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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How is the log likelihood calculated for bayesian networks?

In structure learning, there are score-based methods which rely on information criteria such as BIC or AIC. BIC, specifically, is defined as: $$ BIC = k \ln(n) - 2\ln\left(\hat{L}\right) $$ Where $k$ ...
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How to orient the undirected edges in the CPDAGs learned by some Bayesian Network structure learning algorithms?

Some Bayesian Network (BN) structure learning algorithms (such as the PC algorithm) learns a CPDAG as the output, which contains both directed and undirected edges. One common evaluation metric for BN ...
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Bayesian Network: tools for simulation to create a sample set from reference Bayesian Networks?

There are some commonly used reference Bayesian networks, which can be found in the Bayesian Network Repository, and I want to simulate a data set from such a reference graph. Are there any tools that ...
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Laplace distribution as an Exponential Distribution and Minimizitaion of KL Divergence

In the context of Expectation Propagation [Minka's thesis-2001], I would like to approximate an unknown distribution with a Laplace distribution. This can be solved by minimizing KL-Divergence. In ...
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the variational family used to approximate the weight posterior of a BNN

Why the variational family used to approximate the weight posterior of a BNN is often chosen to be Gaussian?
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Why Assumed Density Filtering is also called Moment Matching?

I am learning about Assumed Density Filtering (ADF) and Expectation Propagation in the context of bayesian deep neural networks. I have seen in some textbooks and papers that ADF is also called moment ...
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Moment Matching for a Laplace Distribution

I have this derivative It belongs to this paper. In the paper, they are trying to model a lightweight bayesian deep neural network by having the distributions on only the activation functions. They ...
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Conditional Probability and Bayes Net Problem [closed]

I have two questions: Given the following Bayes Net: I know that p(D|A)*p(A|C) doesn't necessarily equal p(D|C); however, is there any case where that might happen, if D and C are independent? I ...
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What are Large Scale and Complicated Priors?

We use priors in Bayesian networks to include prior knowledge in our models. In this context, what are these two terms: -complicated prior -large scale prior I have seen priors like Laplace, zero-mean ...
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Joint and Conditional Distributions in Bayesian Network

In such a graphical model, how can I express the conditional probabilities $p(x_4|x_1,x_2)$ and $p(x_4,x_5|x_1,x_2)$? My work: $p(x_4|x_1,x_2) = p(x_1,x_2,x_4) / p(x_1,x_2) p(x_1,x_2) = p(x_1)*p(x_2|...
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Calculating path coefficients in a simple linear Bayesian Network

I am confused after studying diverse educational material about Structural Equation Modeling (SEM) and Bayesian Networks (BN) over the last years. Others also seem to experience a similar issue, e.g. ...
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Measuring uncertainty with bayesian neural network

One of the ways to measure epistemic uncertainty, is using bayesian inference in neural networks. The idea is to learn the posterior over the weights $P(\phi|X)$ which describe the probability ...
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Relationship between Bayes Rule and Bayesian Networks

Learning about Bayesian Networks in school - I ran across a problem which ask to find the probability of $Pr(Alarm|Storm=T)$ given a column of event data for four variables: Storm, Burglar, Cats, and ...
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45 views

Where to learn probabilistic deep learning/baysian methods for machine learning

I have completed the machine learning course and deep learning specialization by Andrew Ng on Coursera, and now learning TensorFlow 2 for Deep Learning Specialization by the imperial college of London,...
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Markov condition on collider

I am studying Bayesian Networks using the Neapolitan book (Learning Bayesian Networks). In section 1.3.2 it is stated the following: Definition 1.9 Suppose we have a joint probability distribution $P$...
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How to eliminate graph cycles?

I checked Why do Bayesian Networks use acyclicity assumption and read two books on Bayesian probability but I haven't found why DAGs (Direct Acyclic Graphs) are must and what would possible be wrong ...
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32 views

How to design a filter to remove the influence of factors on the values of a measurement

Is anybody aware of methods that are appropriate to modify the values of a time series to account for factors that are known to artificially inflate or deflate the measurement. An example of the ...
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114 views

What is the difference between Bayesian Regression and Bayesian Networks

I had actually posted an earlier question about the applications of Bayesian networks, and I received a very good response. I understand that Bayesian networks are usually used to answer probability ...
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Why using point estimates instead of integrating out the unknown?

I was just wondering why you often use point estimators like MAP and MLE when you have to calculate the posterior distribution for them anyway? Is it because you don't have to calculate the evidence ...
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1answer
36 views

Learning resources for Bayesian Dynamic Networks?

Increasingly, I've stumbled on the term Bayesian Dynamic Network(s). The field seems to be at the intersection of probabilistic graphical models, time series, Kalman filters, etc. Because there's so ...
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Deep Bayesian networks learning techniques

I am trying to compare different learning techniques to train deep Bayesian neural networks. do you have any suggestions or papers that do compare different learning techniques such as mean-field ...
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1answer
85 views

Clarifying the applications of Bayesian networks

I have been looking at Bayesian networks, using the book by Koller, Probabilistic Graphical Models. The book is very large, so I might have missed the answer to my question ;). But I was trying to ...
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104 views

How to specify a prior on the network structure while learning a Bayesian network structure?

I don't have experience with Bayesian networks. Bayesian network learning libraries like BANJO and bnlearn can learn the structure and fit the parameters of Bayesian networks on data. I see that there ...
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Book Recommendation for Graphical Models and Bayesian Networks, good for self-study (meaning problems and solutions)

I am watching some of the videos from the Stanford CS 221 course, which goes over issues including Bayesian Networks and Graphical models. There are models where I am trying to learn the joint ...
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Active paths during marginalization in a bayesian network

Given is the following bayesian network: Now I need to construct a new bayesian network over all of the nodes except for A which is a minimal I-map for the marginal distribution over those variables. ...
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Calculate the probability of a variable on a Bayesian Network

Let's assume we have a bayesian nework with discrete variables like shown below. For simplicity, assume all variables are binary. Assume we know the states for V1 and V2 and we want to calculate the ...
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Calculate probability of state with information of underlying distribution

I have a problem with this setting: There are 2 possible states (1,-1), there are j agents, each agent receives an iid normally distributed signal with the state as the mean and std dev x. Each agent ...
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59 views

Graphical Representation of Dynamic Bayesian Network

Some tourists visiting a cabin are interested in finding out if there are animals nearby. They can observe outside of their window every day whether there are animal tracks and whether the food they ...
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Improvement in NN regressor by Negative Log Liklihood loss vs MSE loss

I am trying to write a simple NN based regressor, and I have noticed that if i take two identical NN, one with mean square error loss, ane with sample drawn as gaussian prior over final output, with ...
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29 views

Forecasting with Dynamical Bayesian Networks

I am trying to forecast some variables of a dataset (time series) with Dynamical Bayesian Networks (DBN) using pgmpy. I could be mistaken, but what is being called "forecasting" in the ...
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121 views

Calculating Probabilities in a 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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98 views

Number of Variables Needed to Represent Bayesian Network and Independence

Consider the Bayesian Network Structure Below, decide whether the statements are true or false. a) If every variable in the network has a Boolean state, then the Bayesian network can be represented ...
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25 views

Dynamic bayesian model conditional independence

I have just started learning probabilistic graphical models, so my knowledge of this subject is relatively weak. Hope I don't make any mistakes in my question. Given the Dynamic Bayesian model shown ...
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35 views

Belief propagation on Polytree

I'm working through exercises on Belief Propagation and the Junction Tree Algorithm and I'm stuck with the following problem. Consider the distribution P(A,B,C,D,E,F,G,H)=P(A)P(B)P(C)P(F) P(D|A,B)P(E|...
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Probability of at least one success in a long string of connected events

I have N events (i from 1 to N), each with an estimated probability of success, p(i). If all my events were independent I'd be able to calculate the probability of at least one success as (1 - product ...
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47 views

How can a random variable be independent of a member of its minimal Markov blanket?

Consider the following Bayes network of random variables on some probability space: The local Markov property asserts that any variable is independent of its non-descendants given its parents. Here, $...
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25 views

Factor graph equivalent to markov networks

Consider the following potential on three nodes. represented by the following factor graph. Now the notes claim that we can represent this factor graph as both a Bayesian network and a Markov ...
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105 views

How to count the number of independent parameters in a Bayesian network?

I'm currently going through Prof. Daphne Koller's probabilistic graphical models course on Coursera and had a question regarding an exercise problem. The problem is as follows: How many independent ...
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Question regarding assuming independence in a V-structure in a Bayesian network

I'm currently solving the same problem that was posted in this Stack Overflow question but had a question regarding another aspect of the problem. The source of this problem is the course regarding ...
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37 views

Bayes by backprop unbiased monte carlo gradients

I am currently trying to understand a paper on bayesian neural networks whereby the authors use a bayes by backprop approach to learn weight uncertainties in the neural networks. I am trying to ...
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Algorithm for inference on continuous bayesian networks?

I am currently working with Bayesian Networks, and I would like to try some inference on continuous variables. On the book from Neapolitan "Learning Bayesian Networks", on chapter 4, it is ...
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Where do the “semantics” of a Bayesian network come from?

On Bayesian Networks, Ghahramani (2001) says: A node is independent of its non-descendants given its parents. This point is fundamental enough that Ghahramani calls it the “semantics” of a Bayesian ...
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Making sense of the belief propagation on graphs

I sort of understand when do I use variational Bayesian and when do I use expectation maximization. But now I want to know when do I use belief propagation in graphs to solve an estimation problem. ...
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46 views

How to use belief propagation sum product algorithm in a factor graph to solve inference problem?

I've read about belief propagation and sum product algorithm but still don't know how to apply it. For simplicity, I want to apply it to estimate the variable $x$ from this equation, $y=x+n$, where $n$...
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71 views

Modern applications of Bayesian Model Selection

I'm trying to understand the merits of this field so I'll try to break down my question. Research: Is Bayesian model selection considered a popular topic of research these days? Variable selection: ...
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1answer
66 views

Introduction to approximate message passing

I'm interested in learning approximate message passing from the paper "Message Passing Algorithms for Compressed Sensing: I. Motivation and Construction". My background is in computer ...
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20 views

Learning parameters for a bayesian network from data with different oberservation frequencies

I have a Bayesian network of a given structure and nodes A, B, C, D, E and want to learn the parameters of the network, i.e. the conditional probabilities, from data with differing frequencies of ...
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Why does the causal markov condition allow for the interpretation of a bayesian network as a causal diagram?

A related question is here. As far as I can understand from scanning reviews on causal discovery, there are two critical conditions, (1) the causal markov condition and (2) causal faithfulness. It is ...
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Bayesian mixture model joint posterior

I am just starting to learn about bayesian mixture models. There is a few clarifications that I want to make which I am not sure myself. The graphical model below describes a gaussian mixture model ...
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How to combine continuous and discrete variables for bayesian network? [duplicate]

Basically the title says the question. I have a data set with both types of variables and AFAIK bayesian networks are constructed for discrete variables. Is it possible to somehow use them together?

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