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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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Conditional Independence in Bayes Network

I have just started working through Michael Jordan's notes on Probabilistic Graphical Models and seem to be stuck on the exercise on page 5. I summarize the question here: Suppose $G = (V,E)$ is a ...
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Tool to draw neural network directed graphs [closed]

I would like to reproduce the kind of graphs used in the book Deep learning. Do you know the tool which can do that kind of graphs? Ideally I would like the apparence to be exactly the same. Here is ...
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forward sampling for Bayesian network with continuous variables and equation-based causal relationships

I have a physical system which can be represented by the following Bayesian network. It has the following characteristics 1) The encoded variables are continuous variables 2) The causal ...
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How do PGMs factor in to modern ML?

I just finished the three-part series of Probabilistic Graphical Models courses from Stanford over on Coursera. I got in to them because I realized there is a certain class of problem for which the ...
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1answer
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Uncertainty and confidence in classification

I have a multi class classifier with 30-40 different classes. When i predict a class i would like to get an estimation about how certain my model is with its own prediction of that single sample . i....
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Understanding probabilistic inference graphs

I am having trouble understanding inference graphs. In the diagram below I understand the graph on the left (forward graph) where the arrows describe the direction that data flows when training for ...
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If I(G) = I(G') do they have the same skeleton and the same v-strucures except those in complete (sub-) graph?

I thought if two different graphs G, G' have the same skeleton and the same v-structure, then I(G)=I(G′) and I(G)≠∅. But does the converse also holds? In this case a complete graph doesn't apply ...
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Do all P-Maps for a distribution share the same skeleton or/and v-structures?

I learned that a distribution may have multiple P-Maps because even if we are sure about the independences in a graph we cannot gurrantee the causal direction, then I just wonder if those P-Maps share ...
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Resources for prerequisites to Probablistic Machine Learning Models

I am a self-learner and have done several machine learning courses but diving into Bayesian or Probabilistic Graphical Models I feel like my prior knowledge is inadequate. I have done some Probability ...
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How to use a G-Wishart distribution in stan

I would like to use the following kind of prior in a Stan simulation $$ f_{K \mid G} (k \mid g) = \frac{1}{I_g(b,D)}|k|^{\frac{b-2}{2}} \exp \biggl \{ -\frac{1}{2} \text{tr} (Dk) \biggr \}\mathbb{1}_{...
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EM Algorithm for Bayesian Networks with missing data

Setting: learning parameters of Bayesian Network (BN) with missing data. Algorithm: Expectation-Maximization. Question: suppose I am in the M-step, and that in the complete data there are no ...
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1answer
108 views

Is this formula related to the energy function / boltzmann distribution?

I am reading research done in this thesis. On page 20-21 (section 2.1) of the thesis, it describes the following stochastic model: ... let us focus for the rest of this chapter on time-varying ...
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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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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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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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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
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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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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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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
153 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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56 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
68 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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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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106 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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131 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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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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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
106 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
64 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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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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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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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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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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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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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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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
199 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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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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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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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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Directed Acyclic Graph of Stan Model

I have the following Stan model: ...