# 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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### Implications of violating Bayesian network independence assumptions during inference

Consider the example Bayesian network below where $X \perp \!\!\! \perp Y$ (X is independent of Y). Assuming that this is the true independence structure of the process that is generating the data, ...
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### Problems with zero probability events in Bayesian Networks

In the book Probabilistic Graphical Models: Principles And Techniques by Daphne Koller, the author at one place (Box 3c), states the challenges in picking probabilities for a Bayesian network model. ...
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### sigma-separation question in cyclic causal graph - understanding sigma-separation

Main Question In https://arxiv.org/pdf/1807.03024.pdf, a generalization of d-separation in DAGs is introduced, called $\sigma$-separation for cyclic graphs. I am wondering how $v_1 \perp v_6$ using ...
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### ignorable assignment mechanism in causal studies

In the causal studies, there is so-called ignorable assignment mechanism. For instance, The vast majority of causal studies assume certain versions of an ignorable assignment mechanism, where the ...
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### How many parameters on a Bayesian network

I'm taking Coursera's course on probabilistic graphical models, and I'm stuck on a question. The discussion forums there are dead, and I can't find any resource to help me, so I hope someone could ...
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### Expression for $p(\mathbf{s}|\mathbf{d})$ and the respective Markov Network

I would like to check if I correctly derived my the expression for $p(\mathbf{s}|\mathbf{d})$. Here's the question: Consider a model of diseases and symptoms. $s_i\in\{0,1\}$ is a binary random ...
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### Quick way to determine the different independence assumptions

This question is different than my previous question in that I'm asking sort of a "meta" question. Here's two graphical models (a Belief Network and a Markov Network): I would like to ...
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### Determining unconditional independence in Markov Networks

I would like to know whether $E \perp\kern-5pt\perp A$ in the following Markov Network and would like to know if my reasoning is correct: So, since this is a Pairwise Markov Network, it factorizes ...
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### Checking for conditional independence in graphical models

I would like to know whether $B \perp\kern-5pt\perp C | D,A$ and $D \perp\kern-5pt\perp A | B,C$ in the following two graphical models and would like to know if my reasoning is correct: For the ...
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### Is $C \perp\kern-5pt\perp D | A$ for the two graphical models? [duplicate]

I would like to know whether $C \perp\kern-5pt\perp D | A$ in the following two graphical models and would like to know if my reasoning is correct: For the left model (Belief Network), here's my ...
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### Is $B \perp\kern-5pt\perp C | A$ for the two graphical models?

I would like to know whether $B \perp\kern-5pt\perp C | A$ in the following two graphical models and would like to know if my reasoning is correct: For the left graphical model, which is a Belief ...
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### What exactly would be a perfect map in this situation? Is a perfect map a distribution which has the same independence assumptions?

I am currently studying Bayesian Reasoning and Machine Learning by David Barber, the 4th chapter exercise 4.7 (p 80). The exercise is the following: Consider the following belief network: Write down ...
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### Is it always possible to find a joint distribution $p(x_1,x_2,x_3,x_4)$ consistent with these local conditional distributions?

I am currently studying Bayesian Reasoning and Machine Learning by David Barber, the 4th chapter exercise 4.1 (p 79). The exercise is the following: Exercise 4.1 Consider the pairwise Markov network, ...
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### How can I find Conditional Probabilties from dataset points of features (random variables)?

I am trying to solve the following at work and will dummify for the sake of making it easier to explain myself and getting an answer. My main query is about Step 4 below. But if something is wrong or ...
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### Why are undirected graphical models (MRFs) not represented directly in terms of probability like directed graph models?

I have been reading the Deep Learning Book by Ian Goodfellow, and in that, there is a discussion about graphical models like Bayesian belief networks and Markov Random Fields. Here: One key diﬀerence ...
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### Bayes graph model parameter dependencies problem with prior density

Suppose I have a graph model with underlying density (denote $f(\theta_1|\theta_0):=f(\theta_1)$) $$f(\theta|x)\propto \prod_{i=1}^k f(x_i|\theta_{1:i})f(\theta_i|\theta_{1:i-1}).$$ Suppose markov ...
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### How can I model, and train a Bayesian Netwok from a given dataset for predicting cause-effect scenario?

I have a dataset that I used to train my ML model for prediction. I created my prediction models using XGBoost and Neural Networks. Now I want to create another model that can give me the causal ...
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### Why do we calculate probability distribution on leaf nodes at Sum-Product Networks (SPN)?

I am new to Sum-Product Networks (SPN) and still trying to understand some concepts. I understand that we need to give inputs at the leaf nodes of SPN. But why do we have gaussian distribution and ...
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### Are Graphical Models more accurate than simpler regression models and why?

I am looking at graphical models again--such as Bayesian networks and also undirected Markov Random fields. I was hoping to benchmark these models against simpler regression models, but was just ...
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### Inference on a Gaussian random field / undirected graph?

Assume I have an undirected graph with $D$ nodes, and a $D$-by-$D$ matrix with edge strengths between $0$ (implying conditional indepedence given all other nodes), and $1$ (implying complete ...
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### Question about using potential outcomes in DAGs in real world example

I am trying to understand how DAGs and potential outcomes look together. I came across these excellent posts (here and here, but I am trying to understand how this looks in a real world example. ...
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### Posterior distribution is impossible depending on which prior hyperparameters are used?

Suppose we randomly select one of two coins and flip it. In that situation we have random variables $\alpha$ and $\delta$, where $\alpha$ tells us which coin we select, and $\delta$ tells us whether ...
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### Conditional independence in EM algorithm

Let $X$, $\theta$ and $Z$ denote observed, parameter and latent nodes in a graphical model. The EM algorithm attempts to find a local maximum likelihood estimate $\theta^\ast$ for the likelihood of ...
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### Parents in a directed acyclic graph vs a partial ancestral graph

In DAGs, parents are defined as follows: A is a parent of B if 'A -> B' edge is in the graph. In PAGs, there are mixed type of edges, so you can have A -> B, A o-> B. Obviously if A -> B,...
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### Good example of a walk-through of the FCI algorithm to ensure all steps are done

The FCI algorithm is a common algorithm used for learning a Markov equivalence class of causal graphs from observational data. I am wondering if there are any good examples that walk through a causal ...
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### Algorithm to check if there is an inducing path between two nodes - constructing maximal ancestral graph (MAG) given a DAG

In causal inference, one generally learns a Markov equivalence class of causal graphs when trying to reconstruct causal structure from data. This is known as a maximal ancestral graph (MAG). I am ...
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### Why do I even need DeepWalk and Node2Vec when I can build a visual graph structure?

While studying DeepWalk, I started wondering why I need "DeepWalk" when I can build a graph from data and visualize the structure of a graph. With a visualized graph, I can see which nodes ...
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### 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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### 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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### 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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