# Questions tagged [graphical-model]

Also called Probabilistic Graphical Model, used for statistical models expressed via graphs, causal or not. (Nb, "graph" as in graph theory, *not* as in figure or plot).

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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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### Directed graphical models and independence (exercise)

Context: this is Ex. 1 in these notes http://www.stat.cmu.edu/~larry/=sml/DAGs.pdf . The exercise asks to prove that, given a directed graphical model associated to a DAG (directed acyclic graph) $G$: ...
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### R - glasso very slow even with low feature space [closed]

I have generated a positive definite, symmetric inverse covariance matrix to use with graphical lasso. However, the glasso package takes an extremely long time to ...
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### Drawing graph of variance using R [closed]

I am a self -learner and try to learn statistics with R ,but i encounter with a problem i could not handle it such that I want to produce a graph of the variance of a binomial distribution with a ...
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### Metropolis Hastings on hierarchical bayes update question:

[I have this somewhat complicated hierarchical bayesian model]1 Here the $y$ on $\theta$ are Poisson, $\theta$ are deterministically generated from the $att, def$ (and $home$). Then the last ...
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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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### Are all statistical models also causal models?

I'm just starting to learn about causal inference methods, focused on Pearl's do-calculus. So the point between Pearl's causal graphs and rules for manipulating causal graphs appears to be to turn a ...
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### Reference Request: Variational Expectation-Maximization algorithm for Latent Dirichlet Allocation with an added time component

This link has a pretty good runthrough on the variational inference (via variational E-M) for LDA with calculations expanded and explained. I am now considering a modified LDA which adds a time ...
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### Proof of multivariate distribution using exponential families and Hammersley Clifford Theorem

I'm reading the following seminal paper by Besag http://www2.stat.duke.edu/~scs/Courses/Stat376/Papers/GibbsFieldEst/BesagJRSSB1974.pdf I'm unsure how they prove on page 10 equations 4.4 and 4.5 ...
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### Differentiating entropy in Reinforcement Learning as Probabilistic Inference

I am studying the paper Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review (https://arxiv.org/abs/1805.00909) and I do not understand how the author differentiate the ...
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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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### 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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### 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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### Factor graph vs "moral graph" (preprocessing for belief propagation)

Some articles* about belief propagation formulate the algorithm in terms of undirected graphical models. Thus if we had a directed (acyclic) graphical model, it would need to be preprocessed into an ...
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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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### Variational Autoencoders and Probabilistic Graphical Models

I am just getting started with the theory on variational autoencoders (VAE) in machine learning and I keep reading that VAEs belong to the category of Probabilistic Graphical Models (PGMs). As I ...
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### Node2Vec: BFS versus DFS

In the paper that introduced Node2Vec, the authors mention the following: The neighborhoods sampled by BFS lead to embeddings that correspond closely to structural equivalence. Intuitively, we note ...
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### modification of variable elimination for underflow

In Daphne Kollers book on Probabilistic graphical models exercise 9.3 asks the following Ex 9.3 Consider a modified variable elimination algorithm that is allowed to multiply all of the entries in a ...
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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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### Stochastic Block's Model : Number of edges in a block?

So I am really confused about the number of (maximum possible) edges between two blocks in Stochastic Block's Model. In my understanding given two blocks or communities $b_r$ and $b_s$ containing $n_r$...
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### What does the superscript triangle (△) symbol mean in graph/causality notation?

I am reading a paper called Robustly Disentangled Causal Mechanisms: Validating Deep Representations for Interventional Robustness and in stating a proposition the authors use a triangle superscript ...
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### Which DAG would explain the lack of correlation between height and performance in NBA players?

A classic example of "selection bias" involves looking at the performance of professional basketball players. The example goes, among NBA players there is no correlation between height and ...
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### Training in Restricted boltzman machine

I am having doubt in training part of RBM's. I am confused between whats the difference between training RBM by block gibbs sampling and training RBM using contrastive divergence?
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### Build graph of transitive relationships [closed]

I am wondering given the type of directed graph A, how do I convert it into the type of directed graph B? Basically, in graph B, I want to ignore Node X and only retain the Node T. Conceptually, I am ...
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### Estimating future graph size given partial graph size

(This question compares a branching-fiction novel to a disease, bear with me.) This is for fun, my friends and I are writing a branching-fiction novel: A black node is a concluding chapter ("The ...
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### How to fit a mixture of 2D Gaussian in BUGS/JAGS?

I am trying to estimate the parameters of a mixture of 2D Gaussian distribution using JAGS. I first created two components from a multivariate normal distribution and then combined them to get a ...
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### Understanding original LDA article

I decided to write a different question as a follow up to a comment here about LDA : Upgrading weight parameters to random variable in Gaussian mixtures I am trying to read about latent dirichlet ...
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### 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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### Name of statistical animated visualization

What is the name of the kind of animatrd graph that show a development over a period of time - and the vertical bars change length and order. Fx country on y-axis, no of COVID-19 cases on x-axis, and ...