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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 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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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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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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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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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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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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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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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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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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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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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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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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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 ...
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Is it possible to use Bayesian networks to predict numerical values? (non-categorical)

Is it possible to use Bayesian networks to predict numerical values? (non-categorical) For example is it possible to build a Bayesian network in the case of a house price prediction? I found answers ...
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Are there useful applications for Bayes Nets (vs. Naive Bayes)?

I am trying to learn about Bayesian networks and try to make them work in the context of a simple prediction problem. But my question is more theoretical: For argument's sake, assume we have a ...
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What is the purpose of finding the Maximum Spanning Tree?

I'm referring to Chow-Liu algorithm in Bayesian network structure learning. We first construct a Mutual Information Graph, and from that we find the Maximum Spanning Tree. But, once we got the tree, ...
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Working out the direction of undirected arcs in a learned structure using bnlearn

I'm using the Dublin census data to test out bnlearn. If anyone wants the data, I'm using the processed data (data_train) from this self organising map tutorial. All the columns are actually the ...
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A node in Bayesian network model with a hybrid parents (i.e., contentious and discrete Parents)

I have a Bayesian network model that has a node with hybrid parents. Assume that the discrete nodes are beta distributed and the continuous is CLG (continuous linear Gaussian) distributed. If I ...
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How to determine if two directed probabilistic graphical models are I-equivalent?

I'm trying to figure out how to determine if these two models are I-equivalent. Google didn't properly give me a solid answer so far. Any idea on to determine it? Thank you.
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Machine learning to estimate p(y>N | X) where N is a duration

To illustrate, let's say I have a mobile game and I want to predict the duration of each session $y$ when they start. Say I have a training set with multiple useful features $X$ from previous ...
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How to approximately sample an unknown non-parametric joint distribution given a complete set of partial conditional distributions?

This question is related somewhat to Bayesian networks. In a BN, you have a DAG (directed acyclic graph). By supplying the root nodes with a sample, you can then follow the directed arcs to sample ...
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How to use Bayesian belief Network map/Causality map for segmentation?

I have obtained the causality map for my data. I have an event of interest and the evidences for the event. How do I make the use of this information to come up with segmentation/clustering such that ...
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Log or MSE loss for hyperparameter tuning of probabilistic NN

I am building a predictive model of a dynamical system using a NN whose output neurons enconde the mean and diagonal covariance of a Gaussian distribution. For training, the negative log prediction ...
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Bayes R2 computation

I am working on evaluating the performance of a Bayesian network. One of the metrics I'm considering is the Bayes R-squared. On going through this publication, http://www.stat.columbia.edu/~gelman/...
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Conditional Independence in Bayes Network

I have just started working through Michael Jordan's notes on Probabilistic Graphical Models and seem to be stuck on the exercise on page 5. I summarize the question here: Suppose $G = (V,E)$ is a ...
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forward sampling for Bayesian network with continuous variables and equation-based causal relationships

I have a physical system which can be represented by the following Bayesian network. It has the following characteristics 1) The encoded variables are continuous variables 2) The causal ...
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Bayesian network with continuous variable data set in python

I am looking to predict continuous target lets say Sales with KPIs like price distribution using Bayesian network. I have got it done with BNlearn in R but still ...
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probabilistic distribution of a variable which are based on random imputs

In practice, I have a variable x, which is based on (b,c,d). We may have a physics based math formula to describe the relationship between x and (b,c d), i.e., x=f(b,c,d). Beforehand, we may know the ...
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Find Conditional probability distribution given conditions - Bayes Network

I'm taking a course on bayesian statistics and I'm having trouble with one assigment, it goes like this: Construct an example in which two variables have a common effect, and the presence of one of ...
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If I(G) = I(G') do they have the same skeleton and the same v-strucures except those in complete (sub-) graph?

I thought if two different graphs G, G' have the same skeleton and the same v-structure, then I(G)=I(G′) and I(G)≠∅. But does the converse also holds? In this case a complete graph doesn't apply ...
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Do all P-Maps for a distribution share the same skeleton or/and v-structures?

I learned that a distribution may have multiple P-Maps because even if we are sure about the independences in a graph we cannot gurrantee the causal direction, then I just wonder if those P-Maps share ...
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Independence imply d-separation?

In the context of Bayesian networks if two random variables (i.e. nodes) are d-separated, they are independent. However, is there any example of random variables being independent but not d-separated?
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How to assign values over this two variables A and B in an apocryphal “Bayesian Network” like A->B->A?

Let's say that we have a graph A->B->C, and its coditional independence representation is like follows: ...
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Is this task about soft evidence or just creating of Bayesian Network?

I have a task. We have two sensors that are meant to detect extreme temperature, which occurs 20% of the time. The sensors have identical specifications with a false positive rate of 1% and a false ...
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Is this task about soft evidence or just creating of Bayesian Network?

I have a task. We have two sensors that are meant to detect extreme temperature, which occurs 20% of the time. The sensors have identical specifications with a false positive rate of 1% and a false ...
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2answers
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Understanding the parameters needed for a distribution in Bayes networks?

Since I have a discriminative mindset hardly can I intuit the so-called parameters needed to specify a distribution in a generative Bayesian Network. I'd like to borrow an example from this blog. If ...
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What does it mean for a variable to block a path between other two variables?

What does it mean for a variable $Z$ to "block" the path between variables $X$ and $Y$ in a causal model? What is the formal definition of a "block", and how can I intuitively understand this concept? ...
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Meaing for MOAC in Spherical Payoff

I want to implement this metric Spherical Payoff mentioned in both articles and Netica software to validate my bayesian network (through a test dataset), here are the formula that I got from my ...
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In which applications bayesian network are more promising to capture the uncertainities and understanding?

I know, there are lots of question on difference between NN and bayesian network, What i am specifically talking about modelling and uncertainty capturing? As we know, bayesian ML methods are very ...
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Initializing structural expectation maximization for learning Bayes net structures

I am using bnlearn in R to learn Bayesian network structures. It has a structural.em method for learning with missing data that ...
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1answer
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How to validate the results of bayesian causal network?

There are many ways of validating predicting the results: MSE, MAE, AIC, CV, etc.. But I do not hear any validation way of causality. If the true networks not available, how to make sure the results ...
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Algorithms for combining Bayesian networks? [closed]

Are there any algorithms for combining multiple Bayesian networks? For example, let's say I have 5 variables A, B, C, D and E, and I build 5 Bayesian networks on different random subsets of these, let'...
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Order of Conditional Independence Tests

I'm studying the PC algorithm for learning the structure of a Bayesian Network. One of the steps refers to performing several rounds of conditional independence tests of increasing order, zero, first,...
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Which book has the right conditional independence formula? [closed]

I'm getting crazy. I've just started to learn probability and, after it, Bayesian networks. I don't know so much about probability, that is why I'm getting crazy. I'm using this book to study a ...
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Turning dichotomies into a typology

Creating a typology and typing an object is hard. What isn't hard, however, is creating dichotomies and seeing which dichotomies an object satisfies. Here is my case study. Myers-Briggs typology for ...