Questions tagged [bayesian-network]
For questions related to Bayesian networks, the generic example of a directed probabilistic graphical model. Includes dynamic Bayesian networks, e.g. Hidden Markov Models (HMMs) and Kalman Filters. For applications of Bayesian networks in any field, e.g. machine learning. NOT for general questions about Bayes' theorem, Bayesian statistics, conditional probabilities, networks, or graph theory.
335
questions
0
votes
0
answers
26
views
Russell & Norvig: Connecting models of probabilistic reasoning to Stochastic Differential Equations
Artificial Intelligence: A Modern Approach, 4th Global ed.
by Stuart Russell and Peter Norvig contains the following footnote on page 480 of chapter 14:
Uncertainty over continuous time can be ...
1
vote
1
answer
43
views
Probability of complement as fraction
I am trying to work through the paper "Repairing Neural Networks by Leaving the Right Past Behind" (arxiv).
And really struggle working through the mathematics. The paper states that the key ...
- 111
0
votes
0
answers
18
views
How is the lambda message computed? (Bayesian network)
Currently reading through Pearl [1988]. Here is the Bayesian network shown in the book:
Bayesian network
Where the probabilities of each $X$ node are given by the probability vector $(q_i,p_i)$ where $...
1
vote
0
answers
36
views
Bayesian belief network - calculate probability
Given the following Bayesian belief network, what is the probability
that a non-smoking patient with a smoking parent will develop lung
tumor?
In this question, isn't the answer already provided ...
- 387
0
votes
1
answer
40
views
Given a Bayes Net, compute $p(A|B,C)$
I am given the following Bayes Net:
and I am asked to compute $p(A|B,C)$.
This is what I've done:
\begin{align}
p(A|B,C) & := \frac{p(A,B,C)}{p(B,C)} \\
& = \frac{p(A,B,C)}{p(B)\ p(C|A)} \\
&...
- 161
0
votes
0
answers
35
views
Given a decision network, compute the EU of buying a book
I am given this homework:
And this is what I have done up to now:
(a) This is the decision network for that problem
While I think the decision network is correct, I am having struggles with part (b)....
- 161
1
vote
0
answers
22
views
Given a Bayesian Network, calculate $p(a)$
I am given this Bayesian Network:
I need to calculate $p(+d|+a)$
What I have done up to now is:
$$
p(+d|+a) := \frac{p(+d,+a)}{p(+a)}
$$
where
\begin{align}
p(+d,+a) & = \sum_X p(+d,+a,X) \\
&...
- 161
1
vote
1
answer
29
views
Given a Bayes Network, calculate $p(a | b, \neg c)$
I am assigned a homework but I cannot figure out how to solve it.
Given this Bayes' Network:
calculate $p(a | b, \neg c)$.
This is what I have done up to now:
\begin{align}
p(a | b, \neg c) & \...
- 161
0
votes
0
answers
21
views
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:
$$
p(x_i \mid \text{MB}(x_i)) \propto p(x_i, \text{MB}(x_i))....
- 323
1
vote
1
answer
62
views
A Bayesian network with 4 nodes question
Hello. I need to find the following probabilities:
$ \qquad a. P(\neg A, B, \neg C, D) \\
\qquad b. P(A|B,C,D) $
This is my solution:
I would like to get an opinion on my solution.
- 52
0
votes
0
answers
24
views
Master Equation for a Chain of Bayesian Updates
The general Bayes' theorem is well known as:
$$P(X|Y) = \frac{P(Y|X) \cdot P(X)}{P(Y)} $$
where $P(X)$ a prior probability distribution (belief), and $P(Y)$ a data probability distribution (...
- 4,200
0
votes
0
answers
16
views
Determining when two variables are independent from a graphical model (unconditioned)
I am trying to find a general rule for determining when two variables $A$, $B$, are independent given a directed graphical model (Bayes net).
My idea of one such rule was simply that if in the ...
- 21
0
votes
1
answer
101
views
Bayesian network probability problem. Rainy on 3rd day given it rains on 1st day
Given the above bayesian network constructed in order to predict rain during successive days and the conditional probability tables. What would be the probability of P( Rain3∣ Rain1 )?
My approach:
...
- 13
0
votes
0
answers
21
views
Posterior probability, Dynamic Bayesian Network
I need help with part c).
However, these are the answers I got for a) & b):
a) P(S1) = P(S1 | S0) * P(S0) + P(S1 | ¬S0) * P(¬S0) = 0.65
b) P(¬Red_eyes and ¬Yawn | S1) = P(¬Red_eyes | S1) * (¬Yawn |...
- 23
0
votes
0
answers
37
views
Bayesian update of categorical distribution with weights
Background: I am using an Uncertainty Aware Neural Network for semantic classification of objects from an image, the input. The output is a probability distribution over a finite number of classes ...
1
vote
1
answer
64
views
Calculation of conditional probability in Probabilistic Graphical Model.
I'm reading through the Koeller and Friedman PGM book and there's an example PGM in Chapter 3. The student example. On page 54 the authors calculate $P(i^1|g^3) \approx 0.079$. The text states a ...
- 45
0
votes
0
answers
11
views
Posterior in markov random field using belief propagation (message passing)
Assuming a markov random field defined by following potentials $\phi(a,c)\phi(b,c)\phi(c,d)\phi(d,e)$. One knows the joint $p(a,b,c,d,e)=\frac{1}{Z}\phi(a,c)\phi(b,c)\phi(c,d)\phi(d,e)$ What is the ...
- 51
0
votes
0
answers
37
views
Hidden variables in bayes network
I am confused about identifying hidden variables in a given bayes network. In the bayes network given in the image, say we want to calculate $P(B/E)$. Inorder to find this, I understand that we should ...
2
votes
0
answers
51
views
What does it mean to marginalize and condition a causal graph?
In causal inference and Bayesian graphical models, the idea of "marginalization" and being "closed under marginalization and conditioning" is brought up and referred to in "...
- 175
0
votes
0
answers
15
views
Is it Possible to calculate probabilities on a Node, if one or two of Probabilities of the node on Bayes network not Given?
I just curious is it possible to calculate a Probabilities of something, if one of their nodes doesnt have the probabilities?
For example, i want to calculate probabilites of Storm. I know the ...
0
votes
0
answers
64
views
Why is log(p(x)) important in mathematics?
I read many papers for Bayesian Learning, and I can see that in every probabilistic formula they use a logarithm of a distribution p(x) (i.e. log(p(x))) or the negative logarithm of p(x) (i.e. -log((p(...
- 1
1
vote
0
answers
71
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 | ¬...
- 11
1
vote
1
answer
216
views
Conditional Probability in Bayesian Network
I am working on exercise 13.5 from Nong Ye's Data Mining - Theories, Algorithms, and Examples. The problem gives the following Bayesian network
as well as conditional probability tables showing the ...
- 574
1
vote
2
answers
79
views
What is the difference between $p(a|b)$ and $p(a)$?
I know that $$p(a|b)=\frac{p(a, b)}{p(b)}$$
And I also know $$p(a, b) = p(a)p(b)$$
So, algebraically, it all seems to me that $$p(a|b)=p(a)$$
I know something is wrong with this situation that I'm ...
0
votes
0
answers
49
views
Independence in Belief Networks
The belief network for the following questions is given below:
Q1: Which variables must be independent of A given C and S according to the belief network above?
My ans:
Since C is given, there is no ...
3
votes
1
answer
59
views
How to simplify integrals in the conditionals/marginals in a Bayesian Network
I'm trying to calculate the conditionals within a Bayesian network as shown in the picture, e.g. $P(X_t|X_{t-1}, S)$, which resorts to the calculation of the marginals $P(X_{t-1}, S)$ and $P(X_t, X_{t-...
- 31
1
vote
0
answers
37
views
Checking for independence in simple Bayessian network
Having the simple model, for example
$P(W\mid R)= 0.8$
Is probability of wet grass given rain and
$P(W\mid S)= 0.6$
Is probability of wet grass given sprinkler,
It is correct, that the $P(W \mid S,R)$,...
- 165
0
votes
1
answer
42
views
Doesnt seem right; Conditional Probability question
So heres my working out for the question.
I figured that I need to find three probabilities: P(c|x), P(y|c) and P(z'|c) as it is the probability they ate contaminated food given they have symptoms X ...
- 67
1
vote
1
answer
99
views
Conditional Independence, Bayes Network and d-separation
I have a diagram of a Bayes network as shown below:
$$\begin{array}{c}A&&&&B&&&&C\\&\searrow&&\swarrow\\&&D&&&&E\\&&&\...
- 189
0
votes
1
answer
31
views
Bayesian Network calculations given dependence of variables
I've been given this bayesian network 1 where $P(A) = P(A = t) = 0.2, P(B) = 0.5, P(C) = 0.8.$
$$\require{enclose}\begin{array}{c}\enclose{circle}{~~A~~}&&&&\enclose{circle}{~~B~~}&...
0
votes
0
answers
29
views
Bayes Net. How are the values P(G | D,I) calculated?
Example Bayes Net
I have been looking into Bayesian Networks but I keep getting hung up on a simple dependence in most example problems which is how are the values in the conditional probability ...
- 1
0
votes
2
answers
93
views
chain rule ordering
suppose I want to compute the joint probability $P(X,Y,Z)$ with chain rule. Is it true that there will be $3!$ possible factorization ? or is there more ? I got 6 for this example:
$P(X|YZ)P(Y|Z)P(Z)$...
- 37
0
votes
1
answer
115
views
calculate probability using variable elimination
Consider the following Conditional probability for the Bayesian Network:
By using variable elimination, how to calculate the following probability?
I am summing all the terms related to $E$, then ...
- 1
1
vote
0
answers
90
views
Algorithm for computing joint probability distribution from conditional probability table using tensor multiplication in Bayesian Network?
I get stuck on this problem. If in a Bayesian network, how can we do tensor multiplication on the conditional probability table so that it eventually gives the joint probability distribution? If a ...
- 61
0
votes
1
answer
77
views
How to calculate an intersection in bayesian network
I was trying to solve this question, but i don't know how to proceed from there. And i am not sure how to compute $P(A|X_1,X_2,\neg X_3)$ or $P(A \cap X_1\cap X_2)$. It seems like i don't understand ...
- 111
0
votes
1
answer
58
views
Bayes Rule combining two sensors
You are programming a demining robot. As the robot drives along, the
prior probability of a mine being in its immediate vicinity is 0.001
The robot is equipped with a mine detecting sensor which ...
- 1
2
votes
2
answers
356
views
Why does the conditional independent rule of INTERSECTION require STRICT POSITIVE DISTRIBUTION?
Recently, I was confused with the proofs of some conditional independent rules (decomposition, weak union, contraction, intersection), particularly the conditional independent rule of INTERSECTION.
In ...
0
votes
1
answer
52
views
Minimal Bayesian network for a given subset of variables?
Let $G=(V, E)$ be a DAG. Let $\mathrm{dom}$ be a domain for each node in $V$ and $P$ be a joint probabiliy distribution over those domains, that factors as a product of conditional probability ...
- 12.4k
0
votes
1
answer
32
views
How do I find the P(B | D = T) in this bayesina netowrk?
How to find P(B | D = T) in the following Bayesian network?
- 1
1
vote
1
answer
62
views
Shortest path with jumps (dynamic Bayesian network)?
Suppose I have the following graph structure:
It has the following properties:
There are four states $\mathcal{S} = {q,s_1,s_2,s_3}$ where $q$ is some origin state where we start from (though it is ...
- 712
0
votes
0
answers
23
views
Directed edges in Bayes net could have no effect?
After taking a risk analysis course, I am getting myself familiar with Bayes nets. Currently, I am looking at a common example of whether to take an umbrella on a walk. This is in the context of ...
- 189
1
vote
0
answers
84
views
True Loss for Bayes Classifier with Two Classes
For a Bayes classifier of two classes (say 0 and 1), I'm not understanding how the largest possible true risk would be 0.5? I'm assuming that we assign a 0 loss for a correct classification and a loss ...
- 31
-1
votes
1
answer
92
views
Property between probability spaces
$\textit{Q1:}$ Why the statement below holds? If someone could give the intuition and/or a proof I would appreciate it. (this one is answered already so check $Q2$)
Suppose that $\mathcal{I}=(X,\mu)$ ...
- 243
0
votes
1
answer
115
views
How do I calculate the diagnostic inference for Bayes Net with multiple evidence and hidden variable?
I have a Bayes Net for a tsunami alarm at nuclear power plants that looks like this:
Top node is "Tsunami" = (T or F) is the ground truth of whether there is a Tsunami approaching. There is ...
- 51
1
vote
0
answers
35
views
Computing value of noisy-MAX model
I am having trouble computing the remaining probabilities with the use of an interaction model called the noisy-MAX. The noisy-MAX model is an interaction model which helps a network engineer ...
- 127
0
votes
1
answer
24
views
Peripheralization of Conditional Distributions of head to tail model
If we peripheralize the concurrent probability of the head to tail graphical model for c, we get the following equation.
$p(a,b) = p(a)Σ_{c}p(a|c)p(c|b) = p(a)p(b|a)$
The question is, does the ...
- 103
1
vote
1
answer
141
views
Variable elimination, Bayesian network
I'm self learning the topic variable elimination and try to solve some questions see if I fully understand the concept. But I'm stuck on this problem's second question for hours.
Base on my ...
- 15
0
votes
1
answer
63
views
Multiplication of conditional probability
I was looking up on Bayesian networks and came across this video. In which it states:
And I was wondering, how did he get $P(B|A)*P(C|B) = P(B,C|A)$?
- 162
3
votes
2
answers
1k
views
What is the relationship between Probabilistic Graphical Models and Graph Neural Networks?
I would like to learn more about one or both of these. I incline towards Bayesian networks and PGMs but since Battaglia et al, 2018 I have had half an eye on the various kinds of GNN.
You seem to be ...
- 133
-1
votes
1
answer
89
views
Prove that non-descendants of C are conditionally independent given C's parents
I'm trying to understand conditional independence and want to show for the following bayesian network:
$$p(A,B,C,D,E) = p(A)p(B)(C|A)p(D|B)p(E|D,C)$$
that $C$ is conditionally independent of $B$ or $C$...
- 11