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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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 ...
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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 ...
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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 $r$. ...
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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 ...
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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 ...
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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. ...
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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&...
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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 ...
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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 ...
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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 (...
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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 ...
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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 ...
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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 ...
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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 ...
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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 \...
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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 ...
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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) =...
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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 ...
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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 ...