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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What does the log-likelihood say and how is it to be interpreted?

Intro I am new to AI and I started with modeling a bayesian network for my AI agent. I learned the parameters using the EM algorithm. Besides the computed conditional probability distributions, the ...
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Given A and B, C are independent of each other. Given A, B and C, D and E are independent of each other. What is the minimal number of parameters?

Assuming all variables $A, B, C, D,$ and $E$ are random binary variables. I come up with Bayes net: $D \rightarrow B \rightarrow A \leftarrow C \leftarrow E$ which has the minimal number of parameters ...
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Why are Directed Graphical Models considered ML methods?

Consider the following problem. The probability of being born in countries [1,2,3,4] is given by [a, b, c, d] respectively. This is a categorical problem. Now, assume that the height of a person ...
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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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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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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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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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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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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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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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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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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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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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2 answers
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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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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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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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3 votes
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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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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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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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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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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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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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2 answers
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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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1 answer
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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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3 answers
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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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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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2 votes
1 answer
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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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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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