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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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Can Conditional Random Fields(CRFs) become a discriminative model by changing partition function?

In Introduction to conditional random fields, page 24, equation (2.18) and (2.19), the linear-chain CRFs is defined as: $$p(y|x) = \frac{1}{Z(x)}\prod_{t=1}^{T}exp\{\sum_{k=1}^{K}\theta_kf_k(y_t,y_{t-...
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About discriminative/generative and directed/undirected graphical model?

I feel that most generative models happen to be DGM(directed graphical model), and most discriminative models are UGM(undirected graphical model). Is there any correlation between these concepts? ...
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Why does Judea Pearl call his causal graphs Markovian?

In his texts on causality, Judea Pearl always refers to the simplest graphs he uses, i.e. the acyclic graphs with independent confounders, as Markovian. I don't see why these graphs contain anything ...
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Graphical model of phylogenetic linear regression

I have been trying to give the graphical model of the PGLS (phylogenetic generalized least squares) but can't seem to fully understand something. PGLS is a generalization of the general linear ...
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Is the Markov Network (Markov Random Field) property biconditional?

As far as I know, the property of a Markov Random Field is defined as follows: Let $G = (V, E)$ be a Markov Network. Let $X, Y, C \subseteq V$. If every path from a vertex in $X$ to a vertex in $Y$ ...
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Convert joint probability distribution in Gaussian graphical model to the general form in the general graphical model?

In the Gaussian graphical model, the joint distribution $p(x_1,\cdots,x_n)$ of p continuous random variables is a multivariate Gaussian: $$ p(x_1,\cdots,x_n)=\frac{1}{(2\pi)^{p/2}|W^{-1}|^{1/2}}exp(-\...
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What is the best method of visualising binary classification preditcions?

I have 2 columns in a dataset, "Device" and "Classification". I want to plot a graph that shows how well the "Classification" result is predicted given the data in the "Device" column. Both columns ...
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Level curves and functions of pair of Random Variables?

I came across the following question: I tried solving it, the following is my 1st attempt:(2nd method at the end) 𝑃[𝑊≤𝑤]=𝑃[𝑋𝑌≤𝑤]=𝑃[𝑌≤𝑤/𝑋] And then I simply double integrated keeping the ...
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How to determine if two directed probabilistic graphical models are I-equivalent?

I'm trying to figure out how to determine if these two models are I-equivalent. Google didn't properly give me a solid answer so far. Any idea on to determine it? Thank you.
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In directed acyclic graphs, is there a dependency in opposite directions?

Suppose we have this graph: (a) ==> (b) ==> (c) Does this mean that P(a|b)=P(a) because the arrows indicate that b is dependent on a and not the other way? If not, then why do we use arrows?
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Why is a single element getting better results than the sum?

I need an intuition how this is possible - Imagine I have a DAG(directed acyclic graph), so a graph without cycles and only directed edges; Now for every DAG with $d$ nodes there is (at least) one ...
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Examples of applications of Markov random fields to data with a small number of variables

I am learning about some of the common applications of Markov random fields (a.k.a. undirected graphical models) to data science. A common feature of many applications I have read about is that the ...
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Can we apply Gaussian mixture model to all kinds of scensrios where some variables are unobserved?

I learned from this answer that: A mixture distribution combines different component distributions with weights that typically sum to one (or can be renormalized). A gaussian-mixture is the ...
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Graph problem with X nodes looking for Y paths with the most similar length. (shortest path / Chinese post man problem)

There is exactly 1 start node and 1 end node. There are also X (in this case 7) nodes, each connected to all other nodes and the start and end node with different lengths of the paths. The visitor ...
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What is the difference between homogeneous Markov chains and unhomogeneous Markov chains?

I learned that a Markov chain is a graph that describes how the state changes over time, and a homogeneous Markov chain is such a graph that its system dynamic doesn't change. Here the system dynamic ...
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Why does different factorisation matter in Markov networks?

I have been reading about Markov Networks that given some set of factors we can construct a unique graph G but not the other way around: "It should also be noticed that, given a set of factors, the ...
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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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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
111 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
58 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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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
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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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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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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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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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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 ...