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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19 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. ...
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31 views

Antique Dealer Problem

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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11 views

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 = \...
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61 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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22 views

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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33 views

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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33 views

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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Is “how happy you are” a categorical variable?

I've decided to make a mood tracker I want to track my weekly progress. Anyways, the most random question popped into my head. So, in my mood tracker graph, my x-axis is the days of the week (monday, ...
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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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Simpson's paradox in Judea Pearl's book

I'm looking at the following question in Juda 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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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 Daphne Koller's book on probabilistic graphical models under the topic of conditional random fields. One of the advantages in using CRF is that we can avoid modelling the correlations ...
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101 views

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 ...
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24 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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36 views

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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42 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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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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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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57 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 $q$ ...
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How to incorporate multiple likelihoods in a probabilistic graphical model with Stan?

Data composition: In beta testing of a video game, users were assigned tasks in a many-to-many relationship. At the end of every day, users were asked to self evaluate (for each task) whether they ...
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32 views

Effect of treatment on the treated using the graph

From the diagram, I need to find the effect of education on those students whose salary is $Y=1$. I was given the hint to use $E[Y_1 − Y_0|Y = 1]$. My attempt: I tried to expand the above equation and ...
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If the sample size is > 100, which graphical summarization is the best? [closed]

Box and whisker plot 3D doughnut plot Heatmap depicting expression levels Line plot Column scatterplot
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Interpretation of concentration of posteriors in the limit of infinitely many independent versus dependent random variables

Disclaimer: the setup and specific example may not be a minimal example to illustrate the point, but I am not well-versed in these topics enough to construct a smaller example without accidentally ...
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Why can't Bayesian and Markov networks represent all conditional independencies in a joint distribution?

From here: An I-map is said to be perfect if $I(G)=I(p)$. Given a distribution $p$, it is not always possible to find a DAG $G$ such that $I(G)=I(p)$. Consider a joint distribution over four random ...
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34 views

Finding the probability based on the given graph

I have a graph $G_1\rightarrow G_2\rightarrow G_3\rightarrow G_4$ which has random variables and it's probabilities are given by $$P(G_i=1|G_{i-1}=1)=a$$ $$P(G_i=1|G_{i-1}=0)=b$$ $$P(G_1=1)=a_0$$ I ...
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Predict edge weights from known connectivity but limited edge weight data

If I have a known adjacency matrix for a connected, undirected graph, and if I know some of the edge weights, what methods or techniques could I use to predict the weights of other edges? So in my ...
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What is the name of this weakened naive Bayes assumption?

The naive Bayes assumption is just the assumption that a probability distribution over several variables factors into the product of all the one-dimensional distributions. This is equivalent to saying ...
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99 views

Do we assume graphical LASSO explanatory variables to be normally distributed? And what if this assumption fails?

I am working on a graphical LASSO (GLASSO) shrinkage of the variance-covariance matrix of financial log-returns data for 10 years. I tested for normality and the Jarque-Bera test (but also other tests)...
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1answer
39 views

Spirtes' example of d-separation not leading to independence in a directed cyclic graph with non-linear structural equations

In Spirtes (1995) there is an example (Fig. 4 on page 495, reproduced below) of a directed cyclic graph with non-linear structural equations in which $d$-separation of $X$ and $Y$ given $\{Z, W\}$ ...
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55 views

imputing high percentage of missing data in multivariate time series

In a dataset with time-series, that is dependant on a given input, which the time-series are given only on an irregular cycle of 10-12 time steps that makes lots of missing observations what is the ...
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33 views

Graphic model factorizing, marginalization

This is actually a probability marginalization question that I encountered in graphic models section of PRML by Bishop (question about equation 8.26 page 391). Assume I have the following graphic ...
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Packages for autoregressive HMM?

I have data I'd like to fit a generalized HMM on: my observations $\{Y_t\}_{t=1}^N$ and my states $\{X_t\}_{t=1}^N$ are both time series. The specific task I'd like to do is decoding the states given ...
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41 views

Do variational approximations capture the flow of influence or “conditional independence” relationships in graphical models?

Probabilistic Graphical Models (PGMs) are used to model all sorts of complex decision processes, such as medical diagnoses or robot positions, etc. In common machine learning textbooks, like ...
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22 views

properties of Gaussian graphical model of sub-covariance matrix

I'm working on Gaussian graphical models. The precision matrix is $$\Theta = \Sigma^{-1}$$ What properties does the sub-matrix have? To be more specific, $$\Theta' = (\Sigma_{A,A})^{-1}$$ $A$ is the ...
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25 views

What is the benefit of adding control flow to probabilistic programming?

I was watching an interesting video on the Pyro package in Pytorch for probabilistic programming. One of the things that they ...
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1answer
29 views

Are nodes outside the markov blanket unconditionally independent?

Apologies if my question is deeply flawed, I've been working through a lot of material in the past few weeks and have a few blind spots here and there. On one level my question is this - given a ...
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672 views

Strong ignorability: confusion on the relationship between outcomes and treatment

In the research area of potential outcomes and individual treatment effect (ITE) estimation, a common assumption called ''strong ignorability'' is often made. Given a graphical model with the ...
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25 views

Deriving Hyperparameter updates in Online Interactive Collaborative Filtering

I've been going through "Online Interactive Collaborative Filtering Using Multi-Armed Bandit with Dependent Arms" by Wang et al. and am unable to understand how the update equations for the ...
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39 views

Bayes network, what is the purpose of it?

I really don't understand what is the purpose of the Bayes network, actually how to implement it into a useful application. It all starts with the data. Let's assume I observe some universe and I ...
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d-separation and implication of its theorem

Let $(X\perp Y | Z)_P$ represents the conditional independence of X and Y separated by Z. I am very confused about the following theorem about d-separation from Judea Pearl's text which says the ...
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Causality: Implication of d-separation

I am confused about the following theorem about d-separations from Judea Pearl's causality textbook which reads as follow: "If sets X and Y are d-separated by Z in a DAG G, then X is independent of Y ...

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