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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Why a undirected graph is Markov equivalent to a directed graph iff it is decomposable?

Claim 1. A undirected graph is Markov equivalent to a directed graph iff the undirected graph is decomposable. I am trying to prove Claim 1 and to find a relationship between decomposable and v-...
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Bayesian Networks vs traditional stats approaches to Causal Inference? [duplicate]

I've been reading the 'book of why' by Judea Pearl and come to understand that Bayesian Networks can be used to establish causality given a directed acyclic graph (DAG) and that the methods are non-...
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Node that depends on the particular values of it's parents in a Bayesian network?

Consider a Bayesian network containing a binary variable C which denotes whether a certain person has a child or not. There is a second variable B which denotes the birthdate of the person's youngest ...
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Proof that the Markov Blanket in a Bayesian Network is parents, children, and children's parents

I'm looking for a proof of this fact from wikipedia: The Markov boundary of a node $A$ in a Bayesian network is the set of nodes composed of $A$'s parents, $A$'s children, and $A$'s children's other ...
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Discrete Bayes Net learning under parameter constraints

What is some relevant research available on estimating the parameters of a Bayes Net (with known structure) when there are known constraints on conditional and marginal probabilities? For example, ...
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Bayesian hierarchical model inference problem image segmentation

it might be really confusing question. I am working on my thesis and I am stuck at a problem. It's a problem in image segmentation and finding parameters of border lines of continuous region in an ...
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Calculating conditional probability on bayesian network

In one of my lectures the Bayesian Network below sprung up and I am puzzled because there's no explanation on how did we calculate the denominator of first and second fractions. I already know how to ...
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mutual information and edge weights in a bayesian network

The mutual information between two random variables X and Y can be stated formally as follows: I(X ; Y) = H(X) – H(X | Y) Where I(X ; Y) is the mutual information for X and Y, H(X) is the entropy for ...
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When and why converting a Bayesian network into a Markov Random Field?

I found many slides and tutorials (e.g., [1,2]) on the probabilistic graphical model introducing the procedure of "converting a Bayesian network (BN) into a Markov random field (MRF) by ...
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Neural network regression not learning due to non-uniform data distribution?

I am working on a non-linear multi-output regression problem. I have created a simple neural network. The net is supposed to be a point estimator of $\hat{\theta}_{MAP}$, where $\theta$ are the ...
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How to calculate $P(A|B,C)$ from Bayesian Network?

Say I have a bayesian network B <- A -> C. I need to calculate $P(A|B,C)$. How can I do that? I tried doing: $P(A|B,C)=\frac{P(A,B,C)}{P(B,C)}$ I also tried various other combinations of ...
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Specifying conditional distribution in a Bayesian network

I am trying to learn about Bayesian networks and am really having a hard time to figure out how to setup some simple models. Say, I have a model as: ...
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Can we ignore graphs for inference in linear/Gaussian settings?

Assume I have a linear Bayesian network/graph like the following: where i can derive a joint pdf $$p(\mathbf{x})=p(x_1,x_2,x_3,x_4,x_5)=p(x_1)p(x_2|x_1)p(x_3|x_2)p(x_4|x_3)p(x_5|x_4)$$ Assuming that ...
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Instantiating a Bayesian network with continuous nodes

I am having some confusion regarding how to instantiate Bayesian networks. Let us take an example with smoking and lung cancer. So, we have a simple Bayesian network as: $$\textrm{SMOKING ------> ...
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Initializing the nodes of a bayesian network

I am doing some reading about Bayesian networks and how to represent them with a DAG. I have a question about how to initialize the distribution properties of the nodes. Say there is a Bayesian ...
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I-map Bayesian Network, Practical Explanation

I am having diffculty understanding the concept of an I-map in the context of Bayesian Networks. According to the PGM textbook by Koller & Friedman, an I-map is essentially a set of conditional ...
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In bayesian approach, what is the difference between full posterior and MAP [duplicate]

Consider a classic machine learning problem, which we want to solve using NN. And suppose that we want to use bayesian learning for that. In the bayesian approach the posterior is described as follows:...
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Proving Equivalence between Multivariate distributions and Gaussian Bayesian Networks

I am studying Probabilistic Graphical Models by Daphne Koller. In Chap 7, the authors say the following. I can't convince myself of the highlighted part. Induction typically has a statement for n, ...
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47 views

Pearl's Front-door and Back-door

I've encountered lots of causal inference terms and jargons (under the Neyman-Rubin potential outcome framework), and I had a question regarding how Pearl's DAG restrictions relate to ignorability and ...
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48 views

How can we attribute observations to observers in a hierarchical Bayesian model?

I am trying to make a hierarchical Bayesian model of latent variables based on many observations by noisy oracles. I want to leverage the information of which observations are from which oracles, as I ...
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80 views

Is it practical to distinguish aleatoric uncertainty from epistemic uncertainty?

I know the difference between the two, but don't know if it is practical to tell them apart technically. Say, I have trained a deep neural network and I use some techniques to get the posterior ...
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log trick on message passing in factor graphs

I'm reading Barbers book on Bayesian reasoning and Machine learning http://web4.cs.ucl.ac.uk/staff/D.Barber/textbook/200620.pdf page 90 To give context this is a proof of using the log trick for the ...
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Bayesian and Markovian Networks: How do we obtain the probabilities at each node in a Bayesian or Markovian network

I just have a very basic 2 part question about Bayesian and Markovian networks. I suppose my confusion stems by trying to learn about these things through blog posts and videos, and not being able to ...
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Need help with this Bayesian Network problem?

From the problem above, is P(X|Y) not possible to determined since we are not given P(Y)? I've been stuck with this for days. Please give me some hints. Btw, from the given information, we have P(Y|X) ...
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While Bayesian hypergraphs seem very interesting, won't they be even more data-hungry than Bayesian networks?

There is a part of me that is absolutely enthused that someone has developed Bayesian hypergraphs and that it has causal interpretations related to Judea Pearl's work. But with Bayesian networks ...
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Best way to handle missing data for Network Modelling?

I'm planning to undertake Network Modelling. However, I've been told that multiple imputation is a problem for Network Modelling. I have a lot of missing data. Any suggestions? Thanks!
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Notation of the Likelihood Term in Bayesian Neural Networks

I see that in Bayesian neural networks likelihood function is defined in two ways: $p(W|D) = Z^{-1} p(D|W)p(W)$ or $p(W|y,x)=Z^{-1}p(y|x,W)p(W)$ Are there a slight difference in interpreting $p(D|W)$ ...
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Probabilistic Bethe Lattice Growth: Bayesian or Markov?

Is the growth of a probabilistic Bethe lattice considered a Markov process or a Bayesian network? Consider a Bethe lattice where the coordination number, z, where z is probabilistic and has maximum ...
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Why is the set of parents written as a random variable in Zuk 2012?

There is a convention in statistics to write random variables in capital form, and their instantiations (realizations) in lowercase form. In a given Bayesian network each node will have a given (...
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Moments of Linearly Transformed Laplace Distribution and Assumed Density Filtering

I have been occupied with a question that I assume is not as difficult as I find it to be. The question I want to solve boils down to finding the moments of a linearly transformed Laplace distribution....
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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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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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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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39 views

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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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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348 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
46 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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