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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What is the junction tree of the following graph?

I got so confused in the remaining steps (from triangulated graph to junction tree) after turning my Bayesian network to a triangulated graph. Would anyone please help?
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Bayesian Dirichlet equivalent (BDe), Bayesian Dirichlet equivalent uniform (BDeu) and Mutual Information Test (MIT)

To estimate structures of Bayesian networks, I am thinking about three score functions, BDe, BDeu and MIT. I have several questions. What are the differences between BDe and BDeu? Can I convert BDe ...
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199 views

Why computing P(x,D) is simpler than P(x|D) in exponential bayesian networks?

I am reading this tutorial on variational inference and wonder why the statement in the question title which is mentioned on page 3 is true.
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causal correlations for binary variables

Let's assume we have binary vectors where we want to find correlations and the possible causal relations between the variables in R. 1- does "Bayesian Network structure" give the correlated variables?...
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37 views

Conditional probability table and Bayesian Network strength (R bnlearn package)

I'm using bnlearn package in R, what is the interpretation of the conditional probability tables ? as an example the output for the following code: ...
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101 views

In Bayesian networks does hard evidence make P(evidence) = 1?

I've been attempting to understand how Bayesian networks work when evidence is applied to them, and in the book I'm currently reading, there are what appear to be contradictory statements, and I don't ...
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16 views

how to use a Bayes Network Classifier weka model in our application

we are working on a Persian news summarizer algorithm. we used Weka API and BayesNet classifier to build a model for predicting sentences to be include in summarized text. the output result of Bayes ...
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67 views

showing causality between police killings and demographics (i.e. race, class, gender, location)

I've got a whole lot of police data and was wondering what sort of approaches I could use to show strong correlation, and if possible, causal effects, between police killings/arrest & call-ins for ...
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1answer
34 views

Bayesian networks and weird probabilities

I have to solve the following problem: Suppose we have a bayesian net in which we have the following variables: R, PA and PR Let: P(R) = 0.1, P(PA) = 0.5, P(PR|R, PA) = 0.6, P(PR|¬R, PA) = 0.4, P(...
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38 views

Causal Graph using Bayesian Network

I am currently doing a project in which the dataset is a lung cancer dataset. There is a training file which consists of 7 unnamed parameters (Attributes) and each of them have around 1000 values ...
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Modelling a Static Bayes Net versus Dynamic Bayes Net

I have a Bayes Net with 20 variables, but I found out that one of the Parent variables is dependent on the previous value of its Child as: C(t-1)->P(t)->C(t) C and P are binary (True or False). All ...
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How does loop belief propagation differ from variational message passing?

I'm reading Yedidia et al.'s paper and Winn et al.'s paper. The two approaches (LBP and VMP) are pretty similar to each other: Eq (5,7) in Yedidia are similar to Eq (19,20) in Winn. They both update ...
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About the evaluation of covariance of linear Gaussian model in PRML

Section 8.1.4 of Pattern Recognition and Machine Learning introduces the linear Gaussian model where each node has distribution $$ p(x_i \big|pa_i) = \mathcal{N}\left ( x_i \Bigg| \sum_{j\in pa_i}w_{...
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54 views

Probabilistic Graphical Model - Modelling a Bayesian Network on Real Life Data

Recently, I have started studying about Probabilistic Graphical Models (PGMs). While the examples provided in the textbook essentially convey the message of what and how things are happening, I am ...
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30 views

R - how to deal with massive number of nodes in Bayesian Network

I have a event correlation problem for which I want to use Bayesian Network, the problem is the number of nodes (almost 1500) and polynomial computation time. I know many of the nodes are not ...
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21 views

Specifying conditional probability tables for nodes with large number of Parents in a Bayesian Belief Network

What is the ideal way to specify the conditional probability tables for belief propagation in a Bayesian Network, for nodes with large number of parents? I am currently using gRain package in R. But ...
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1answer
40 views

Chain rule for Bayesian Networks

Suppose we have a simple Bayesian Network as follows: $X_1$ --> $X_3$ <-- $X_2$. Using the chain rule of Bayesian Networks, we can say the following: $$ f(x_1,x_2,x_3) = f(x_1) f(x_2) f(x_3 | x_1,...
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18 views

Using likelihood for event correlation in Bayesian network

Assume we have a simple Bayesian network, each event (alarm propagation) is a binary vector. Each node can trigger an alarm independently, but alarm propagates in the network with the probabilities of ...
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1answer
45 views

How to do calculate both causal and diagnostic inferences simultaneosly in bayesian networks?

Consider a simple Bayesian network as given below. Question: How to find $P(S|C,W)$? It is fairly straight forward to compute the causal inference $ P(W|S) = P(W|S,R)\cdot P(R) + P(W|S,\bar{R}...
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10 views

How do I do feature selection using Bayesian networks?

I have two classes and a load of high dimensional data and samples, how does one go about selecting features by Bayesian networks? I can find details on how to make the network, but no packages in R ...
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8 views

How to evaluate the quality of Bayesian network sampling?

I have generated a sample from a Bayesian network by applying Forward Sampling. I learn the parameters of the network (the same structure) from this sample so as to evaluate the quality of the sample (...
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39 views

Bayesian networks - prediction question

Let's consider a dumb spam filter BN (see figure below) for which I've already calculated the a posteriori parameter distributions (see normalized table values). I want to predict if next email ...
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1answer
24 views

Confusion about the concept of Bayesian Networks

I read a lot about Bayesian networks, including focused literature. However, what I have not yet understood properly is this: What is the use case of Bayesian networks that contain of more than 2 ...
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1answer
24 views

Simple Marginalization Explanation Please

I am having difficulty understanding this marginalization. Let's say you have this relationship $p(a,b,c) = p(a)p(c|a)p(b|c)$ From that you are trying to get $p(a,b)$ $p(a,b) = p(a) \sum\limits_{c} ...
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65 views

Estimating P(C|A,B) from P(C|A) and P(C|B): Bayes Rule? Bayes Net? Classifier?

Doing some ecommerce analytics, I want to understand click propensity broken out by different features present in users' profiles. In this scenario, it's easy to test click propensity $p(C)$ broken ...
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8 views

How to deal with the factors when moralize a directed network?

Consider we have a simple V-Structure Bayesian network which we use it for model some random variables. in other words we have a distribution $P(C|A,B)$ where A and B are the parents of C in the ...
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93 views

Bayesian Network produces different directions depending on order

I'm trying to fit a Bayesian Network model with bnlearn to determine the direction that users go from different actions (i.e.: do seeds lead to joins, or joins to ...
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63 views

Combining one class classifiers to do multi-class classification

I am working on a 3-class classification problem. The classifier I'm using is Bayesian Networks which provides me with a classification accuracy of around 60%. When I do a two-class classification, I ...
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34 views

Got an entropy-ish function for a multinomial distribution? Graph theory and Bayes net related

I have a discrete variable $X$ that can take on one of three states; $a$, $b$, and $c$. Thus it has two parameters $p_a = P(X = a)$ and $p_b = P(X = b)$, of course $P(X = c) = 1 - p_a - p_b$. I am ...
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1answer
47 views

How to apply a fitted Tree-augmented Naive Bayes classifier to new cases

I am running Tree Augmented Naive Bayes algorithm in R and I have got the desired network. However, unlike logistic regression, Bayesian is non-parametric i.e. I do not have any coefficients which I ...
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12 views

Can optimising thresholds for discretisation lead to overfitting in Bayesian networks?

In Bayesian networks continuous data is often made discrete, for example: < 21.5 becomes 0 21.5 > .. < 43 becomes 1 > 43 becomes 2 If you run an ...
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21 views

Discretization for a bayes network model with small sample

I have been playing around with a Bayesian network toolbox for prediction and classification. I have had good success with the examples but I'm now stuck on how I should proceed with my scenario. I ...
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52 views

Improving the results coming from an image recognition API

We are developing a software application that will automatically suggest tags (keywords) for images that are being uploaded into a database of already-tagged (by a human) images. We are using a 3rd ...
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13 views

Looking for algorithm that is a discounted min-cost-maximum-flow calculation

In terms of graph theory I am very familiar with minimum-cost maximum flow, connectivity and ...
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69 views

With complete data and a factored prior, the posterior also factors

In the second paragraph of Section 11.3 in Machine Learning A Probabilistic Perspective, the author concisely summarizes Section 10.4.2 by saying that for the standard bayesian model $$P({\boldsymbol\...
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78 views

Inference in Bayesian network Using bnlearn package

In this link Prediction of continuous variable using "bnlearn" package in R , the author talk about how I can find the conditionl probability of P(node(C)\ the rest node)=P(C\A,B,D,E,F,G) ...
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23 views

Confuse conditional mutual information and mutual information to get better DAG

I use both : mutual information conditional by class I(X,Y|C) mutual information. to ...
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1answer
40 views

How to compute standard error of the log-hazard in the baseline arm from an n-arm study

I'm trying to use GeMTC (a package for Bayesian Network Meta Analysis) for an analysis that mixes contrast-based data (Hazard Ratio;HR) with arm-based data (event counts). The documentation specifies ...
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22 views

How can I use a significance test to choose parents in a Bayesian network?

I am trying to improve the KDB algorithm (Sahami, 1996) which creates Bayesian classifiers. Currently, for the first $k+1$ attributes added to the (initially empty) Bayesian network, the algorithm ...
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44 views

get probabilities of inference in bayesian network in R

I have a question about how continuous variables can be used for building models and prediction in a bayesian network. With some help, I was able to get it to work for continuous variables as follows ...
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34 views

Does this Bayesian network consist of 'hidden nodes' or 'observed nodes'?

Following the discussion on this website, hidden nodes are "nodes whose values are not known" whereas observed nodes are "the ones we condition on." This seems like a pretty vague description and I'm ...
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1answer
46 views

E-step in EM algorithm with non trivial latent variables

I am trying to derive the E-step for an EM algorithm for this model: The interesting fact is that there are two sets of latent variables: $z$ and $y$. The E-step involve a derivation of the ...
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41 views

Markov blankets and 'soft evidence'?

Consider a Bayesian network. For simplicity, assume that the variables take on two values, either $0$ or $1$. To review, a Markov blanket of a node in a Bayesian network is defined as the nodes ...
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10 views

How to set arbitrary number of values for variables in Banjo

I'm using Banjo (BAyesian Network inference with Java Objects) to analyze a set of data. I want each variable to take a range of more than 7 values (Banjo put this limit in the amount of values a ...
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1answer
31 views

Bayesian posterior marginal probabilities

I feel like this should be obvious, but I don't see the approach. This question comes from the philosophy of science, so I will pose it first in that context and then in a probability context. In ...
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13 views

How to determine independence in a Bayes Network using joint distribution

So I've got a practice problem and I'm really confused by our prompt. We're given the typical "Burglar Alarm" scenario ( http://i.stack.imgur.com/QTXrZ.gif ) for explaining bayes network. We are told ...
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18 views

Value of X that maximizes P(Y|X) in a bayesian network

Given two discrete variables $Y$ and $X$ that belong to a bayesian network, and an assignment $y$ to $Y$, how can one find the assigment $x$ to $X$ that maximizes $P(Y=y|X=x)$? Is there a name to such ...
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Variational bayes precision on network with categorical hidden nodes and observed gaussian nodes

I have a bayessian network that has a basic DAG structure where each node of this basic DAG has categorical (Bernoulli - only two values, in fact) distribution and each of this categorical nodes has ...
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Terminology of “Polytree graphical models” in the context of graphical models, HMM, Naive Bayes

I'm reading a paper in which they are attempting to balance between cost of obtaining information and information value in graphical models. At one point they talk about chain graphical models such ...
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Marginalizing multivariate-normal distribution canonical form

Regarding the problem of margenalization of canonical forms of multivariate gaussian distribution it was mentioned in probabilistic graphical models text book that $$\int{C(X,Y;k,h,g)}dY$$ is ...