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.
518
questions
2
votes
0
answers
19
views
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 ...
3
votes
1
answer
24
views
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 \...
1
vote
1
answer
43
views
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 (...
- 11
0
votes
0
answers
22
views
Markov Assumption: Given parents or given *only* parents
According to most sources I see (e.g. Wikipedia), the Markov assumption states that:
every node in a Bayesian network is conditionally independent of its nondescendants, given its parents
Two ...
- 185
3
votes
0
answers
65
views
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 ...
1
vote
0
answers
11
views
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 ...
- 11
0
votes
0
answers
36
views
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(...
- 291
1
vote
0
answers
26
views
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 ...
- 121
1
vote
2
answers
129
views
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) + ...
- 13
0
votes
0
answers
7
views
a question on model comparison when 2 different training techniques are used (dropout and variational inference)
i have a doubt :
considering 2 different neural networks, one trained through the variational inference technique with denseflipout layers and the other through dropout/concrete dropout
In the first ...
- 259
0
votes
0
answers
27
views
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(...
- 101
0
votes
0
answers
17
views
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.
0
votes
0
answers
16
views
Bayesian Network predictive analysis calculation
Given the case from above, is the "predictive analysis" correct?
Case: P(T=T|R=F) - Toxins Analysis is Positive, given the Tuna has lived in Radioactive waters:
P(T=T|R=F) = P(T=T,R=F)/P(...
- 1
0
votes
0
answers
8
views
How to efficiently caclulate probability of a state in HMM when a random shuffle operation happens on emitted observations
The problem setup is as follows(it's from a book and may not be tied to reality):
Suppose we have some speakers s_1, s_2..s_k seated around a table speaking at ...
- 101
0
votes
0
answers
33
views
Bayesian Network Probabilities Calculation "diagnostic reasoning"
Given the above example, are the steps to calculate "diagnostic reasoning" correct?
Case: P(R=T|E=F) - Tuna has lived in radioactive waters given Tuna is not edible:
P(R=T|E=F) = P(E=F|R=T)...
- 1
1
vote
1
answer
22
views
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 ...
- 259
0
votes
0
answers
124
views
Bayesian Network: Calculate probability of a parent node given child node
I have a Question about Bayesian Networks.
Given a child node, how to calculate probability of the given parent node(using probability of all nodes).
The bayes net is :
I was able to solve for P(E | ¬...
1
vote
1
answer
27
views
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 &...
0
votes
0
answers
12
views
Can the evidence be the parent of the nodes of Dynamic Bayesian Network?
I am trying to build the structure of my DBN for my system, but I am a bit lost when I compare it to examples of DBN; especially concerning the evidence.
At each time $t$ I am getting data from my ...
- 11
0
votes
0
answers
14
views
EM algorithm for finding discrete latent variables with gaussian child in Python
I have the following Bayesian network model:
$P(A, B, C, D) = P(D|B)P(C|B)P(B|A)P(A)$
A and B are discrete variables, while C and D are continuous variables. I've looked around and it seems in a ...
- 61
3
votes
0
answers
56
views
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 ...
- 131
0
votes
0
answers
83
views
Applying Particle Filter to Dynamic Bayesian Network
I have a DBN where the probabilities are unknown, and then I fill my CPTs randomly. I want to calculate those probabilities over time with the data from my sensors, and according to Artificial ...
- 11
0
votes
0
answers
7
views
Finding the most likely point an intermittent failure was introduced
I have a sequence of state changes (changes in computer source code) and a test that I can run on a state that never produces a false positive, but frequently produces a false negative (even incorrect ...
0
votes
0
answers
75
views
Probabilistic Graphical Models, Daphne Koller, Exercise 3.22
Context:
I need some help regarding an exercise problem (3.22) from Probabilistic Graphical Models by Daphne Koller. This exercise is to explore cases where an algorithm for finding P-map fails when P-...
5
votes
1
answer
74
views
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 ...
- 303
1
vote
1
answer
382
views
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 ...
- 11
0
votes
0
answers
101
views
How to get correlated output from multiple tensorflow probability distributions
I'm building a tensorflow probability model that will output multiple (2+) predictions where the outputs will be draws from learned probability distributions. It currently looks something like this:
<...
- 61
1
vote
0
answers
13
views
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, ...
- 43
3
votes
2
answers
115
views
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. ...
2
votes
0
answers
25
views
In what ways do conjugate priors compose?
A lot of conjugate priors are known for a lot of likelihood distributions (mostly the exponential family). But most Bayesian models in practice don't just consist of one distribution. Usually, you ...
- 180
0
votes
1
answer
111
views
Does the classic burglar,earthquake conditional independence example only apply depending on the state of the known parent?
If I recall, this example forms a graph with (earthquake, burglary) being the two parents of a child (alarm), and the statement is that the two parents are conditionally independent only when child is ...
- 273
0
votes
1
answer
43
views
Understanding rare definition of the likelihood function and corresponding posterior from research paper
Reading the paper https://storage.googleapis.com/pub-tools-public-publication-data/pdf/b20467a5c27b86c08cceed56fc72ceadb875184a.pdf i came across a rare definition of the likelihood function that in ...
2
votes
1
answer
341
views
BNLearn Bayesian Networks - how is the structure decided?
I'm currently playing around with BNLearn on Python, and creating BN's from Pandas datasets. I'm not really sure why/how the package decides on the structure of the BNs it creates; see for example ...
- 43
0
votes
0
answers
34
views
Compare Probabilistic Graphical Models and Probabilistic Reasoning In Intelligent Systems
I am new to probabilistic graphical models. I am currently reading Probabilistic Reasoning In Intelligent Systems by Judea Pearl. I found the first two chapters (and first half of third chapter, till ...
0
votes
0
answers
29
views
Derive and validate a probability using a causal diagram
Given a causal diagram and the conditional probabilities for every adjacent node, I want to calculate a specific probability in two ways - let's call them the "simple" and "alternate&...
- 101
0
votes
0
answers
32
views
question about notation of Bayes theorem
i was reading Yarin's thesis on Bayesian neural networks and MC-dropout and , at section 2.1 at page 18, I stumbled upon this formula
$$ p(\bf{w}|\bf{X},\bf{Y})= \frac{p(\bf{Y}|\bf{X},\bf{w})p(\bf{...
- 259
2
votes
2
answers
144
views
Derive Probabilities from Bayesian Network
I have given the following Bayesian network.
I already know the fundamentals, for example, pairwise dependencies and how to calculate the total joint probability:
$$P(M,B,S,C,H) = P(M)\cdot P(S|M)\...
- 145
1
vote
1
answer
37
views
Impact of sample size when using exponential random graph modeling
I am working on revising a manuscript centered on identifying the drivers behind certain types of student interaction. One critique that I'm having trouble addressing is that they are worried about my ...
- 11
0
votes
0
answers
39
views
Calculating Probability in Bayesian Networks
I'm trying to work out how to calculate the outcome probability $\Pr(Y)$ for the following BN:
I know the joint probability $\Pr(a,b,c,Y) = \Pr(a) \Pr(b \mid a) \Pr(c) \Pr(Y \mid b,c)$ (which I'll ...
- 43
1
vote
1
answer
43
views
Bayes Nets - Understanding Inference
I was wondering if anyone could explain the following to me (from https://lips.cs.princeton.edu/complexity-of-inference-in-bayes-nets/):
"Briefly, recall that a Bayesian network consists of a ...
- 43
2
votes
1
answer
110
views
How to evaluate validity about Causal Discovery?
When I was trying to do structural learning for causal inference, I perplex for too many causal discovery algorithms(PC, FCI, GES, NOTEARS and more...)
There are many structural learning algorithm for ...
- 53
0
votes
0
answers
25
views
How to apply the the conditional probability and chain rule formulas in a multivariable case?
I'm learning about Bayesian Fusion and have a question regarding an expression that I wasn't able to prove.
It poses the following statement:
Assume $y_1, y_2, y_3$ are three observations which are ...
- 1
0
votes
1
answer
38
views
What is 'factored models'?
What is 'factored models'?
I've seen the term 'factored models' in paper 'The Bayesian Structural EM Algorithm'.
But I see it for the first time and it is hard to understand...
I tried searching it ...
- 53
1
vote
1
answer
27
views
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 ...
- 522
2
votes
1
answer
33
views
How to convert a Gamma GLM to a Pearl's Structural Causal Model (SCM) with exogenous noise terms?
Assume both X and Y are univariate for this. So in Judea Pearl's SCM, you have endogenous variables and exogenous noise. A regular causal Bayesian Network like X->Y where X and Y|X is normal can be ...
- 232
0
votes
0
answers
55
views
What is the required sample size for Bayesian Network?
I have used Krejcie & Morgan's table for my survey questionnaire to identify the sample size of my study, and it turns out 384 samples. However, specifically, how many sample size (in minimum) is ...
- 1
0
votes
0
answers
40
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 ...
1
vote
1
answer
321
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 ...
- 27
0
votes
0
answers
13
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 ...
- 503
0
votes
1
answer
250
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 ...
- 53