Questions tagged [bayesian-networks]

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

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18 views

How do I know the matrix dimensions when summing out variable from product of factors?

Figure 14.10 on p. 527 of Norvig and Russell's book "Artificial Intelligence: A Modern Approach" shows: I see how the submatrices are formed by fixing the variable to each value of $A$, ie. ...
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31 views

Variational Inference: Approximate expected log likelihood via sampling

I'm working my way through a simple variational inference from scratch. For that, I assume that z denotes the probability of a coin showing ...
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32 views

What makes Sequential Bayesian Filtering and Smoothing tractable?

I'm currently diving into the Bayesian world and I find it pretty fascinating. I've so far understood that applying the Bayes' Rule, i.e. $$\text{posterior} = \frac{\text{likelihood}\times \text{prior}...
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24 views

specifying a hybrid Bayesian network in pyro

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: ...
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42 views

What does all the formula and pictures mean?

https://www.nature.com/articles/s41467-020-17419-7 I am a medical school graduate and I really want to learn AI/ML for computer-aided diagnosis. I was building a symptom checker and I found the ...
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13 views

In the original GAN paper, why is it mentioned that you can sample deep directed graphical models without a Markov chain?

In the original GAN paper (table 2), why is it mentioned that you can sample deep directed graphical models without a Markov chain (well, they say without difficulties, but others list MCMC as a ...
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20 views

What are the practical problems where full bayesian treatment is affordable?

Suppose, I have a problem, where there is rather a small number of training samples, and transfer learning from ImageNet or some huge NLP dataset is not relevant for this task. Due to the small number ...
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1answer
36 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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26 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 ...
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1answer
110 views

How are the "Link Strength true", "Link Strength blind" and "Mutual Information" calculated in this report on Bayesian networks?

I'm trying to understand how to calculate the strength of every arc in a Bayesian Network. I came across this report Measuring Connection Strengths and Link Strengths in Discrete Bayesian Networks, ...
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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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260 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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249 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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62 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
59 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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108 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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50 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
95 views

Is it possible to compute $P( F \mid S )$ given $P(F \mid S,A)$ and $P(F \mid S, \lnot A)$ in Bayesian network?

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
84 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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167 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 the chain rule of probability in order to ...
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2answers
64 views

Can we derive the distribution of a random variable based on a dependent random variable's distribution?

In the diagram below, there are three variables: X3 is a function of (depends on) X1 and X2, ...
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1answer
40 views

How to perform structure learning for Bayesian network given already partially constructed Bayesian network?

Let's assume that we have a dataset of variables (random events)I apriori would like to set dependency conditions between some of them and perform structure learning to figure out the rest of the ...
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3answers
653 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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394 views

What does a hybrid Bayesian network contain?

The field of artificial intelligence is so vast. There are many methodologies for handling continuous data, and I have just read about the hybrid Bayesian network. I just want to know that what a ...
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1answer
593 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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723 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 ...