Questions tagged [bayesian-network]

A Bayesian network is a probabilistic directed acyclic graph. Nodes represent random variables in the Bayesian sense (observable or unobservable); edges represent conditional dependencies between nodes.

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BN node probabilities calculation

In the paper The use of Bayes and causal modelling in decision making, uncertainty and risk by Norman Fenton and Martin Neil following BN is presented: Quote from ...
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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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Stable violation of faithfulness

Faithfulness is often justified by the argument that any violations of it require very specific "fine-tuned" parameters (for some appropriate SCMs/SEMs/SFMs), and that such violations are ...
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Use of composite dependent variable in Economics

I'm curious about research that employs a composite dependent variable in empirical studies. Specifically, I'm interested in analyses that utilize any composite indexing method while taking into ...
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Calculating Porbabilites in a Bayesian Network

I have got the following Network and porbabilites And I need to Calculate the probability $P(C=False)$ I triend using the formula for joint porability distributions $P(X_1,…,X_n)= \prod_{i=1}^{n}P(...
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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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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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How can I compute a counterfactual query for discrete binary variables?

In computing counterfactual queries for structural causal models (SCMs), J. Pearl says to go through 3 steps. Abduction Action Prediction In his book, Causal Inference in Statistics, he shows how to ...
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Optimization of fault diagnosis sequence using probability and cost [closed]

I am developping the algorithm to optimize the fault diagnosis sequence using probability and cost. For exemple, I have 3 diagnosis actions possibles : option 1 : probability which can detect the root ...
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Explaining the approximation to the variational free energy in Bayes by Backprop

In the paper Weight Uncertainty in Neural Networks, Blundell et al., 2015, the authors approximate the exact cost (variational free energy) $$ \mathcal F(\mathcal D, \theta) = \mathrm{KL}[q(\mathbf w \...
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Sampling from large Bayesian network of particular form

I want to know whether there is an efficient way of sampling from this special kind of Bayesian networks of the following form (like thousands or millions of variables in principle). Here is a picture ...
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Prior BPN based on Multi Linear Regression Model Output and Monte Carlo Simulations

On page 286 in the Prediction of road accidents: A Bayesian hierarchical approach paper. The passage describes the construction and parameter learning of Bayesian Belief Networks (BPNs), specifically ...
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Marginalization BN

Is my marginalization over C of P(A)P(B)P(C|A,B)P(D|C)P(E|C) below correct? Because wouldn't this imply that there are no dependencies once you marginalize over C?
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Why do we need the variance term in SWAG method?

My question is about the SWA-Gaussian paper. I do not really understand why they need the 1/2 factor for the covariance matrix (as underlined in the picture). I understand that it is needed because ...
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Temperature scaling a bayesian neural network?

I am trying to calibrate a Bayesian neural network. I have already approximated the posterior density for its weights. In order to make predictions the Bayesian way, I am taking samples from the ...
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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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Removing immoralities in bayesian networks

In many toy examples of bayesian networks, including the ones used in university courses, there are immoralities in the graph (see here, for example). Is it common practice to leave them in the ...
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Given a known Bayesian Belief Network or Causal DAG, how can we score the value of different pieces of evidence?

Assume we know the BBN (Bayesian Belief Network), how can we score the value of each additional piece of evidence that the system ingests? In simpler terms, here are two example use cases: Make an app ...
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How can we estimate the combined causal effect of two separate parents in a Bayesian network?

Consider the following partially-defined Bayesian network: We know the probability of C given A is True and B is False We know the probability of C given A is False and B is True We know that C can ...
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BNN predictive distribution $p(y(x)|D) = \int p(y(x)|w)p(w|D) dw$, what is $p(y(x)|w)$?

When we use approximation methods to try to approximate the predictive distribution, I am slightly troubled by $p(y(x)|D) = \int p(y(x)|w)p(w|D) dw$. Since $y(x) = f(w, x)$ (as $y(x)$ is the neural ...
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Do we need stationarity for Bayesian network modelling?

Most of the Bayesian network packages in R dealing with continuous data require data to be Gaussian. Does this necessitate the data should also be stationary in order to run the model?
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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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Markov and Faithfullness Condition in disconnected DAG/Bayesian network

I'm very confused about the Markov- and the faithfulness condition in disconnected DAGs, as I've never seen such examples. Assume for example I had a DAG where X -> Y, Z. Thus, Z is disconnected ...
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How many free parameters are needed in Bayesian Network?

If X is observed and unobserved, how many free parameters are needed respective?
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Inference in Bayesian networks with hidden variables

Suppose I have the Bayesian network in the figure and the corresponding conditional probability table for each node, where A and B are the hidden variables, and C and D are the observed variables. ...
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Prior term in SGHMC implementation

I am working with SGHMC (Stochastic Gradient Hamiltonian Monte Carlo) models. I found an implimentation of the algorithm in pytorch here. The part of the code that represents momentum variable update (...
Mikhail Petrov's user avatar
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Too large KL-divergence in training

I tried to train bayesian network using ELBO loss function. \begin{align*} \mathcal{F}(D, \theta) = KL[q(w|\theta)||P(w)] - \mathbb{E}_{q(w|\theta)}[\log p(D|w)] \end{align*} My question is, if model ...
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Markov blanket - probability derivation

Is this correct reasoning? Let $x_i$ be a variable in a Bayesian Network and $\text{MB}(x_i)$ denotes its Markov blanket. Let us note that: $$ p(x_i \mid \text{MB}(x_i)) \propto p(x_i, \text{MB}(x_i))....
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Biased sample same like conditioning on a collider?

I am studying chapter 5 "The many variables & the spurious waffles" of the book Rethinking and trying to answer the following question: How is biased sample like conditioning on a ...
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Why implied Conditional Independencies of mediator and confounder are the same?

I am trying to understand why the impliedConditionalIndependencies function of the rethinking package returns the same value for ...
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Why there is no need for a test dataset when using bayesian inference methods? [duplicate]

In a comment one user said that the true guard against overfitting is the adopted priors but, for example, in bayesian neural networks we still have priors on the weights and the common advice is to ...
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Regarding the bayes rule derivation of posterior distribution, $p(\omega|x,y),$ for a given dataset $D$ over $\omega.$

So I was going through this paper and under Uncertainty modeling it says So I tried deriving it on my own and I got $p(\omega | X, Y) = \frac{p(Y | X, \omega) \cdot p(X,\omega)}{p(Y | X) \cdot P(X)}$ ...
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Is P(D | A) = P(D | A,B) * P(B | A) according to the Bayesian Network in the description?

if I consider the Bayesian network in the picture below: https://i.stack.imgur.com/nZKN2.jpg So A is the parent of C,D and B. But B is also the parent of D. Is it then correct to write: P(D | A) = P(D ...
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Constrained optimization between two bayesian variables

I have 2 separate Bayesain networks and I was hoping to maximize Value within the constraint of the Cost. What are is a good way ...
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Justification of definition 2.7.1 (Potential cause) in Causality by Pearl

In Causality - Models, Reasoning And Inference by Pearl, definition 2.7.1 says - Potential Cause definition: A variable $X$ has a potential causal influence on another variable $Y$ (that is ...
Anirban Chakraborty's user avatar
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In what sense is one latent causal structure "preferred to" another? Definition 2.3.3 from Causality by Pearl

In Causality - Models, Reasoning, And Inference by Pearl, definition 2.3.3 reads as follows - One latent structure $L$ = $\langle D,O \rangle$ is preferred to another $L^{'}$ = $\langle D^{'},O \...
Anirban Chakraborty's user avatar
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Bayesian Linear Regression on the top of deterministic neural network

I understand the concepts of Bayesian linear regression and regular neural networks separately, but I cannot wrap my head around how to combine both. In a general setting, lets say I have a (...
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How can I compute the set of interventional probability distributions compatible with a DAG?

Let $P$ be a probability distribution on a set $V$ of variables and for any $X\subseteq V$ and any possible realization $x$ of $X$ let $P_x$ be a distribution on $V\setminus X$. Let $P^*$ the ...
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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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Sampling from Unnormalized Posterior in Prediction Stage

Background: Given a trained model, $y$, parameterized by $W\text{~} P$ and dataset $D$, for a testing point $x_{test}$, the predictive probability distribution is given by $$P(y(x_{test})|D) = \int P(...
rando's user avatar
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How to chain separate models into a single unified model (where predictions of one sub-model form an input to another)?

Our team is tasked with forecasting several timeseries at the daily (or hourly) level: number of calls ('demand') number of calls catergorised as important mean vehical travel time to caller mean ...
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Bayesian Network calculation questions

update The solution follows obtain the right answer now. ----------------------------------------------------------------------------- The Question is here And my answer is here $P(a_0)=P(a_0|r_0) + ...
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How do I calculate the probability P(x | z) from a Bayesian Network?

I have a bayesian network as illustrated above and I want to calculate probability for $P(x|z).$ I am applying the formula: \begin{align}P(x|z) &= \sum\limits_{y} P(z, x, y)\\&= P(x) \times[P(...
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How do we know that two events are independent in a v-structure?

Given this Bayes net, how do I show that R and F are independent? Every "proof" I have attempted seems to involve the assumption that P(F) and P(R) are already independent.
user374773's user avatar
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Question on the interpretation of the predicted results

I would like to understand something that is bothering me. Suppose you have a dataset and a probabilistic model that depends on few parameters $\alpha, \beta $ etc, and suppose that you find an ...
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Meaning of $\uparrow$ in below d-separation algorithm from Koller

In Probabilistic Graphical Models by Koller and Friedman there is an algorithm to find the nodes reachable from node $X$ via trails that are active, given conditioning set $Z$. What is the meaning of &...
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How to incorporate prior knowledge into a CNN?

I'm pretty new to Bayesian inference and machine learning, so I think I'm just lacking the right words to search for a paper that addresses this topic, so here goes: I'm trying to do image ...
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Causal Diagram and multiple regression

I have 4 nodes: A causes B and C, and C by itself causes D. However, C is not measurable, and my interest is to test the association between B and D. What would be the right causal diagram and ...
Taotao Tan's user avatar
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How to get the conditional probabilities from joint probability table?

I have a table of 3 binary variables whose joint probability is given. a b c p(a,b,c) 0 0 0 0.192 0 0 1 0.144 0 1 0 0.048 0 1 1 0.216 1 0 0 0.192 1 0 1 0.064 1 1 0 0.048 1 1 1 0.096 I see ...
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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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