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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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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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Is there any relation between BDeu (Bayesian Dirichlet) score of subsets of nodes in learning structure of a bayesian network?

I'm learning about BDeu score in learning bayesian network structure problem and I want to know if there is any relation between BDeu scores of different subsets of a network. for example, can we ...
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120 views

Variance of evidence lower bound(ELBO) loss function

When using Bayesian optimisation in a neural network our loss function is equal to: Here the first term is the KL divergence between the approximate and true posteriors. The second term is the ...
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Decision boundary for categorical Bayesian network

I know that categorical Naive Bayes (categorical predictors, binary target) has a linear classification boundary. I'm wondering what the decision boundary for an arbitrary categorical Bayesian network ...
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1answer
25 views

Complete graphs have different v-structures?

From the book "Probabilistic Graphical Models", here says two complete graphs have different v-structures. As I understand, v-structure is like "X->Z<-Y" without edge between X and Y. If so, ...
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18 views

Any research on learning Bayesian network structure with a limit on the parent set size?

Learning a maximum-scored Bayesian network structure with bounded treewidth is rather popular in recent years, as stated in the paper A survey on Bayesian network structure learning from data in 2019. ...
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19 views

Are Bayesian Networks parametric or non-parametric models?

After searching Wikipedia, I found that there are both parametric Bayesian models and non-parametric Bayesian models. What about Bayesian Networks? When building up a Bayesian Network model, I don't ...
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27 views

Dealing with deterministic simulations via Bayesian analysis

Problem Set-Up Suppose I have a random variable $a \sim \mathcal{U}(\cdot)$, that is distributed uniformly, and some other random variable $X \sim \mathcal{N}(\cdot)$, that is distributed normally. ...
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91 views

Factorized Gaussian distribution

I am reading this post about Bayesian deep learning. It mentions that we can approximate a distribution $p_t(w\mid x)$ by a simple distribution $q_t(t)$. Then it mentions that this distribution can be ...
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40 views

How to find root cause of effect with multiple distractors

I am writing an app to determine most likely cause of stomache-aches of users. Reducing the problem to its simplest form, for each user I have a multiple lists of ingredients that leads to his/her ...
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13 views

How to do inference in Bayes networks incrementally?

Suppose that we have a Bayes network $B$ and we have already spent the computational resources to do inference in $B$. For instance, we already have the calibrated junction tree for $B$, or we have a ...
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37 views

What is the point of doing simulation on Markov Chain?

I am studying Markov Chain and I am currently reading about simulation on Markov Chain but I can't see the point of simulation on Markov Chain. What does simulation mean in Markov Chain and what can ...
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6 views

What are the relationships among Markov Property, Stationarity, and Time Invariance

I am wondering if there is or are any relationship among those. I have understood Markov Property by reading Wikipedia, but it is still confusing to figure out if there is any relationship among those ...
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1answer
39 views

How to evaluate the accuracy of a probability distribution?

I've trained a Gaussian Bayesian Network. If I feed input values for the parent variables of my output variable, I get a normal distribution. How can I quantify the accuracy of this distribution when ...
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What is the meaning of generating data from a probabilistic model such as a naive bayes classifier?

I am studying probabilistic modeling but I am stuck with the concept of generating data from the probabilistic model. Say I have built a naive bayes classification model, what is the point of ...
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44 views

Learning Causal Graph from data

I am quite new to the theory of causal graphs, but from what I understand they are DAG, like Bayesian Networks. Since we have structure learning methods for Bayesian Networks like score based ...
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15 views

To say my model is a stochastic model,what assumptions do I need to make?

I am trying to understand what a stochastic model is and assumptions to be able to say my model is a stochastic model. I am new to it, so I may confuse you. I have gone through Markov chain, Markov ...
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Efficient GPU (batch) implementation of Empirical Fisher information matrix?

I have seen many implementations. It seems to be a limitation of autograd itself that we can compute the gradient of loglikelihood only one sample at a time. The batch version has been used but in a ...
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15 views

Is Chow Liu's scoring algorithm to have at most one root node?

I am told that Chow Liu's algorithm can have at most one root node. In the fisr place what does it mean? I am wondering how I can apply Chow Liu's scoring function for more than one root node to do a ...
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1answer
31 views

Calculations in a Bayes Network

I am working through a text book (Probabilistic Graphical Models, Principles and Techniques) to learn BNs, but I am confused as to the accuracy of the example. The text references the figure above. We ...
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15 views

What is the difference between Bayesian Network and Dynamic Bayesian Network?

I just got the sentences below from a web site while studying Bayesian Network: "​A dynamic Bayesian network (DBN) is a Bayesian network extended with additional mechanisms that are capable of ...
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1answer
42 views

How to infer a missing observation in a state space model?

I read here that "structural time series models handle missing values naturally, following the rules of conditional probability. Posterior inference can be used to impute missing values, with ...
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27 views

Computing Local Evidence for Bayesian Networks

I am reading through Kevin Murphy's "Machine Learning: A Probabilistic Perspective" book. I'm interested in understanding how to do exact bayesian inference over a tree structure, as discussed in ...
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1answer
39 views

What is the meaning of calculating Maximum Likelihood from complete data for Bayesian Nework paremeter learning?

I am taking a subject on Bayesian Network on Youtube. Somehow, I am struggling from understand the meaning of calculating Maximum Likelihood estimates from complete data for a for bayesian nework ...
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1answer
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What is the idea behind Bayes By Backprop?

Having looked through the internet and the paper, I find Bayes by Backprop very unaccesible for my intermediate understanding of variational inference. Most online guides also lack some explaining ...
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1answer
53 views

What is the Markov blanket of a deterministic variable?

The following Bayesian network contains a node which is deterministically dependent on its parents: the variable $either$ is simply the $OR$ function of its parents $tub$ and $lung$. By the graph, ...
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1answer
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How can I normalize Bayesian Network query result?

While taking a Bayesian network tutorial on YouTube, I was watching a video explaining the Bayesian Network probability inference. Somehow, at the end of the tutorial, the lecturer did not explain how ...
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42 views

Bayesian hierarchical coin flip model

My question is: what is the marginal probability $P(x_1, x_2, \dots, x_n | y_1, y_2, \dots, y_n, \alpha, \beta)$ or $P(X|Y, \alpha, \beta)$? in the following model: $\phi \sim \text{Beta}(\alpha, \...
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1answer
34 views

Understanding of conjugation relationship in Bishop book

Referring to Pattern Recognition and Machine Learning by Bishop(Page 367, Section 8.1): Such models have particularly nice properties if we choose the relationship between each parent-child pair in ...
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1answer
64 views

Dirichlet process mixture modelling for a Gaussian likelihood

Let $\mathcal{Y} = (\mathbf{y}_1, \dots, \mathbf{y}_N)$ be data observed, such that each $\mathbf{y}_i \in \mathbb{R}^2$. Now conditional on unobserved cluster centres (means) $\mathcal{X} = (\mathbf{...
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46 views

Conditional Probability Table in R

I want to perform Bayesian network analysis in R. I have a large network and i am bit confused with defining conditional probability tables! In my network i have a node with in-degree of centrality ...
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41 views

Normalizing output of Viterbi algorithm

Viterbi algorithm can be used to solve problems in belief networks of the following kind: $$argmax_{x_{1:t}}P(x_{1:t}| e_{1:t})$$ where $e_{1:t} \in E^t$ are evidence variables and $x_{1:t} \in S^t$ ...
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How can we cast an optimisation problem as an inference problem?

The main idea of variational methods is to cast inference as an optimisation problem. In the paper Junction Tree Variational Autoencoder for Molecular Graph Generation, the authors state that the ...
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52 views

What is the relation between message passing and probabilities in Bayesian inference?

The belief propagation algorithm is a message passing algorithm that can be used to estimate marginal probabilities on Bayesian networks. What is the definition of these messages? What is the ...
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1answer
63 views

What is the difference between belief propagation and loopy belief propagation?

Belief propagation (BP) is an algorithm (or a family of algorithms) that can be used to perform inference on graphical models (e.g. a Bayesian network). BP can produce exact results on cycle-free ...
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81 views

What are the differences between Bayesian networks and hidden Markov models?

Bayesian networks and HMMs are both probabilistic graphical models and they are both represented by DAGs. What else do they have in common? What are their differences, both in terms of architecture ...
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1answer
35 views

What is a factor in the context of Bayesian networks and inference?

I have come across the term "factor" in the context of Bayesian networks and inference (which I am not very familiar with). I've also heard of the expression "factor graph", which is an undirected ...
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22 views

Complete a Bayesian Network by specifying the probability distributions

I have a hierarchical Bayesian Network like this: Here: $R≡$ log level of poisonous gas (radon) in a house $B≡$ type of house (With a basement or without) $C≡$ a county in Minnesota where the ...
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Classification using Bayesian Network

I'm trying to do a two-category classification similar to what you would do with logistic regression, where all the predictor variables are continuous. In the BN, the response variable would end up as ...
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39 views

software for one class classification with a Bayesian Network

I'm looking for a software package that would allow to do a one class classification with a Bayesian Network (anomaly detection). I was planning to use bnlearn but so far I'm unable to find out if ...
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111 views

Implementing ETC (Edge Tree Construction) algorithm for Bayesian Networks using Python

I am trying find a bayesian network and have been successfully able to use the Chow-Liu algorithm through the pomegranate library. I wanted to use the ETC algorithm to learn the network but I'm having ...
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1answer
47 views

What happens if the observations are connected in a hidden Markov model (HMM)?

Suppose that we have an HMM with hidden variables $X_t$ and observed variables $Y_t$. Why do we always assume $p(Y_t|X_t)$? What happens if we have $p(Y_t|X_t, Y_{t-1})$? Is it because that wouldn't ...
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BNLearn: How to merge the estimating parameters of a Gaussian Bayesian network with its conditional structure?

I define the structure of a gaussian baesian network usind " iamb" function and then estimated the coeficients of the nodes using "bn.fit". ...
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Independence in this Bayes net

Consider this Bayes net A,B,C forms a v-structure. $B \not\!\perp\!\!\!\perp C | A$, B is not independent with C if A is observed. My question is, if B,A,D are all given, can we write $p(C|B,A,D) = p(...
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Is every distribution factorizable by an MRF also factorizable via a Bayesian network? And vice versa?

This has probably been asked before, so if it has please provide a link to the original question and close this as a duplicate -- I was not able to find the original question myself. Question: Let'...
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1answer
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Determining Conditional Independence from Marginal Independence?

so if I have a 3 columns of binary variables X, Y and Z with their respective values and I would like to determine whether X,Y are conditionally independent given Z. How can I go about doing this? ...
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1answer
96 views

Clarifying Dirichlet Process Mixture Probability Terms

Suppose I have a Dirichlet Process Mixture model defined as follows: $\alpha \sim G(a,b)\\ \pi|\alpha \sim \text{Dir}(\alpha)\\ z|\pi \sim \text{Cat}(\pi)\\ $ where $G$ is just a standard Gamma ...
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21 views

Can Deviance Information Criterion be used for model comparison when the response variable has Poisson distribution?

I just constructed a Bayesian Hierarchical Model for my response variable Y that follows Poisson distribution with the parameter $\lambda$. In my model, I have modelled $log(\lambda)$ as a linear ...