Questions tagged [graphical-model]
Also called as Probabilistic Graphical Model, 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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Factor Graphs for Distant Supervision
Are factor graphs the state-of-the-art for relation classification with distant supervision? It seems to be the original way (Riedel et al 2010) of dealing with wrong relation mentions. Is it still ...
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How are bayesian networks created from an attribute matrix and target vector?
I'm very familiar with correlation networks but I can't seem to grasp my head around how Bayesian Networks are constructed.
How are the "edges" determined? How is the structure determined? I was ...
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Bayesian Networks - Factor Graphs - Belief Propagation - Numerical stability
I am trying to do inference for a Bayesian Network with discrete probabilities.
I converted the network to a factor graph and implemented the sum-product algorithm (belief propagation). My goal is ...
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138 views
Step-by-step tutorials on Bayesian Networks
I'm trying to study Bayesian Networks (BN), but during classes [1] we covered just some theory and no exercises were given.
Therefore I'm looking for step-by-step tutorials or solved exercises for BN ...
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How can I generate random DAG's in a good way?
I am trying to generate random DAG's (Directed Acyclic Graphs)... However, the result is not very satisfying to me;
What I am doing:
I generate a random graph with the Erdős–Rényi model; More ...
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Algorithm to find number of active paths wrt d-separation in graphical models?
Given a directed acyclic graph $G=(V, E)$ I would like to know how many active paths there are between a pair of variables $v_1, v_2 \in V$ conditioned on a set $K \subset V \ \{v_1, v_2\}$.
I know ...
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Finding a marginal distribution from other overlapping marginal distributions
The setup:
Say you are interested in the marginal distribution $P(X_1, X_2, X_3)$ from the joint distribution $P(X_1, X_2, X_3,X_4)$, but you do not have access to the joint distribution. You do, ...
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1answer
27 views
Definition of distribution conditioned on both a categorical and Dirichlet prior
If we have a conditional categorical distribution, with unknown parameters, we can represent with a table, as in the example below:
\begin{align*}
&z \quad P(z|\theta)\\
&0 \quad \theta_0\\
&...
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When to use all 3 variables in a graph to estimate a conditional expectation of 2
The title might not be perfect. But here goes:
Suppose there are 3 variables $(A,X,Y)$. And they have the following dependencies :
$\Pr(Y,A,X)=\Pr(Y\mid A,X)\Pr(X\mid A)\Pr(A)$
$A \rightarrow (X,Y)$...
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1answer
20 views
How maximal clique parameterization obscures original structure
While reading the chapter on Markov networks, I came across the following statement:
Although it can be used without loss of generality, the parameterization using maximal
clique potentials ...
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1answer
35 views
Interpretation of the forward algorithm
I was reading the book of Jurafsky about HMM and came along this graphic:
The problem that I have is in the interpretation of the graph. According to the problem the hidden states are the weather ...
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51 views
Cox model regression - interpretation of survival graph
I fitted a Cox model and plotted that kaplan-Meier curve with a library survminer and survival in ...
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21 views
Finding most valuable paths
I am trying to analyze a data set of user journeys. My data looks as follows
...
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1answer
130 views
Bayesian networks for one-class classification
From the definition of one-class classification in wikipedia:
In machine learning, one-class classification, also known as unary
classification or class-modelling, tries to identify objects of a
...
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Computing power for linked (i.e., graphs) vs. non-linked data
Why processing linked data (i.e., graphs) require much higher computing power than processing non-linked data?
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How to calculate associated degree of freedom of linked nodes in graph
I am working on text analytics and building a knowledge graph with high frequency entities (noun chunks) as graph nodes and their linkage between co-occurrence in a sentence as edges.
I am able to ...
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51 views
Can someone explain why Bayesian networks are called “Bayesian”
I have been reading Jensen's book on Bayesian Networks and Decision Graphs as well as the Deep Learning book by Bengio, et. al. I am trying to understand why undirected graphs are referred to as ...
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1answer
65 views
Usefulness and Methodology of Probablistic Graphical Models
I took the online course of probabilistic graphical models (PGM) online from Daphne Koller and Eric Xing's videos, but I do not think I get the main idea of PGM, and I would appreciate it if someone ...
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1answer
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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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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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99 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
29 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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26 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
$$ \Pr(A|B) = \frac{\Pr(B|A) ...
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1answer
75 views
Dependency of non descendant in Bayesian Network
I am learning Probabilistic Graphical Models from a book by Daphne Koller and the basic definition of a Bayesian Network says this:
I tried to make a counter example to this and am confused if the ...
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1answer
57 views
Joint distribution in latent Dirichlet model
Given the graphical model of LDA (latent Dirichlet model)
We have the factorization of the joint distribution
$$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
49 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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27 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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66 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
27 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
11 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
23 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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13 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
164 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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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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35 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
25 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
$$
p(a,b,c) = p(a)\,p(c|a)\,p(b|c), \quad p(a,b)= \...
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32 views
computing marginal dependence
I have three random variables $x$, $y$. Let $z$ both $y$ and $z$ depend on $x$ through known distributions $Pr(y|x)$, $Pr(z|x)$ but be otherwise independent: $y \perp z$. The distribution of $x$ is ...
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1answer
114 views
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1answer
47 views
Is there a probabilistic graphical model for this situation?
Suppose we have $3$ random variables, $X, Y, Z$, which verify:
$$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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48 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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47 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
138 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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14 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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0answers
106 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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28 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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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
15 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
35 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
23 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 ...
