# 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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### The sum of $O_p$ --$O_p \left(s^2\frac{\log d}{n}+s\sqrt{\frac{\log d}{n}} \right)$

I read papers in the area of inference for high-dimensional graphical models and these papers always state the convergence rate of the estimator. Using $O_p$ is a good choice. Maybe I made some ...
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1 vote
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### When does a extended BIC curve for a Gaussian Graphical model/GLasso look incorrect?

I have a model for a network, and I wanted to analyze the extended BIC curve for a graphical lasso model as according to Foygel and Drton 2010. The paper gives a list of assumptions for the data/model ...
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### Average treatment effect: counterfactual and graphical derivation

I have some (shameful) doubts about the Average Treatment Effect (ATE), also known as Average Causal Effect (ACE). In this setting, I am interested in a binary exposure/treatment variable ...
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### Do Bayesian networks have any rules with regards to zero probability RVs?

I am currently learning about Bayesian networks through Berkeley's AI course. In a Bayesian network, each node encodes the conditional probability of the random variable (RV) represented by the node ...
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### Definition of $\text{do}$ operator [closed]

I'm looking for a hint in understanding semantics of $\text{do}$ operator. Starting from the original distribution $P$, an intervention $\text{do}(X=x)$ takes us to another distribution $P_x$ - in ...
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### How to perform random walk on multilayer network to predict new edges

I have a multi-layer network that is a union of 3 networks (field of human biology/ Omics data). The 3 networks have dense connections within each other (local), however sparse connections to each ...
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### Usefullness of Graphical Models in practice

Graphical Models uses that correlation 0 is equivalent to independence for multivariate normal distribution. Then we can make a graph where there is an edge between two nodes if the correlation is not ...
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### On showing indepdedence of a collider in graphical model

In the following slide: it seems how it got A and B are independent is rather circular. The reason is it assumes $p(a,b,c) = p(a)p(b)p(c|a,b)$ and then marginalizes over $c$ to get $p(a,b) = p(a)p(b)$,...
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### Deriving conditional independence statements for causal graphs with selection nodes

In "basic" causal graphs / DAGs / probabilistic graphical models (PGMs), conditional independence statements can be derived using the d-separation criterion. How does this work if selection ...
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### What is the meaning of graph singal for graph constructed from correlation matrix?

In the highly cited paper "The Emerging Field of Signal Processing on Graphs", the authors defined graph singal for a graph of N vertices as a vector of length N, with each element of the ...
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### A question of "elementary imsets" in an ADMG

In [The m-connecting imset and factorization for ADMG models] (https://doi.org/10.48550/arXiv.2207.08963), it was mentioned the notation of an "elementary imset". The definition of ...
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### Is i(G) equivalent to i_l(G), the local independency set of BN?

Reference: Koller, D., & Friedman, N. (2010). Probabilistic graphical models: Principles and techniques (Nachdr.). MIT Press. Bayesian network $\mathcal{G}$ encodes that for any node $X_i$, there ...
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### Converse of pairwise Markov property

Random vector $X$ follows a pairwise Markov property on graph $G=(V,E)$ if for any $(i,j) \notin E$, $X_i$ and $X_j$ are conditionally independent given $X_{V \setminus \{i,j\}}$. My question is, why ...
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### Causal discovery on partially known causal DAG

Often in data science, we have partial knowledge of the causal DAG structure. Regarding some of the possible edges in the DAG, we are in doubt. Are there any resources to tackle this setting? The ...
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### Isn't strong ignorability an incorrect assumption in complex causal structures?

I have seen that in many papers/competitions for causal inference, the assumption of strong ignorability is made - $P(Y^{x}\perp X\mid V)$, where $X$ is the treatment, $Y$ the outcome and $V$ ...
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### What is an inducing path in causal inference?

In causal graphical models, an inducing path is defined as: [Definition Inducing Path] An inducing path relative to L is a path on which every non-endpoint node ...
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### What is the suitable Graph Machine Learning model for dynamic graph forecasting with changing nodes and edges features

I have a graph where each node carries a feature value(s). The edges in the graph are weighted and each edge carries a single value (weight). The weight of the edge is some value calculated using the ...
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### Model causality: graphical models and PCA

If we build a graphical model (DAG) we (may) interpret the arrows as causal dependences. If we build a graphical model based on the variables returned by principal component analysis (PCA) we should ...
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### Specifying a terminal node in a Bayesian Network

I am writing R script using bnlearn package for learning a DAG from a dataset. Is it possible to define a terminal node beforehand? ie I want a node Y to be the final one in the graph, which will not ...
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### What is a "directed path" in context of causal graphs?

I am going through Causal Inference In Statistics by Pearl and I have come across the definition of path and directed path (section 1.4, page 25). Path: A path between two nodes $X$ and $Y$ is a ...
1 vote
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### Pearl's Causal Inference In Statistics, equation 3.11 - Calculation of group specific causal effects

In the book Causal Inference In Statistics by Pearl, page 63, while referring to the below DAG, it says - Thus to compute the $w$-specific causal effect, written $P(y|do(x),w)$, we adjust for $T$, ...
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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 ...
• 143
1 vote
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### Show that intersection property - $I(X,Y\cup Z, W)$ and $I(X,W\cup Z,Y)$ $\implies$ $I(X,Z,Y\cup W)$ - requires strict positive distribution

Question It is stated in Probabilistic Reasoning In Intelligent Systems by Judea Pearl that, intersection property of information relevance axioms - $I(X,Y\cup Z, W)$ and $I(X,W\cup Z,Y)$ $\implies$ \$...