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.

Filter by
Sorted by
Tagged with
0 votes
0 answers
4 views

Propagation of change through a Bayesian Network with continuous variables

I have created a Bayesian network from a number of continuous variables using the bnlearn package in R. One of the things that the package provides is the regression coefficients of each node vs. its ...
user avatar
1 vote
1 answer
43 views

What is Gaussian approximation for the variance of a function?

In Orre 2000, the author provides an asymptotic approach to computing the variance of information component and conditioned posterior distribution. In part 2.2 weights and information components So ...
user avatar
0 votes
0 answers
7 views

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 ...
user avatar
  • 419
0 votes
1 answer
134 views

Application of Bayesian Networks to tabular data

I have been going through some tutorials regarding Bayesian Networks, but i have yet to see them applied to tabular data, i.e. a dataset. I have created this dummy example to experiment, and attempt ...
user avatar
0 votes
0 answers
12 views

Compute joint distribution from fully connected factor graph

I've searched but can't find a meaningful answer (I'm more a software dev than math person, so I'm likely misunderstanding something) Assume I have several variables (A, B, C, D, E, etc) from a ...
user avatar
0 votes
0 answers
28 views

How is backdoor criterion used in practice?

Is the backdoor criterion applicable only for "learning" in a causal model (i.e. for estimating the causal effects between variables) or must it also be used when running that model, as in ...
user avatar
7 votes
2 answers
364 views

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 ...
user avatar
  • 278
1 vote
1 answer
21 views

Clarification on Bayesian ensembling

I was reading a paper https://arxiv.org/pdf/2007.06823.pdf and at the end of page 3 the author presents the technique called "ensembling" for the estimation of the expected outputs and the ...
user avatar
  • 113
1 vote
1 answer
49 views

Conditional independence proof

I want to prove that $\mathbb{P}(X|U,P) = \mathbb{P}(X|U) \implies \mathbb{P}(X|U,P,T) = \mathbb{P}(X|U,T)$ Where all the letters denote random variables. I'm not sure that this is right, but it seems ...
user avatar
0 votes
0 answers
10 views

Bayesian Network edges and their meaning

I was wondering why are we not able to conclude dependencies between nodes/variables from edges in a Bayesian Network, while we are able to conclude independence between nodes/variables from the ...
user avatar
1 vote
1 answer
42 views

What justifies the multiplication step in the proof of the front-door adjustment?

$\newcommand{\doop}{\operatorname{do}}$ The proofs of the front-door adjustment that I've read take three steps: Show $P(M|\doop(X))$ is identifiable Show $P(Y|\doop(M))$ is identifiable Multiply the ...
user avatar
1 vote
0 answers
35 views

How to compare Bayes nets and Deep learning networks from performance vs explainability tradeoffs?

Machine learning models with higher performance are often based on more complex algorithms and therefore lack interpretability or explainability and vice versa. How to compare the two important ...
user avatar
1 vote
0 answers
26 views

What are the priors in Bayesian Neural Network?

So I have knowledge of Bayesian statistics/econometrics, but I only recently found out about Bayesian Neural Networks. I was wondering what the priors are in a Bayesian Neural Network? And is it ...
user avatar
0 votes
0 answers
16 views

BayesNet Independence

For BayesNet, can anyone explain how we can check the independence between the set of random variables? e.g. $\{B, D\} \perp \{G, I\} | A?$
user avatar
1 vote
1 answer
14 views

where to find the reference Bayesian networks of XMLBIF(.xml) format?

The XMLBIF(.xml) format is XML Belief Network Interchange File Format, which is one of the standard formats for the storage and manipulation of the Bayesian networks. It is widely used by some ...
user avatar
  • 113
1 vote
1 answer
29 views

what does the alpha symbol represent in the standard equation used for inference by enumeration

can anyone tell me what the alpha means in the following equation (used for inference by enumeration)?
user avatar
0 votes
0 answers
43 views

Gaussian Bayesian Networks versus Multiple Linear Regression

I have a set of predictors, $X_1$ to $X_5$, and four response variables, $Y_1$ to $Y_4$. All variables are continuous and distributions are either approximately Gaussian or can be easily transformed ...
user avatar
  • 476
1 vote
0 answers
18 views

Hybrid Bayesian Network with Continuous Parents and Ordinal Child Node (Softmax Function)

Upon reading about hybrid BNs with discrete child nodes and multiple continuous parents, I came across the possibility of using the softmax (multinomial logit) function (below) in order to query ...
user avatar
0 votes
0 answers
14 views

What is the t deterministic transformation in Bayesian Neural Networks?

I am learning Bayesian neural networks and have one question about the t deterministic transformation function, which builds the bridge between the neural weights and the variational parameters. Known ...
user avatar
  • 1
2 votes
1 answer
33 views

Finding the maximum likelihood parameter estimates for a given bayesian network

I am studying the book by Adnan Darwiche (Modelling and Reasoning with Bayesian Networks), specifically Chapter 17. I am unsure about how to proceed with this exercise. Since A leads to B and B leads ...
user avatar
  • 7,565
0 votes
1 answer
61 views

How to show mathematically whether the following conditional relationships hold?

In the following Bayesian network, the variables $ x_{i} $ are mutually independent (let's assume that these are the positions of $N$ boats). The variables $ y_{i,j} $ are distance measurements ...
user avatar
  • 133
0 votes
0 answers
7 views

Bayesian Interpretation of Deep Ensembles

I was wondering if training a neural network in the deep ensemble setting can lead to a network with a posterior vs. a point estimate architecture? Recently there have been discussions over the ...
user avatar
0 votes
0 answers
23 views

How do you compute the messages in a Bayesian network?

I'm just starting to figure out simple Bayesian Networks. This tutorial (https://towardsdatascience.com/belief-propagation-in-bayesian-networks-29f51fdc839c) has been the most accessible so far, but ...
user avatar
  • 509
0 votes
0 answers
65 views

How are Judea Pearl's Bayesian Nets different from Google's Causal Impact?

At a high level, how are these two approaches, similar and different? I understand that both use Bayes rule, however, I'm unclear on how they differ. Causal Impact uses structural time series to ...
user avatar
  • 1,700
0 votes
0 answers
21 views

How to calculate the number of parameters in a network analysis and what that means for sample size

I'm hoping to conduct a network analysis (Ising model then later add LASSO regularization) on a biobank sample with a lot of data. Something like 2,000+ variables and 90k+ patients. It'd be nice to do ...
user avatar
  • 11
0 votes
0 answers
25 views

Understanding Bayesian Hierarchical Model in Practice

I have a Bayesian hierarchical model with datapoints $y_{ij}$ which are samples from distributions with parameters $\theta_j$. For each distribution parameter $\theta_j$, there are $n_j$ datapoints ...
user avatar
2 votes
1 answer
61 views

Causal Inference in a Bayesian Network with unobservable backdoor and no frontdoor

Just like the Bayesian network shown above. I want to identify the average treatment effect(ATE) from Smoking to Lung Cancer. If Genetics is observable, I can easily identify the ATE with Pearl's ...
user avatar
0 votes
0 answers
11 views

Conditional indepencies in Bayesian network. Redundant edges in structure learning?

I am confused about whether I can have connected 'triangles' in BN assuming that all variables are observed (no missing values). I see that 'bnlearn' software and other softwares too give me a network ...
user avatar
  • 1
2 votes
1 answer
95 views

Conditional independence tests not respecting d-separation

Wrong example, please refer to the second example I just tried to model a Bayesian network composed of 3 variables as follows $A\sim N(0,1)$ $B\sim A + N(0,1)$ $T\sim A + B + N(0,1)$ In the DAG ...
user avatar
  • 133
0 votes
0 answers
18 views

Bipartite Bayesian Network?

I have a set of $n+\binom{n}{2}$ random variables $\{x_i\}^{i=n}_{i=1}\cup \{x_{ij}\}_{i\leq j}$ and their probability distribution is given as: $$P(x_1,...,x_n,x_{12},...,x_{ij},...x_{(n-1)n}) = \...
user avatar
  • 151
0 votes
0 answers
26 views

State of the art methods for identifying DAG parameters

Say I have written down a directed acyclic graph (a causal model) with a few dozen variables. Moreover, I have a dataset with observations for many (though not all) of the variables. For simplicity, ...
user avatar
  • 954
1 vote
0 answers
21 views

Why a undirected graph is Markov equivalent to a directed graph iff it is decomposable?

Claim 1. A undirected graph is Markov equivalent to a directed graph iff the undirected graph is decomposable. I am trying to prove Claim 1 and to find a relationship between decomposable and v-...
user avatar
  • 11
1 vote
0 answers
21 views

Bayesian Networks vs traditional stats approaches to Causal Inference? [duplicate]

I've been reading the 'book of why' by Judea Pearl and come to understand that Bayesian Networks can be used to establish causality given a directed acyclic graph (DAG) and that the methods are non-...
user avatar
  • 1,700
0 votes
1 answer
32 views

Node that depends on the particular values of it's parents in a Bayesian network?

Consider a Bayesian network containing a binary variable C which denotes whether a certain person has a child or not. There is a second variable B which denotes the birthdate of the person's youngest ...
user avatar
  • 51
1 vote
0 answers
80 views

Proof that the Markov Blanket in a Bayesian Network is parents, children, and children's parents

I'm looking for a proof of this fact from wikipedia: The Markov boundary of a node $A$ in a Bayesian network is the set of nodes composed of $A$'s parents, $A$'s children, and $A$'s children's other ...
user avatar
  • 111
0 votes
0 answers
18 views

Discrete Bayes Net learning under parameter constraints

What is some relevant research available on estimating the parameters of a Bayes Net (with known structure) when there are known constraints on conditional and marginal probabilities? For example, ...
user avatar
  • 1,428
0 votes
0 answers
15 views

Bayesian hierarchical model inference problem image segmentation

it might be really confusing question. I am working on my thesis and I am stuck at a problem. It's a problem in image segmentation and finding parameters of border lines of continuous region in an ...
user avatar
  • 1
0 votes
0 answers
51 views

Calculating conditional probability on bayesian network

In one of my lectures the Bayesian Network below sprung up and I am puzzled because there's no explanation on how did we calculate the denominator of first and second fractions. I already know how to ...
user avatar
  • 11
1 vote
1 answer
161 views

mutual information and edge weights in a bayesian network

The mutual information between two random variables X and Y can be stated formally as follows: I(X ; Y) = H(X) – H(X | Y) Where I(X ; Y) is the mutual information for X and Y, H(X) is the entropy for ...
user avatar
0 votes
1 answer
85 views

When and why converting a Bayesian network into a Markov Random Field?

I found many slides and tutorials (e.g., [1,2]) on the probabilistic graphical model introducing the procedure of "converting a Bayesian network (BN) into a Markov random field (MRF) by ...
user avatar
0 votes
0 answers
95 views

Neural network regression not learning due to non-uniform data distribution?

I am working on a non-linear multi-output regression problem. I have created a simple neural network. The net is supposed to be a point estimator of $\hat{\theta}_{MAP}$, where $\theta$ are the ...
user avatar
1 vote
0 answers
53 views

How to calculate $P(A|B,C)$ from Bayesian Network?

Say I have a bayesian network B <- A -> C. I need to calculate $P(A|B,C)$. How can I do that? I tried doing: $P(A|B,C)=\frac{P(A,B,C)}{P(B,C)}$ I also tried various other combinations of ...
user avatar
1 vote
0 answers
19 views

Specifying conditional distribution in a Bayesian network

I am trying to learn about Bayesian networks and am really having a hard time to figure out how to setup some simple models. Say, I have a model as: ...
user avatar
  • 4,420
0 votes
0 answers
19 views

Can we ignore graphs for inference in linear/Gaussian settings?

Assume I have a linear Bayesian network/graph like the following: where i can derive a joint pdf $$p(\mathbf{x})=p(x_1,x_2,x_3,x_4,x_5)=p(x_1)p(x_2|x_1)p(x_3|x_2)p(x_4|x_3)p(x_5|x_4)$$ Assuming that ...
user avatar
  • 419
0 votes
0 answers
23 views

Instantiating a Bayesian network with continuous nodes

I am having some confusion regarding how to instantiate Bayesian networks. Let us take an example with smoking and lung cancer. So, we have a simple Bayesian network as: $$\textrm{SMOKING ------> ...
user avatar
  • 4,420
0 votes
0 answers
21 views

Initializing the nodes of a bayesian network

I am doing some reading about Bayesian networks and how to represent them with a DAG. I have a question about how to initialize the distribution properties of the nodes. Say there is a Bayesian ...
user avatar
  • 4,420
0 votes
1 answer
83 views

I-map Bayesian Network, Practical Explanation

I am having diffculty understanding the concept of an I-map in the context of Bayesian Networks. According to the PGM textbook by Koller & Friedman, an I-map is essentially a set of conditional ...
user avatar
0 votes
2 answers
71 views

In bayesian approach, what is the difference between full posterior and MAP [duplicate]

Consider a classic machine learning problem, which we want to solve using NN. And suppose that we want to use bayesian learning for that. In the bayesian approach the posterior is described as follows:...
user avatar
  • 1,033
3 votes
0 answers
77 views

Proving Equivalence between Multivariate distributions and Gaussian Bayesian Networks

I am studying Probabilistic Graphical Models by Daphne Koller. In Chap 7, the authors say the following. I can't convince myself of the highlighted part. Induction typically has a statement for n, ...
user avatar
  • 805
1 vote
1 answer
94 views

Pearl's Front-door and Back-door

I've encountered lots of causal inference terms and jargons (under the Neyman-Rubin potential outcome framework), and I had a question regarding how Pearl's DAG restrictions relate to ignorability and ...
user avatar
  • 173

1
2 3 4 5
10