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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Bayes network, what is the purpose of it?

I really don't understand what is the purpose of the Bayes network, actually how to implement it into a useful application. It all starts with the data. Let's assume I observe some universe and I ...
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Why does conditioning on a mediator variable makes the ancestor and the child independent?

The example and question are from the book Book of Why by Judea Pearl. Suppose we have three random variables: $A \rightarrow B \rightarrow C$. $B$ is a mediator. Conditioning on $B$ would screen-...
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What is the link between the queries Bayesian Networks can answer, and inference algorithms?

I have seen two concepts linked to Bayesian Networks: Bayesian Networks can answer different types of queries. These types include proof of evidence, most probable explanation, computing maximum a ...
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Inference on Author model

The Author Model is an LDA based model that first time introduced in paper [The Author-Topic Model for Authors and Documents]. I have studied the inference of the LDA model and know how to obtain the ...
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parameter estimation on the LDA model

I have a problem with estimating the parameters of $\theta$, and $\phi$ in the Latent Dirichlet Allocation (LDA) model. The article Finding scientific topics has done the estimation of the parameters ...
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Causality: Models, Reasoning and Inference, by Judea Pearl: Causal Bayesian Networks and the Truncated Factorization

Background: $\newcommand{\doop}{\operatorname{do}}$ Definition 1.2.2 (Markov Compatibility) If a probability function $P$ admits the factorization of $$P(x_1,\dots,x_n)=\prod_i P(x_i|\operatorname{...
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How to choose the order of variable elimination in Bayes Network

I have the following Bayes net with me. I want to find P(+h|+e). So I have to find A = P(+h,+e) and B = P(+e) to find P(+h|+e). I wanted to follow variable elimination for find the probability. ...
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Bayesian Estimation, What is Equivalent Sample Size or Imaginary Sample Size?

I am trying to understand the formula given in the book Bayesian Networks, With Examples in R, by Marco Scutari & Jean-Baptiste Denis. The formula estimates the parameters of a categorical ...
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Does the P(D | +a) in the context of bayesian network mean that we have to compute both P(+d |+a) and P(-d|+a)?

I've been asked to calculate P(D|+a) using inference by enumeration. My attempt resulted in : $P(D|+a) \:\propto{D}\:P(D,+a)\\ =\sum_{b,c} P(D,+a,b,c)\\ =\sum_{b,c} P(D|c) P(c|+a,b) P(+a)P(b|+a)\\ =...
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How to obtain marginal distribution from joint statistics of a multivariable sensor network

My question is related to calculating marginal distribution from a multivariate joint distribution. Suppose we have one source "x" and multiple receivers denoted as y1,y2,y3. Suppose we are given p(x,...
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How to calculate $P(A, B | C)$ from Bayesian Network?

I have this bayesian network: A -> B -> C I need to calculate $P(A, B|C)$. How can I do that? I tried doing: $P(A,B | C) = P(A|B,C)P(B|C)$ But I don't ...
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Bayesian Networks Node Definition

The educational content online for Bayesian Networks is not the best. (It's a subtle topic which leads to subtle questions and I'm having a hard time understanding it.) It is my understanding that ...
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Estimating conditional probabilities on a large corpus of parsed documents

Scope I have a large corpus of (parsed) documents where each has multiple terms and few associated codes. My objective is to estimate the conditional probability $P(code | terms)$. First attempt ...
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Dataset + NN architecture that demonstrate regularization superiority

I'm working on a course on Bayesian Machine Learning and want to show an example that demonstrates the superiority of the NN training with regularization over the NN training without it. In ...
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If A and B are independent, can P(C | A, B) be expressed only in terms of P(A), P(B), P(C | A), and P(C | B)?

Conditional probability question. Let's say I have... three random variables: A, B, C <...
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How to learn dependency of variables from data?

I have a data set $X$ that consist of $m$ vectors $\vec{x}$ of $n$ real valued components. Each vector component lies within a corresponding predefined interval of valid values, which is the same for ...
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Does bayesian neural network good for text/document classification?

I've tried to do my research online, but I find most of them are image classification. I guess that is because nature(downside) of Bayesian DL: it's significantly slower than traditional DL, then few ...
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R - how to use `structural.em()` (from package `bnlearn`) to implement hidden variable learning in simple Bayesian network

I want to use the function structural.em() to infer a hidden variable. As an example, consider the following code. ...
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Strict positivity of densities for additive noise models (Problem 7.14, Elements of Causal Inference)

I'm working through Problem 7.14 of Elements of Causal Inference, and wanted to see if the problem statement held more generally than described. $$ \newcommand\vx{\textbf{x}} \newcommand\vp{\textbf{p}}...
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Can latent variables be used in Bayesian networks?

I have successfully implemented a hill climbing approach to Bayesian structure learning using a Gaussian Bayesian network. I want to now implement a more sophisticated model with latent variables. ...
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What is the relationship of Probabilistic Graphical Model and Bayesian statistics?

I am reading about Probabilistic Graphical Model on a machine learning textbook written by a computer scientist. Even though Probabilistic Graphical Model is more of an engineering approach, its idea ...
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Causal networks with correlated variables

I've been reading about Bayesian networks and one of the central assumptions these networks require is conditional independence. However, the problems I'm working on involve variables that are often ...
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Bayesian Neural Network in Keras: transforming simple ANN into BNN

I am starting to learn about Bayesian Neural Networks. As such, apologies if my question may be too simple. As a first step in my learning curve, I would like to transform a traditional ANN to a BNN. ...
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Bayes network - independence of nodes

Let's say that the Bayes network consists of node K that represents knowledge. Since knowledge is evaluated using questions, each question is represented by the node related to the knowledge node (Q1, ...
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Doubts on sum-product algorithm (bayesian networks)

I have studied sum-product algorithm for factor graphs obtained by Bayesian networks (let's say polytree shaped bayesian networks for now), but I have some doubts which I hope you will help me to ...
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Problems with using Gibbs Sampling for Bayesian DAGs

Assume we want to sample from the variables of Bayesian belief network, which is a Directed Acyclic Graph (DAG), where we observe some of the variables, and do not observe the others. We can usually ...
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What is a valid sample size for Conditional Probability Tables?

I have a Bayesian Network model, for which I designed a study with the purpose of having empirically informed conditional probability tables (CPT). Below, I post the image of my network. The type of ...
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How do I sample a multivariate posterior when I can sample the likelihood and prior?

Suppose I want to sample the posterior distribution of a multivariate $\beta$ given some scalar $x$. By Bayes' theorem, this distribution is $$P(\beta|x) \propto P(x|\beta)P(\beta) $$ I don't have ...
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Example of a real Causal Bayesian Networks?

In the book: Bayesian Networks With Examples in R, in section 4.7 Causal Bayesian Networks. The author says: Learning such causal models, especially from observational data, presents significant ...
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Bishop PRML Question 8.10: d-separation [closed]

I have trouble with solving the second part of question 8.10 from Bishop's PRML (attached as image). I tried several things. Here's my latest attempt: \begin{align} p(a, b, d) &= \int p(a)p(b)p(...
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Bayesian updating with correlated data

I’m looking for some readings on the topic of correlation between data used for Bayesian inversion. There are a lot of discussions about the correlations between the parameters being updated i.e. $\...
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Doubt on d-separation

In the book: Bayesian Networks With Examples in R, the author shows three examples of d-separation: He cites: Then, just a few lines below, the author uses the dsep function, which returns FALSE for ...
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bayesian network conditional independence test

In the book: Bayesian Networks With Examples in R, the author does this independence test: As I see it, this works both ways, we test if travel is independent of education likewise if education is ...
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bayesian network interpretation doubt [duplicate]

I am new to stats. I am reading the book: Bayesian Networks With Examples in R and already in the first pages, some claims are made which I don't follow. The author says: If the author will only ...
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Proving conditional independence using a bayesian belief network / factorization

I have a bayesian belief network with 4 binary variables $A, B, C, D$. I now need to proof that for joint probability distributions factorized according the Bayesian network given below the ...
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Bayesian structure learning: how to identify z as a collider in x-z-y structure?

In BNSL(Bayesian Network Structure Learning) problem, we are asked to learn a DAG(Directed Acyclic Graph) over a randon variable set $U$, given samples of the underlying distribution of $U$. The ...
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1answer
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Bayesian networks basic doubt

I am new to stats. I am reading the book: Bayesian Networks With Examples in R and already in the first pages, some claims are made which I don't follow. The author says: Age and Sex are not ...
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Considering the Sentiment rather than the topic in lDA model

I have a question about the lDA model, what if I consider sentiment rather than topic in this model? In this way, will the model classify the documents by sentiment? I have tested it, but it not work.
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What does prediction mean in Bayesian Network and how can I make predictions in Bayesian Network?

I am currently working on a Bayesian Network(1 parent node, 2 children nodes, for example) and want to do predictions on my Bayesian Network. Conditional probabilities are all set and I wonder the way ...
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Quantify the output variance of a neural network classifier

Lately at work we are dealing with a theoretical problem concerning the output variance of a neural network classifier. To set the scene, suppose you have an image classifier, which takes an image as ...
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Infering noise conributions on the sum of normal RV's

Suppose multiple factors affect the noise in a measurement, e.g. a manufacturer may have some variance between production runs ($\sigma_1^2$), and some variance between products within the same ...
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Expectation Maximisation vs Expectation Propagation in the context of Bayesian Networks

I am confused about Expectation Maximisation and Expectation Propagation algorithms in the context of Bayesian Networks, especially whether one comprise another. What is the difference between ...
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Why do we have to convert Bayes' net to MRF before applying Belief propagation?

is that even correct in the first place? if yes, then why? I've seen articles talking about inference in Bayes' nets, and I've seen others talking about conversion. I don't have the full picture.
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How do I factor this conditional probability?

I am having a brain freeze. Could you show the steps to get from line 1 to line 2? Thanks!
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How to quantify a parent's influence of a node in a Bayesian Network?

Consider a toy bayesian network that models purchase of items at a store. The nodes include: {Brand, Price, Purchased}. It is possible that when you marginalize over price, P(purchase|brand) may ...
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Mixing probabilities and probability densities

I'm currently working on a Bayesian network designed to find the probabilities for various lung diseases. In the network there are, among others, a normally distributed random variable (body ...
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Why is this conditional dependency statement not correct?

I am taking an online Bayesian statistics course and here is a question from the quiz: "Is the following statement correct? $$p(a∣b,c)=p(a∣b)p(a∣c)$$ when $b$ and $c$ are independent." I thought it ...
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Conditional probability table from deterministic relationships of two discetizied distributions - for Bayesian Networks

Consider a simple Bayesian Network of three variables A, B, and C. All of the variables are discrete variables between (0,1] that are discretized as below: ...
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Bayesian network exact inference

Could someone please write step-by-step solution to get $P(D|L,B)$ ($P(D=true|L=true,B=true)$) by exact inference? I tried variable elimination but I am getting some weird numbers and I want to check ...
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Drawing a bayesian network and then converting to a factor graph to implement max-product algorithm

I'm trying to understand the fully worked example 5.2 in "Bayesian Reasoning and Machine Learning" by David Barber. Frustratingly the explanations around the example are all about potentials and ...

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