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).
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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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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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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, $\...
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1answer
40 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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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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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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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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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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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 ...
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1answer
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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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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 ...
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1answer
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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. ...
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13 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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19 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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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:
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1answer
129 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, \...
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1answer
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Build graph of transitive relationships in R [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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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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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 ...
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1answer
29 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 ...
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1answer
36 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 ...
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1answer
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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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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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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. ...
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1answer
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Antique Dealer Problem [closed]
I have a problem related to the industry I work in which I think can be addressed with a probabilistic graph model. Unfortunately, this is something I know nothing about.
I'm paraphrasing the problem ...
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What is a sepset in a probabilistic graphical model?
The terminology sepset is used quite often in the Probabilistic graphical models and causality. What does it mean and what is its relevance ?
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What if zero mean assumption is relased in graphical LASSO?
I am working on a graphical LASSO (GLASSO) shrinkage of the variance-covariance matrix of financial log-returns data for 10 years. The objective of the graphical LASSO is:
$$\ell(0,\Sigma) = {-\text{...
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What exactly is the point of computing a lower bound for the log partition function in variational methods in probabilistic graphical models?
Variational methods are applied when we are interested in a probability distribution $P$ but only have a tractably computable unnormalized form $\tilde{P}$ of $P$. Knowing the partition function $Z = \...
2
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1answer
187 views
Gibbs sampling with Poisson Gamma models
I am trying to obtain a Gibbs sampler for a Poisson-Gamma topic model. Essentially, for each document $d$, the likelihood of $d$ depends on a Poisson parameter $\lambda_d = \sum_k \pi_{k,d}\phi_{k,w}$....
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Learning unknown independent sets of variables
Let $(X_{j})_{j\in S}$
be random variables where $S=A\cup B$, $A\cap B=\emptyset$ and
$$
P(X_1,\ldots,X_{|S|})
=P(X_A)P(X_B).
$$
Given $n$ iid samples, the problem is to learn $A$ and $B$, which are ...
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Learning Event Order of Non-ordered Events from Already Ordered Events
Is there a name for the problem of taking ordered and non-ordered nodes, and creates an ordering of the non-ordered nodes based on the ordered nodes, with the requirement that preexisting ordering be ...
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Formalizing variable length recurrences of random variables
I'm not a statistician (just a barely proficient user of rudimentary bayesian stuff in the context of ML), so the questions I have below may be very dumb and easily answered by pointing me to lecture ...
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Most likely assignment in MRF with a global constraint
I have a MRF where all potentials are on pairs and all variables are binary. I want to find the most likely assignment of variables, under the constraint of at most $k$ variables being 1.
Can this be ...
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How can one solve house price prediction problem with probabilistic graphical models? [closed]
for predicting house prices one typical way is to create a dataset with various input variables (such as area of the house, number of rooms, etc.) and the output variable (price of the house) and then ...
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Graphical Representation of Dynamic Bayesian Network
Some tourists visiting a cabin are interested in finding out if there are animals nearby. They can observe outside of their window every day whether there are animal tracks and whether the food they ...
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1answer
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Disconnected components in graphical models
Suppose we have a graphical model defined by a directed acyclic graph $G$. Suppose that a node $a$ divides $G$ into two connected components. By this I mean that:
$G=G_1 \cup G_2 \cup \{a\}$
$G_1 \cap ...
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1answer
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Simpson's paradox in Judea Pearl's book?
I'm looking at the following question in Judea Pearl's primer on causality
In an attempt to estimate the effectiveness of a new drug, a randomized experiment is conducted. In all, 50% of the patients ...
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81 views
Temperature in Softmax and simulated annealing in Metropolis-Hastings?
We can add a temperature to the Softmax to make the Softmax softer or harder by setting it higher or lower(refer to this answer). And in reinforcement learning, a high temperature will lead to the ...
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How do you write factor operations for rule-based conditional probability distributions?
Supposing I have rule-based conditional probability distributions (CPDs), $\{P(X|\text{Pa}_{X}), \cdots\}$, in a graphical model each represented as a set of rules $\mathscr{R}$ such that:
For each ...
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Why does using conditional random field avoid independence assumption
I am reading about conditional random fields in Daphne Koller's book on probabilistic graphical models. One of the advantages to using CRF is that we can avoid modelling the correlations between ...
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1answer
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Sufficient statistic definition in Koller's Probabilistic Graphical Models
In Daphne Koller's Probabilistic Graphical Models, the sufficient statistic is defined as follows (p 721):
A function $\tau(\xi)$ from instances of $\chi$ to $\mathbb R^l$ (for
some $l$) is a ...
2
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1answer
25 views
Dynamic bayesian model conditional independence
I have just started learning probabilistic graphical models, so my knowledge of this subject is relatively weak. Hope I don't make any mistakes in my question.
Given the Dynamic Bayesian model shown ...
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Likelihood of a latent graphical model
What is the approach to take when trying to find the likelihood of the observations on a latent graphical model, with intertwining conditional distributions?
The model:
Each vertex $X_i$ of a binary ...
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45 views
Computing factor function in a factor graph
Consider a factor graph with three binary variables X1, X2, X3 connected to one hard constraint factor f whose compatibility function imposes a OR function, i.e. f(x1, x2, x3) = 0 if x1 = x2 = x3 = 0, ...
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Where do the “semantics” of a Bayesian network come from?
On Bayesian Networks, Ghahramani (2001) says:
A node is independent of its non-descendants given its parents.
This point is fundamental enough that Ghahramani calls it the “semantics” of a Bayesian ...
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1answer
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Is there any work on, given a set of conditional independences, build the graphical model?
The graphical model Represents probabilistic independence.
Given a set of conditional independence assumptions, how to find the probabilistic graphical model that maximizes some metrics (e.g, minimum ...
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Making sense of the belief propagation on graphs
I sort of understand when do I use variational Bayesian and when do I use expectation maximization. But now I want to know when do I use belief propagation in graphs to solve an estimation problem.
...
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1answer
96 views
What is the application for using the `Boltzmann Machines`?
I've came across this post from wikipedia about Boltzmann machines, which concludes that it is not a model that is usually used in practice, and that its' ...
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1answer
66 views
Introduction to approximate message passing
I'm interested in learning approximate message passing from the paper "Message Passing Algorithms for Compressed Sensing: I. Motivation and Construction". My background is in computer ...
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Purpose of the hidden variables in a Restricted Boltzmann Machine [duplicate]
From the part titled Introducing Latent Variables under subsection 2.2 in this tutorial:
Introducing Latent Variables. Suppose we want to model an $m$-dimensional
unknown probability distribution $q$ ...
