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Used for statistical models expressed via graphs, causal or not. ("graph" here as in graph theory). See https://en.wikipedia.org/wiki/Graphical_model

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What is an “undirected associative memory” in Hinton et al 2006?

In A fast learning algorithm for deep belief nets, the authors use the term "undirected associative memory". I am not sure what they are referring to, and unfortunately Google searches for this term ...
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9 views

How to aggregate various weak signals to predict a latent variable?

A Modelling Question This is a high-level question, I want help on how to model a situation like this. It's easier to explain with an example. Let's say we want to estimate the probability that ...
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0answers
69 views

Problems with Graphical Lasso

I'm trying to use the Graphical Lasso algorithm (more specifically the R package glasso) to find an estimated graph representing the connections between a set of nodes by estimating a precision matrix....
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0answers
23 views

Probability of correct classification

I am studying this article https://arxiv.org/pdf/1212.0478.pdf, in which the authors propose a method to predict the graph structure of a graphical model. In the "Simulations" paragraph, they plot ...
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0answers
26 views

HOW TO - Applying MCMC to conditionally select random variables?

I am quite new to the using Graphical Models, so pardon me for the naivety. My intention is to have some fun for the weekend and impress my friends on Monday. I am trying to understand MCMC and ...
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0answers
12 views

Deterministic Functions in Probabilistic Graphical Models

Suppose I have two variables, $A$ and $B$, where $B$ is the observed (measured) variable, and $A$ is the one we want to infer. Bayes rule would give us the inference rule $$ \Pr(A|B) = \frac{\Pr(B|A) ...
3
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1answer
49 views

Dependency of non descendant in Bayesian Network

I am learning Probabilistic Graphical Models from a book by Daphne Koller and the basic definition of a Bayesian Network says this: I tried to make a counter example to this and am confused if the ...
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1answer
33 views

Joint distribution in latent Dirichlet model

Given the graphical model of LDA (latent Dirichlet model) We have the factorization of the joint distribution $$P = \prod_{d = 1}^{D}P(\theta_{d}|\alpha)\prod_{n = 1}^{N}P(z_{d, n}|\theta_d)P(w_{d, ...
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1answer
33 views

Understanding parameter sharing within Bayesian Networks

I am learning about probabilistic graphical models and am a bit confused by the idea of parameter sharing. In the image below, I have been told that the parameters of time slice 0 are copied to time ...
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0answers
14 views

gLASSO - regularization makes upper and lower triangles of estimated matrix equal

The overall goal is to get an estimate of the precision matrix (inverse of a covariance matrix given some nxp data), which can be translated into a graph showing the partial correlation relationships ...
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0answers
15 views

How to remove the effect of confounding variables in sparse linear models?

I would like to build sparse linear regression model, but I would like to remove the effect of (hidden) confounding variables that control the input features and output variables jointly. I was ...
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0answers
25 views

How to interpret graphical model for Dirichlet process mixture for variational inference?

I am working through this paper by Blei and Jordan, which introduces variational inference for Dirichlet process mixtures. They derive an evidence lower bound (ELBO) function based on a stick breaking ...
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0answers
9 views

What is the effect of conditioning on more than one variable in partial correlation?

I'm computing different of correlation and partial correlation for two different situations: $A=cor(y_1 ,y_2) - pcor(y_1,y_2|x_1)$ $B=cor(y_1 ,y_2) - pcor(y_1,y_2|x_1,X_2)$ Is it possible that $A<...
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0answers
13 views

A Modified Regression Algorithm for Estimation of an Undirected Gaussian Graphical Model with Known Structure

I tried to learn the modified regression algorithm given the the chapter "Graphical model" in the book "Elements of Statistical Learning". But all effort is in vain. Would someone explain me the ...
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0answers
12 views

Fitting undirected graphs with fixed missing edges

How can we fit a model like the one below, forcing the missing edges to be omitted? X can be assumed as Gaussian distribution. I tried to solve this using the modified regression algorithm and using ...
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1answer
53 views

How to find the conditional distribution of gaussian from covariance matrix?

I know that the conditional distribution of two gaussian is gaussian. But in the following statement how does the Θ captures the conditional distributions? And what do they mean by the term "captures"...
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0answers
25 views

Derivation of gaussian graphical model in undirected graphical models

I tried to figure out the mathematical calculation related to gaussian graphical model given in the book "Elements of Statistical Learning". But I am not able to conclude (1) How they calculated ...
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0answers
30 views

factorizing a joint density by its undirected graph

For an undirected graphical model, we can find the set of maximal cliques. For each maximal clique $C$, we can define a potential function $\psi(x_{C})$. Thus, the joint distribution $P(x)$ that is ...
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1answer
23 views

graphical models: integration rules over conditional prob distns

Suppose we have a graphical model over three RVs $a,b,c$  [![enter image description here][1]][1] whose conditional independence structure gives  $$ p(a,b,c) = p(a)\,p(c|a)\,p(b|c), \quad p(a,b)= \...
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0answers
16 views

computing marginal dependence

I have three random variables $x$, $y$. Let $z$ both $y$ and $z$ depend on $x$ through known distributions $Pr(y|x)$, $Pr(z|x)$ but be otherwise independent: $y \perp z$. The distribution of $x$ is ...
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1answer
62 views

Directed Acyclic Graph of Stan Model

I have the following Stan model: ...
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1answer
36 views

Is there a probabilistic graphical model for this situation?

Suppose we have $3$ random variables, $X, Y, Z$, which verify: $$I(X,Y), I(X,Z), I(Y,Z),$$ where $I(·,·)$ means the variables are independent, and $$D(Y,X \ | \ Z), $$ meaning $Y$ and $X$ are ...
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0answers
38 views

Do I have to use Relative standard error?

I have longitudinal data from 2 different groups of treatments. I want to express the data as the percentage from baseline. I have been told since the data is in percentage, then I have to express the ...
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0answers
33 views

Inference from Gaussian Graphical Model (using gRim package R)

I am trying to learn GGMs using gRain and gRim packages in R and following Søren Højsgaard's "Graphical Models in R". Using the carcass dataset in the gRbase project, I have created a toy graphical ...
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1answer
130 views

Support vector machines (SVMs) are the zero temperature limit of logistic regression?

I was had a quick discussion recently with a knowledgeable friend who mentioned that SVMs are the zero temperature limit of logistic regression. The rationale involved marginal polytopes and fenchel ...
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0answers
11 views

Building a directed acyclic graph with a fixed covariate and 0 to 3 copies of a 'fluid' covariate

apologies for the possibly confusing title since I myself don't know how to formulate the problem into a suitable ML construct. I have a set of patients (n=60) with neck cancer. From every individuals ...
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0answers
19 views

Unbiasedness of confounding variable models

This is a question based on work in this paper: https://dl4physicalsciences.github.io/files/nips_dlps_2017_14.pdf I am interested in causality and representations using probabilistic graphical ...
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31 views

How to implement weighted centrality in NetworkX

I am using the following code to try implement eigen-vector centrality for a weighted graph G. The nodes represent search terms and the is an edge from node A to node B if someone searches for A and ...
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0answers
21 views

A conditioning simplification in a graphical clustering model

The graphical model associated with this problem is (reproduction from Murphy's Machine Learning a Probabilistic Perspective) and the author argues on page 843 of MLAPP, Intuitively, it is right. ...
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0answers
11 views

generate igraph with varying graph level centralization [closed]

How do I generate several igraphs with varying graph level centralization? I am familiar with sample_(...), that variations of 'sample_' allow me to generate graphs GIVEN a MODEL....but not given ...
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1answer
13 views

Convention on size of graph/network

Is there a standard that can help me define a network/graph as large or small? I am testing a method and would need to see how my proposal works for large and small networks. It would help if there is ...
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1answer
26 views

Bias correction of a sampled igraph

Suppose I have a sample (S) of a graph where S is a subset of G -- the population Graph. Is there a way (theoretical) to compute for bias in the estimation of centralization (as in igraph::...
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0answers
19 views

Can belief propagation be used to infer latent variables?

Consider a simple Bayes net of linear Gaussian, $A\rightarrow B \leftarrow C$. If $B$ is observed, $A$ and $C$ are hidden (assume we have set priors for the hiddent variables), can we use belief ...
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1answer
49 views

Can you claim P(B|C) >= P(B|A,C) for a Bayseian network of the graphical model “A-->C; B->C”?

Consider a Bayesian network where A and B are independent. Intuitively, since both A and B can influence C, the probability of B given C should drop if A is observed. Question Does $$P(B|C)\geq ...
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1answer
191 views

I have conducted a Chi-Squared test in R, and want to know how to display observed vs expected values in a barplot?

Essentially I have my data, and easily calucalated the chi-squared statistic. Now I have this, I want to create a bar plot with my observed values beside the expected, for the relevant groups. I ...
3
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1answer
39 views

Markov random field potentials

Consider a pairwise Markov random field, for any two neighbours $A$ and $B$, is it correct to use any function to describe the relationship between them? Is there any constraint or any condition that ...
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0answers
14 views

Graphical Model Representations for Temporal Point Processes

Are you aware of any graphical model representations of probabilistic model that contain temporal point processes? The only such representation I found was in this paper : https://www.cc.gatech.edu/~...
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3answers
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Predicting which cars and systems were fixed from the parts that were ordered

Interesting problem from the auto industry. Wondering if anyone has suggestions on a good approach. Auto manufacturer sells cars to independent dealers who sells to end-customers. When cars break down,...
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1answer
28 views

Graphical Model: MAP optimization vs belief propagation

Assume there are three types (sets) of variables $X$, $Y$ and $Z$ in a graphical model where $X = \{x_1,x_2,\dots,x_m\}$, $Y = \{y_1,y_2,\dots,y_n \}$ and $Z = \{z_1,z_2,\dots,z_k\}$. Further, $Z$ is ...
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0answers
32 views

Neural Network or Differentiable Graph Matching

Searching for: Neural Network solutions or implementations (learnable algorithm) for inexact graph matching. Graph matching: Given two graphs GM = (VM , EM) and GD = (VD, ED), with |VM| = |VD|, ...
0
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1answer
132 views

Calculate probability using tree diagram and bayes theorem

We have the tree diagram as shown below, I'm asked to find probability that a child who tests as right-handed will be left-handed? I know we have to use Bayes Theorem and find ... P(Actual Left ...
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0answers
16 views

What is the meaning of the clique-function when factorising undirected graphs?

I am currently reading Graphical Models and Message-Passing Algorithms: Some Introductory Lectures and am quite at the beginning. I understand the factorization for directed graphical methods, which ...
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0answers
38 views

Conditional Independence of Gaussian Mixture Models

In this paper, it claims that $\mu_j$s are independent to each other, given the hyperparameters and the observations. However, the Markov blanket of $\mu_j$ includes $\mu_i (i\neq j)$. Why $\mu_j$s ...
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0answers
64 views

how are messages processed in the nodes of probabilistic cluster graph? [closed]

I'm trying to understand the behavior of message passing in cluster graphs used in graphical probabilistic models. Each node is responsible for a set of variables. Does each node store a joint ...
2
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0answers
47 views

Gaussian Mixture Division

In the study of probabilistic graphical models (PGMs), the loopy belief update propagation (LBUP) message passing algorithm requires the division of unnormalised probability distributions. If the ...
0
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0answers
12 views

Simple way to cluster in the rows of a multivariate dataset

I have a multivariate dataset, with variables on the columns and observations on the rows. The raw data is continuous and a multivariate log normal assumption could be feasibly applied, but typically ...
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1answer
29 views

Strongly Correlated Variables in a Bayesian View

Reading about bayesian graphical models, I have come up with an example that I don't really know how to best adress. Let me start with some prose on what I am thinking about, and then get to the ...
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0answers
17 views

Are joint distributions of roots independent in a PGM (Probabilistic Graphical Model)?

As stated in the question: Is the case in general that given the graph below the following relationship will hold? P(A, C) = P(A) P(C) I will edit later to ask this question in a general ...
2
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1answer
93 views

A question about flow of influence in Probabilistic Graphical Models from Daphne Koller's coursera course

The question is about the following slides: I have confusion regarding the second and the third statements. Regarding the second statement ("If I not observed nor is anything else"). Here, we get the ...
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0answers
33 views

Deterministic CPD's independencies in PGM

I am studying Probabilistic graphical model based on this course and book by same professor. I am reading deterministic CPD's independency. Seeing the image below from the lecture, the lecture says if ...