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).
482
questions
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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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13 views
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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11 views
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 ...
0
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1answer
54 views
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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0answers
22 views
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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18 views
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 ...
4
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2answers
317 views
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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0answers
11 views
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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23 views
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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17 views
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 ...
1
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1answer
72 views
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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18 views
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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1answer
42 views
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 ...
1
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0answers
32 views
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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0answers
66 views
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, ...
1
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1answer
72 views
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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67 views
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 ...
2
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1answer
44 views
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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0answers
27 views
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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0answers
10 views
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 $n_r$...
2
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0answers
51 views
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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0answers
44 views
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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0answers
19 views
Uniqueness of covariance graphical lasso
Denote the set of all $p\times p$ positive definite matrices by $\mathcal{M}^+$. For $\mathbf{\Sigma}\in\mathcal{M}^+$,define the following function :
$$
u(\mathbf{\Sigma})=\log\det\mathbf{\Sigma}+\...
2
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1answer
66 views
Bayesian and Markovian Networks: How do we obtain the probabilities at each node in a Bayesian or Markovian network
I just have a very basic 2 part question about Bayesian and Markovian networks. I suppose my confusion stems by trying to learn about these things through blog posts and videos, and not being able to ...
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0answers
35 views
EM Algorithm for Kalman Filters
Say I have the following dynamical system with unknown covariances for $w,v$.
$$
z_n = Az_{n-1}+w\\
x_n = Bz_n +v
$$
where $w \sim \mathcal{N}(0,Q)$ and $v \sim \mathcal{N}(0,R)$.
I want to apply the ...
0
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0answers
19 views
Why do we need unary terms in Ising model (pairwise Markov random field)?
Ising model contains both $\phi(i,j)$ and $\phi(i)$.
For example, consider a Markov random field with only two nodes $i$ and $j$, if $P=\phi(i,j) * \phi(i) * \phi(j)$, then we can also write $P=\phi(i,...
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0answers
18 views
Markov networks which are disconnected
I'm reading Kollers book on PGMs. Some of her examples to show the breaking down of theorems around independencies for non positive distributions involve either empty Markov networks or very sparse ...
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0answers
39 views
How are parameters in graphical models learnt?
This is a request of a good reference. I wanted to have a better understanding of graphical models and I am reading "Pattern recognition and machine learning" of Bishop. chap. 8 (Graphical ...
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0answers
24 views
Standard Error of ERGM Coefficients
I am trying to calculate the standard error of ERGM coefficients, which is estimated by MCMC sample.
For an ERGM $P(y;\eta) = \exp[\eta^\top g(y) - \psi(\eta)]$, denote $\eta$ as the true parameter, $\...
0
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1answer
41 views
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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0answers
24 views
Joint and Conditional Distributions in Bayesian Network
In such a graphical model, how can I express the conditional probabilities $p(x_4|x_1,x_2)$ and $p(x_4,x_5|x_1,x_2)$?
My work:
$p(x_4|x_1,x_2) = p(x_1,x_2,x_4) / p(x_1,x_2)
p(x_1,x_2) = p(x_1)*p(x_2|...
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0answers
35 views
Intended selection bias
Sampling or selection bias is often presented as something that has to be overcome, avoided, or at least appropriately considered because it's a problem otherwise. I wonder how often situations arise (...
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0answers
37 views
Re-generate the exact underlying data from an exact MRF model or any other PGMs
I was wondering if there exist a way to re-generate the actual underlying data (not a sample!) from a given exactly learned MRF. In other words, lets say I have a discrete factorised joint ...
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0answers
20 views
I-map construction for non positive distribution
I'm reading Kollers book on PGMs and i'm reading this example about the local independence i-map construction for a non positive distribution.
Example (As requested to be written out): Consider a ...
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0answers
111 views
Weighted adjacency interpretation and visualisation in mixed graphical models
I was wondering if someone could help me understand a bit more about interpretation and visualisation of parameters in mixed graphical models estimated via neighbourhood selection with generalized ...
2
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1answer
94 views
How many parameters does the following Bayesian Network (Graphical model) contains?
These are the relations defined in the graph.
P(D),
P(E),
P(A),
P(C),
P(G|D, E, A),
P(I|E, A, C),
P(T|E, C),
P(F|E, A, C),
P(S|A),
P(J|G, I)
Hello, I have this network that shows a graph (Graphical ...
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0answers
24 views
Probability Graph Model (PGM) and Linear Model (LM)
I was learning PGM recently and wondering if all linear models can be put into the framework of PGM. We know that the linear model is the most important tool in statistical analysis. It can be ...
0
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1answer
66 views
Interpretation of "log-likelihood" in hidden Markov model, and requisite computations involved
I am currently debugging a hand-coded implementation of a hidden Markov model, and as part of this, am scrutinising whether I have appropriately specified the log-likelihood computation algebraically. ...
0
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0answers
15 views
Zero Mean assumption in theory but not in practice?
The paper "Network Inference via the Time-Varying Graphical Lasso" by David Hallac, Youngsuk Park, Stephen Boyd, Jure Leskovec shows how a (time varying) covariance matrix can be shrunk in ...
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0answers
37 views
Markov condition on collider
I am studying Bayesian Networks using the Neapolitan book (Learning Bayesian Networks). In section 1.3.2 it is stated the following:
Definition 1.9 Suppose we have a joint probability distribution $P$...
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0answers
10 views
Finding the factorization of a lattice graph
I'm quite new to the concept of factorization in probabilistic graphs. Can someone talk me through the process of factorization for this graph:
3
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1answer
188 views
Inference in Dirichlet process mixtures via collapsed Gibbs sampling
I need to cluster some data $\{x1, \ldots, x_n\}$ through a Dirichlet process mixture model.
Consider the following Dirichlet process mixture model, in which the base measure is a $NIW(\mu_0, \...
3
votes
1answer
82 views
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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0answers
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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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0answers
38 views
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 ...
1
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1answer
41 views
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 ...
1
vote
1answer
46 views
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 ...
0
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1answer
26 views
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 ...
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0answers
89 views
Book Recommendation for Graphical Models and Bayesian Networks, good for self-study (meaning problems and solutions)
I am watching some of the videos from the Stanford CS 221 course, which goes over issues including Bayesian Networks and Graphical models. There are models where I am trying to learn the joint ...
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24 views
Active paths during marginalization in a bayesian network
Given is the following bayesian network:
Now I need to construct a new bayesian network over all of the nodes except for A which is a minimal I-map for the marginal distribution over those variables. ...
