Questions tagged [bayesian-network]

A Bayesian network is a probabilistic directed acyclic graph. Nodes represent random variables in the Bayesian sense (observable or unobservable); edges represent conditional dependencies between nodes.

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Does statistical independence mean lack of causation?

Two random variables A and B are statistically independent. That means that in the DAG of the process: $(A {\perp\!\!\!\perp} B)$ and of course $P(A|B)=P(A)$. But does that also mean that there's no ...
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36 votes
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Why is AUC higher for a classifier that is less accurate than for one that is more accurate?

I have two classifiers A: naive Bayesian network B: tree (singly-connected) Bayesian network In terms of accuracy and other measures, A performs comparatively worse than B. However, when I use the R ...
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Difference between Bayesian networks and Markov process?

What is the difference between a Bayesian Network and a Markov process? I believed I understood the principles of both, but now when I need to compare the two I feel lost. They mean almost the same ...
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6 answers
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Difference between Bayes network, neural network, decision tree and Petri nets

What is the difference between neural network, Bayesian network, decision tree and Petri nets, even though they are all graphical models and visually depict cause-effect relationship.
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24 votes
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Structural Equation Models (SEMs) versus Bayesian Networks (BNs)

The terminology here is a mess. "Structural equation" is about as vague as "architectural bridge" and "Bayesian network" is not intrinsically Bayesian. Even better, God-of-causality Judea Pearl says ...
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From Bayesian Networks to Neural Networks: how multivariate regression can be transposed to a multi-output network

I'm dealing with a Bayesian Hierarchical Linear Model, here the network describing it. $Y$ represents daily sales of a product in a supermarket(observed). $X$ is a known matrix of regressors, ...
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18 votes
3 answers
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Understanding d-separation theory in causal Bayesian networks

I am trying to understand the d-Separation logic in Causal Bayesian Networks. I know how the algorithm works, but I don't exactly understand why the "flow of information" works as stated in the ...
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18 votes
1 answer
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Bayesian network inference using pymc (Beginner's confusion)

I am currently taking the PGM course by Daphne Koller on Coursera. In that, we generally model a Bayesian Network as a cause and effect directed graph of the variables which are part of the observed ...
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2 answers
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When to use Bayesian Networks over other machine learning approaches?

I expect there may be no definitive answer to this question. But I have used a number of machine learning algorithms in the past and am trying to learn about Bayesian Networks. I would like to ...
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14 votes
4 answers
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Do edges in directed acyclic graph represent causality?

I am studying Probabilistic Graphical Models, a book for self-study. Do edges in a directed acyclic graph (DAG) represent causal relations? What if I want to construct a Bayesian network, but I am ...
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13 votes
2 answers
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What are the advantages of using a Bayesian neural network

Recently I read some papers about the Bayesian neural network (BNN) [Neal, 1992], [Neal, 2012], which gives a probability relation between the input and output in a neural network. Training such a ...
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12 votes
2 answers
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Explanation of I-map in a Markov/Bayesian network

I am finding the concept of an I-map (Independency-map) in the context of Markov networks and Bayesian networks difficult to understand. From Probabilistic Graphical Models, Koller and Friedman, 2009: ...
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12 votes
2 answers
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building a classification model for strictly binary data

i have a data set that is strictly binary. each variable's set of values is in the domain: true, false. the "special" property of this data set is that an overwhelming majority of the values are "...
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11 votes
1 answer
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Markov blanket vs normal dependency in a Bayesian network

While I was reading about Bayesian networks, I run into "Markov blanket" term and got severely confused with its independency in a Bayesian network graph. Markov blanket briefly says that every ...
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3 answers
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Why use factor graph for Bayesian inference?

I don't understand why converting a Bayesian network into a factor graph is good for Bayesian inference? My questions are: What is the benefit of using factor graph in Bayesian reasoning? What would ...
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10 votes
2 answers
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Marginalization of conditional probability

I am working through these examples of computations on Bayesian networks and came across this claim (part of the last sample computation): $$ P(E=e|A=a) = \sum_{c \in C} P(E=e, C=c | A=a) $$ I am ...
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9 votes
3 answers
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Probabilistic graphical models textbook

Is Koller's "Probabilistic Graphical Models" suitable as a textbook? Or is there another book which is more recommendable as textbook for a master-course? Disclaimer: cross-posted from quora.com, ...
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2 answers
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What is the relation between belief networks and Bayesian networks?

How are Bayesian networks related to deep belief networks? Are they the same? From the post What is the difference between a neural network and a deep belief network?, I gathered that deep belief ...
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9 votes
2 answers
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How to learn Bayesian Network Structure from the dataset?

I need to learn a Bayesian Network Structure from a dataset. I read the book titled "Learning Bayesian Networks" written Neapolitan and Richard but I have no clear idea. According to the book from ...
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1 answer
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Incorporating prior knowledge into artificial neural networks

Artificial neural networks have a bad reputation of being a black box. More over in cases when we do have some prior knowledge about the domain of a particular supervised learning problem it is not ...
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8 votes
3 answers
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What is the number of parameters needed for a joint probability distribution?

Let's suppose we have $4$ discrete random variables, say $X_1, X_2, X_3, X_4$, with $3,2,2$ and $3$ states, respectively. Then the joint probability distribution would require $3 \cdot2 \cdot2 \cdot ...
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1 answer
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Why is the Kalman Filter a specific case of a (dynamic) Bayesian network?

Question: How can this be the case? Why are Kalman filters so much more complicated than any other Bayesian network? Are there any Bayesian networks which are intermediate in complexity? Perhaps one ...
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8 votes
1 answer
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What is a factorized Gaussian distribution?

I am reading the post Online Bayesian Deep Learning in Production at Tencent about Bayesian deep learning. It mentions that we can approximate a distribution $p_t(w\mid x)$ by a simple distribution $...
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8 votes
3 answers
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Prediction of continuous variable using "bnlearn" package in R

I use bnlearn package in R to learn the structure of my Bayesian Network and its parameters. What I want to do is to "predict" the value of a node given the value of other nodes as evidence (obviously,...
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8 votes
1 answer
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What is the point of graphical models?

I spent the day learning about the bnlearn package in R only to discover that Bayesian models do not work with undirected graphs. I'm trying to learn about the Markov Random Field Network, and so far ...
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8 votes
1 answer
791 views

How does explaining away cause problems for learning?

In one of his lectures Geoff Hinton explains that a big problem of sigmoid belief nets is the explaining away phenomenon. I didn't fully understand this. I see that the induced width of the graph ...
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8 votes
2 answers
1k views

normalization in max-sum algorithm (loopy belief propagation)

I was implementing the max sum algorithm for a general graph (i.e., the ones with a cycle). I updated the messages as indicated in http://www.cedar.buffalo.edu/~srihari/CSE574/Chap8/Ch8-...
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8 votes
1 answer
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What is the idea behind Bayes By Backprop?

Having looked through the internet and the paper, I find Bayes by Backprop very inaccessible for my intermediate understanding of variational inference. Most online guides also lack some explaining ...
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8 votes
1 answer
3k views

Why do Bayesian Networks use acyclicity assumption?

Actually, this question is more or less a duplicate of the one which I have asked on math.stackexchange two days ago. I did not get any answer there but I think now here is a better place to ask ...
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7 votes
2 answers
384 views

Posterior distribution is impossible depending on which prior hyperparameters are used?

Suppose we randomly select one of two coins and flip it. In that situation we have random variables $\alpha$ and $\delta$, where $\alpha$ tells us which coin we select, and $\delta$ tells us whether ...
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2 answers
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Gibbs sampling how to sample from the conditional probability? Bayesian model

I want to learn Gibbs sampling for a Bayesian model. How can I sample the variable from the conditional distribution? In this example, arrow means dependent; for example, ...
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7 votes
1 answer
2k views

Bayesian network vs. association rules

Apriori algorithm finds some implication rules. Similar results are provided by Bayesian networks. What is the essential difference? What are the specific advantages/disadvantages? Edit: The ...
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7 votes
1 answer
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What are the downsides of bayesian neural networks?

Bayesian neural nets (BNN) are very popular topic. With development of variational approximation it became possible to train such models much faster then with Monte Carlo sampling. BNNs allow such ...
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7 votes
1 answer
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Dynamic Bayesian Network library in Python [closed]

Can you please introduce me a good python library that supports both learning (structure and parameter) and inference in Dynamic Bayesian Network? Thanks in advance
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7 votes
1 answer
355 views

Causality: Models, Reasoning and Inference, by Judea Pearl: Causal Bayesian Networks and the Truncated Factorization

Background: $\newcommand{\doop}{\operatorname{do}}\newcommand{\op}[1]{\operatorname{#1}}$ Definition 1.2.2 (Markov Compatibility) If a probability function $P$ admits the factorization of $$P(x_1,\...
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7 votes
2 answers
364 views

Why do structure learning for Bayesian networks?

Given a very-large data set, if our goal is to do probabilistic inference, what are the main advantages of learning a Bayesian network from data and then, use the Bayesian network to compute ...
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7 votes
1 answer
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Prediction with Bayesian networks in R

I've been trying to teach myself about Network Analysis, and I've been able to develop DAG charts in R. However, I've looked through three or four R packages and have seen little in the way to a ...
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  • 2,185
7 votes
0 answers
424 views

Bayes Net Parameter Learning in pymc

My goal is to infer the conditional probability tables (CPT) from the classic rain, sprinker, wet grass problem. Normally in this problem we know the CPTs and, given an observation like "the grass is ...
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7 votes
0 answers
422 views

Comparing Factorie and Figaro languages for Statistical Relational Learning

I am looking to implement statistical relational learning, preferably in a modern programming language, and came across Factorie and Figaro for Scala. But most resources online that compare these are ...
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6 votes
4 answers
967 views

Graphical Models and Explaining Away?

So I have fundamental confusion about graphical models. Suppose the following graphical model is given: Now the question is do we have the following equality?: $$p(m_2|\alpha,\beta,y_3)=p(m_2|\alpha,\...
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6 votes
3 answers
1k views

Inconsistencies between conditional probability calculations by hand and with pgmpy (Bayesian Graphical Models)

I am teaching myself about Bayesian graphical networks. I'm attempting to use the python package pgmpy to generate the networks in python. This seems like a great resource. For my first test, I ...
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6 votes
1 answer
3k views

Are D-separation and Conditional independence equivalent?

For a directed graphical model, does D-separation is equivalent to conditional independence. I have got bit confused about this concept from the following statement from this source. if X and Y ...
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6 votes
2 answers
167 views

Regarding the formula of using $\text{P}(Y|X)$ to compute $\text{E}[X]$

When reading a presentation on "expectation propagation," I found a strange formula for computing $\text{E}[X]$ from a conditional probability: $$\text{E}[X] = \frac{\int x P(y_i|x) dx}{\int P(y_i|x) ...
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  • 2,647
6 votes
4 answers
2k views

Combining one class classifiers to do multi-class classification

I am working on a 3-class classification problem. The classifier I'm using is Bayesian Networks which provides me with a classification accuracy of around 60%. When I do a two-class classification, I ...
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6 votes
2 answers
549 views

Latent variables in Bayes nets with no physical interpretation

In Pattern Recognition and Machine Learning Bishop writes about Bayes networks: For practical applications of probabilistic models, it will typically be the highernumbered variables corresponding ...
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6 votes
2 answers
463 views

What is the meaning of generating data from a probabilistic model such as a naive bayes classifier?

I am studying probabilistic modeling but I am stuck with the concept of generating data from the probabilistic model. Say I have built a naive bayes classification model, what is the point of ...
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  • 2,605
6 votes
1 answer
4k views

Inference for Dynamic Bayesian Networks

I have a lot of time-series data for physical systems, where the underlying state-space model is quite complex and definitely not linear, so a Kalman Filter is out of the question. Following the ideas ...
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6 votes
2 answers
1k views

Intuitively how does Bayesian Network Structure Learning Work?

Learning the causal relationship from data in Bayesian Network literature is a mystery for me. Because most of the data in Bayesian network literature does not have the "time order" information. How ...
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6 votes
1 answer
3k views

How do v-structures in graphical models reflect real world data?

I understand d-separation and how v-structures in graphical models work. What i don't understand is how they relate to real world multivariate data. I don't see how v-structures can be separated from ...
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  • 552
6 votes
1 answer
460 views

Bayesian networks for one-class classification

From the definition of one-class classification in wikipedia: In machine learning, one-class classification, also known as unary classification or class-modelling, tries to identify objects of a ...
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