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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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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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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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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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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Relationship between variational inference and sampling in a Boltmzann-machine-like network

In this paper concerning a Boltzmann-machine-like network and its variational mean field approximation, the authors write In the stochastic system as well as the deterministic system, units evolve ...
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How to implement probabilistic PCA with missing data?

There is this site where they show you how to implement probabilistic PCA and they even mention that PPCA can handle missing data, however they don’t show how to tune the model. Do you know of any ...
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The Graph Neural Network- understanding the back propagation mechanism

I am having trouble understanding the derivation of the back propagation algorithm for graph neural networks, as derived in Scarselli 2009 "The Graph Neural Network Model." (IEEE Transactions on ...
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Understanding deterministic models via probabilistic graphical model

I have read a few tutorials how we can think of deterministic neural networks with the help of probabilistic graphical models. Very often they would offer an image as seen bellow and say, our model is ...
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Causality: Models, Reasoning, and Inference: Diagram Question

I am self-studying Causality: Models, Reasoning, and Inference, by Judea Pearl, and there is a question I am particularly stumped on. It reads like this: Problem Statement: Given this fragment of a ...
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How do Graphical Models work in practice?

I know how graphical models work at a high level. I have knowledge about graphs in general, but the message passing is hard to understand and implement. I want to be able to understand what is going ...
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Why do some directed graphical models not imply Bayesian approaches?

I wonder why not all directed graphical models do not imply Bayesian approach(as stated in this article)? A causal scheme is not by itself Bayesian, so using directed graphical models does not ...
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Equivalence between directed and undirected graph?

I am confused over something that may have an obvious explanation I am missing. In Koller's Probablistic Graphical models textbook, page 945, it is said that a Markov network $A-B-C$ is equivalent ...
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What is the difference between probabilistic graphical model and graphical model?

In this note: Lecture 1: Introduction to Graphical Models, it reads that Next, we will elaborate on the difference between Probabilistic Graphical Models (PGM) and Graphical Models (GM). In ...
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graph convolution network

I am trying to understand papers and lectures on graph convolution networks but whenever I open some paper, I get lost on the very first page. I started with some videos like this and this and papers ...
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Gaussian graphical models in regression

I am studying about the Gaussian graphical model (GGM). I have a $N\times D$ matrix X of my observations. The structure of the network has been found by using the graphical lasso method. It means I ...
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Does it make sense to convert a time plot to a distribution

I'm plotting time series data where the 5th-95th percentile values overlap so it looks pretty messy. The data is based on a simulation which tracks military 96,000 military personnel purchase of ...
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What is the relationship of Probabilistic Graphical Model and Bayesian statistics?

I am reading about Probabilistic Graphical Model on a machine learning textbook written by a computer scientist. Even though Probabilistic Graphical Model is more of an engineering approach, its idea ...
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graph classification using ordered nodes and channel-like edges

I am running into a theoretical question and I'm not sure if what I'm hoping for is possible with the current technology. In short I am attempting to perform a graph classification. In one regard, my ...
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Causal networks with correlated variables

I've been reading about Bayesian networks and one of the central assumptions these networks require is conditional independence. However, the problems I'm working on involve variables that are often ...
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Which method would work the best to fill a matrix with empty cells based on the non-empty cells?

Say that you have s students and c courses and therefore a matrix of s x c grades. Suppose also that not all the students have coursed all the courses so there are empty cells in the matrix. Which ...
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Why are autoregressive models neither directed or undirected, as described in the NADE paper?

In the paper Neural Autoregressive Distribution Estimation (Uria et al., 2016), NADE (and other autoregressive models) seem to be described as neither directed or undirected models: We’ve described ...
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What is the intuitive meaning of P(A,B|C)?

I have come across graphical models where we have a node C that is dependent on both A and B. For example a node C with incoming arrows from A and B. In this case I know the intuition behind writing ...
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In a graphical model of C dependant on both A and B, is it possible to get the joint distribution of C and B?

Imagine we have a graphical model of random variable C that is dependent both on A and B. This is like a node C which has two incoming arrows. One from node A and the other from B. An example is me ...
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Understanding the graphical model for a GP for regression, from GPML (Rasmussen and Williams, 2006)

The book Gaussian Processes for Machine Learning (GPML) by Rasmussen and Williams (2006) provides a graphical model for GP regression but does not explain it in great detail, so I have a few questions ...
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Identifying identical graphs or adjacency matrices of graphs

I was wondering if someone has a good idea for checking whether two graphs are the same (for example, based on an adjacency matrix). Ideally, in a computational efficient manner that can be done on ...
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Problems with using Gibbs Sampling for Bayesian DAGs

Assume we want to sample from the variables of Bayesian belief network, which is a Directed Acyclic Graph (DAG), where we observe some of the variables, and do not observe the others. We can usually ...
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Proof of a causual (line) Bayesian graph model

Given a simple Bayesian graph model, and $A$ is observed. A <---- B <---- C The joint model is $$ p(A,B,C) = p(A\mid B,C)p(B\mid C)p(C), $$ which is true....
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1answer
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Intuition behind conditioning Y on X in the front-door adjustment formula

I am trying to understand the practicalities of Pearl's front-door criteria to estimate causal effects under an unobserved unconfounder. First, to give context to the question we have a graph that ...
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What relationships do spatial statistics share with time series analysis?

Spatial statistics is often discussed in tandem with time series. How are the two related? Do they share methodologies? Do overlap in assumptions or conditions of data?
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Derivation of the Objective Function for Expectation Propagation

I was reading Expectation Propagation As A Way Of Life and the original paper by Minka Expectation Propagation for Approximate Bayesian Inference and they both say that a fixed point of the EP ...
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Plotting Vector Embeddings

I am currently working on a project that requires some form of data on the paper. Even though I was able to get some coding done and communicate results, I need some graphs. What I want to do is ...
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Bayesian structure learning: how to identify z as a collider in x-z-y structure?

In BNSL(Bayesian Network Structure Learning) problem, we are asked to learn a DAG(Directed Acyclic Graph) over a randon variable set $U$, given samples of the underlying distribution of $U$. The ...
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Mathematical details in the definition of a Structural Causal Model

Pearl defines (see Causality, Judea Pearl, 2nd ed., Definition 7.1.1) a Structural Causal Model (SCM) as a triple $(\mathscr U, \mathscr V, F)$ where $\mathscr U$ is a set of "exogenous variables," $\...
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Density estimation: the significance of smaller number of samples?

I'm reading Probabilistic Graphical Model: Principle and Techniques by Koller and Friedman. In section 18.5 Bayesian Model Averaging(p825), the author said If we are interested only in density ...
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1answer
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Computing Gradients for a [-1, 1]-valued RBM

The gradient derivation for a binary-valued RBM with values $\in\{0,1\}$ is well-documented, for example in Goodfellow, et al and here on Cross Validated. However, in some works (e.g., associative ...
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Graph representation of relation between DV and IV

If a condition states that $f(I|Y,Z) = f(I|Z)$ How do I represents this relationship using nodes and edges. $I,Y, Z$ are nodes not sure if the following representation is accurate ? Any suggestions ...
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Why is it difficult to sample from Energy Based Models?

I am trying to understand the following claim which is made in the Deep learning book by Goodfellow et. al about a toy energy-based model (with the apparent motivation of introducing Markov Chain ...
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1answer
61 views

Goodness of fit for Copula

I was wondering if the graphical methods can be used instead of formal tests such as Cramer-Von Mises test as the GOF for copulas? The scatter plot of pseudo-observations is as follows: The Q-Q ...
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Graph and statistics multiple regression show different things

I’ve run a multiple regression to find out if visual memory declines differenty for the autism group than for the controlgroup. I did find a significant main effect of age, showing that with ...
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Basic doubt on generative models

I am new to statistics and while reading Bishop's book, in the 'Generative models' part 8.1.2. When explaining ancestral sample, he says: To do this, we start with the lowest-numbered node and ...
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Seeing a tree graphical model as a Markov model

I have been doing an exercise task and I encountered an issue. Let's imagine that we have a graphical model(binary tree) as in the image below. To every vertex a rv $X_v$ is assigned which obtains ...
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Marginalization not understood

In the book "Pattern recognition and machine learning" by Christopher M. Bishop, at page 374 The joint distribution corresponding to this graph is again obtained from our general formula (8.5) to ...
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Why do we have to convert Bayes' net to MRF before applying Belief propagation?

is that even correct in the first place? if yes, then why? I've seen articles talking about inference in Bayes' nets, and I've seen others talking about conversion. I don't have the full picture.
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Is A ⊥ B | C where one path active but another inactive?

I'm trying to determine if A ⊥ B | C? I see two paths flowing through elements of C: (1) B <- C - > A (all variables unobserved, active triple; independence cannot be guaranteed for this path) (...
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Parsing and understanding plate notation for topic modeling example?

I'm trying to understand the following plate notation which is used a lot as an example of topic model to introduce variational methods, etc. I wanted to ask if my understanding is correctly depicted ...
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What's the effect of observed variables on PGMs?

For a class we're going over the basics of PGMs. The below example was illustrated to show how (conditional) independence is somehow related to what variables are observed. This concept is perplexing ...
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Why Boltzmann machine is represented as a fully connected graphical model?

The joint factorizes into unaries and pair-wise potentials. If that is the case, then why do we represent it as a fully connected graph? It is misleading and gives the impression that the joint cannot ...
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How to quantify a parent's influence of a node in a Bayesian Network?

Consider a toy bayesian network that models purchase of items at a store. The nodes include: {Brand, Price, Purchased}. It is possible that when you marginalize over price, P(purchase|brand) may ...

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