# Questions tagged [bayesian-network]

For questions related to Bayesian networks, which are e.g. used to study causality (or causation) in AI.

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1answer
31 views

### What Constitutes Messages in Junction Tree Algorithm?

I'm currently studying the Junction Tree Algorithm: I'm referring to the process of transforming a Bayesian Network into a Junction Tree in order to apply inference. I understand how you build the ...
2answers
92 views

### Can maximum likelihood be used as a classifier?

I am confused in understanding the maximum likelihood as a classifier. I know what is Bayesian network and I know that ML is used for estimating the parameters of models. Also, I read that there are ...
0answers
20 views

### Does the measurement noise refers to the variance in the predicted or observed measurements in Kalman filters?

In the Kalman filter we have s.th. called the process noise and the measurement noise. A measurement is computed by multiplying our state $x$ with a matrix $H$ and adding the measurement noise $r$. ...
0answers
17 views

### Kalman Filter: Intuitive explanation of gain and variability in measurements and estimated states?

I'm trying to understand how Bayesian Filters (especially Kalman Filter) works. My understanding so far (please correct me if I am wrong) Assume I have measurements $y_k$, states $x_k$, the estimated ...
0answers
19 views

### In Probabilistic Graphical Model (written by Daphne Koller), what's the meaning of “parameter” in representation of the distribution?

I just started to read the PGM book written by Daphne Koller. In the chapter of Bayesian Network Representation(Chapter 3), there are some descriptions about the standard parameterization of the joint ...
1answer
33 views

### Does the Bayesian MAP give a probability distribution over unseen t*?

I'm working my way through the Bayesian world. So far i've understood that the MLE or the MPA are point estimates, therefore using such models just output one specific value and not an distribution. ...
1answer
73 views

### Mutual Information and Link Strength in Bayesian Network

I'm trying to understand how to calculate the strength of every arc in Bayesian Network. I came across this paper, https://smartech.gatech.edu/bitstream/handle/1853/14331/GT-IIC-07-01.pdf?sequence=1&...
3answers
583 views

### What is the definition of a heuristic function in the BayesChess paper?

I am reading BayesChess: A computer chess program based on Bayesian networks (Fernandez, Salmeron; 2008) It is a chess-playing engine using Bayesian networks. The following is mentioned about the ...
0answers
25 views

### 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 ...
2answers
176 views

### What is the difference between a Bayesian Network and a Markov Chain?

I am trying to understand the difference between a Bayesian Network and a Markov Chain. When I search for this one the web, the unanimous solution seems to be that a Bayesian Network is directional (...
0answers
229 views

### How can I draw a Bayesian network for this problem with birds?

I am working on the following problem to gain an understanding of Bayesian networks and I need help drawing it: Birds frequently appear in the tree outside of your window in the morning and ...
2answers
670 views

### Are Bayesian networks important to learn in 2018?

I study AI by myself with the book "Artificial Intelligence: A Modern Approach". I've just finished the chapters about the Bayesian network and probabilities, and I found them very interesting. Now, I ...
0answers
45 views

### Why do Bayesian algorithms work well with small datasets?

I read very often that Bayesian algorithms work well on small datasets. Why is that? I think it is because they might generalize more, but why is that? See also Investigating the use of Bayesian ...
1answer
57 views

### How do I determine the most appropriate classifier for a certain problem?

Consider a Bayesian classifier used in spam e-mail filtering. It converts an e-mail to a vector, most of the time using the bag-of-words method. Although it learns first before getting employed, it ...
1answer
470 views

### Why is exact inference in a Bayesian network both NP-hard and P-hard?

I should show that exact inference in a Bayesian network (BN) is NP-hard and P-hard by using a 3-SAT problem. So, I did formulate a 3-SAT problem by defining 3-CNF: (x_1 \lor x_2) \land (\neg x_3 \...
0answers
44 views

### What is the point of converting conditional probability to factor for Variable Elimination?

I have this slide from my AI class on using a Bayes network to compute a conditional probability. I don't really understand the point of converting the conditional probabilities to factors (besides ...
3answers
92 views

### Is it possible to compute $P( F \mid S )$ given $P(F \mid S,A)$, $P(F \mid S, \lnot A)$?

I have a bayesian network, which has the following data: $P(S) = 0.07$ $P(A) = 0.01$ $P(F \mid S,A) = 1.0$ $P(F \mid S, \lnot A) = 0.7$ $P(F \mid \lnot S, A) = 0.9$ \$P(F \mid \lnot S, \lnot A) =...
1answer
75 views

### Problem with Proposition 1 of Google Deepmind's 'Weight uncertainty in Neural Networks'

I'm going through the paper Weight Uncertainty in Neural Networks by Google Deepmind. In the final line of the proof of proposition 1, the integral and the derivative are swapped. Then the derivative ...
0answers
123 views

### What are the main benefits of using Bayesian networks?

I have some trouble understanding the benefits of Bayesian networks. Am I correct that the key benefit of the network is that one does not need to use chain rule of probability in order to calculate ...