sensor nodes at locations $S = \{ S_1 \cdots S_N\}$. Let $S_i^x$ ...
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Is my Bayes belief network theory correct?

I am currently trying to learn Bayes' theorem, and in turn, Bayesian belief networks. I haven't done any 'real' maths in nearly 20 years, so I am rusty to say the least. I am trying to determine the ...
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