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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Calculate probability of state with information of underlying distribution

I have a problem with this setting: There are 2 possible states (1,-1), there are j agents, each agent receives an iid normally distributed signal with the state as the mean and std dev x. Each agent ...
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Graphical Representation of Dynamic Bayesian Network

Some tourists visiting a cabin are interested in finding out if there are animals nearby. They can observe outside of their window every day whether there are animal tracks and whether the food they ...
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Improvement in NN regressor by Negative Log Liklihood loss vs MSE loss

I am trying to write a simple NN based regressor, and I have noticed that if i take two identical NN, one with mean square error loss, ane with sample drawn as gaussian prior over final output, with ...
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Forecasting with Dynamical Bayesian Networks

I am trying to forecast some variables of a dataset (time series) with Dynamical Bayesian Networks (DBN) using pgmpy. I could be mistaken, but what is being called "forecasting" in the ...
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Calculating Probabilities in a Bayesian Network

The Bayesian network below contains only binary states. The conditional probability for each state is listed. From the Bayesian network, calculate the following probabilities: a) $P(b)$ b) $P(d)$ c)...
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Number of Variables Needed to Represent Bayesian Network and Independence

Consider the Bayesian Network Structure Below, decide whether the statements are true or false. a) If every variable in the network has a Boolean state, then the Bayesian network can be represented ...
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Dynamic bayesian model conditional independence

I have just started learning probabilistic graphical models, so my knowledge of this subject is relatively weak. Hope I don't make any mistakes in my question. Given the Dynamic Bayesian model shown ...
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Belief propagation on Polytree

I'm working through exercises on Belief Propagation and the Junction Tree Algorithm and I'm stuck with the following problem. Consider the distribution P(A,B,C,D,E,F,G,H)=P(A)P(B)P(C)P(F) P(D|A,B)P(E|...
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Probability of at least one success in a long string of connected events

I have N events (i from 1 to N), each with an estimated probability of success, p(i). If all my events were independent I'd be able to calculate the probability of at least one success as (1 - product ...
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How can a random variable be independent of a member of its minimal Markov blanket?

Consider the following Bayes network of random variables on some probability space: The local Markov property asserts that any variable is independent of its non-descendants given its parents. Here, $...
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Factor graph equivalent to markov networks

Consider the following potential on three nodes. represented by the following factor graph. Now the notes claim that we can represent this factor graph as both a Bayesian network and a Markov ...
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How to count the number of independent parameters in a Bayesian network?

I'm currently going through Prof. Daphne Koller's probabilistic graphical models course on Coursera and had a question regarding an exercise problem. The problem is as follows: How many independent ...
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Question regarding assuming independence in a V-structure in a Bayesian network

I'm currently solving the same problem that was posted in this Stack Overflow question but had a question regarding another aspect of the problem. The source of this problem is the course regarding ...
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Bayes by backprop unbiased monte carlo gradients

I am currently trying to understand a paper on bayesian neural networks whereby the authors use a bayes by backprop approach to learn weight uncertainties in the neural networks. I am trying to ...
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Algorithm for inference on continuous bayesian networks?

I am currently working with Bayesian Networks, and I would like to try some inference on continuous variables. On the book from Neapolitan "Learning Bayesian Networks", on chapter 4, it is ...
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Where do the “semantics” of a Bayesian network come from?

On Bayesian Networks, Ghahramani (2001) says: A node is independent of its non-descendants given its parents. This point is fundamental enough that Ghahramani calls it the “semantics” of a Bayesian ...
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Making sense of the belief propagation on graphs

I sort of understand when do I use variational Bayesian and when do I use expectation maximization. But now I want to know when do I use belief propagation in graphs to solve an estimation problem. ...
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How to use belief propagation sum product algorithm in a factor graph to solve inference problem?

I've read about belief propagation and sum product algorithm but still don't know how to apply it. For simplicity, I want to apply it to estimate the variable $x$ from this equation, $y=x+n$, where $n$...
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Modern applications of Bayesian Model Selection

I'm trying to understand the merits of this field so I'll try to break down my question. Research: Is Bayesian model selection considered a popular topic of research these days? Variable selection: ...
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Introduction to approximate message passing

I'm interested in learning approximate message passing from the paper "Message Passing Algorithms for Compressed Sensing: I. Motivation and Construction". My background is in computer ...
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Learning parameters for a bayesian network from data with different oberservation frequencies

I have a Bayesian network of a given structure and nodes A, B, C, D, E and want to learn the parameters of the network, i.e. the conditional probabilities, from data with differing frequencies of ...
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Why does the causal markov condition allow for the interpretation of a bayesian network as a causal diagram?

A related question is here. As far as I can understand from scanning reviews on causal discovery, there are two critical conditions, (1) the causal markov condition and (2) causal faithfulness. It is ...
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Bayesian mixture model joint posterior

I am just starting to learn about bayesian mixture models. There is a few clarifications that I want to make which I am not sure myself. The graphical model below describes a gaussian mixture model ...
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How to combine continuous and discrete variables for bayesian network? [duplicate]

Basically the title says the question. I have a data set with both types of variables and AFAIK bayesian networks are constructed for discrete variables. Is it possible to somehow use them together?
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Bayesian Regression Estimates

Hi I am new to Bayesian Regression, I wanted to understand why would the Bayesian regression give exactly the same results as the priors supplied? I tried running a bayesian model on 10% of the data ...
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Bayesian Regression Model

I am new to Bayesian modeling. I am running Bayesian regression model in R using brm function from brms library, which is powered by STAN. I have a data with 10 million records. I took 10% sample out ...
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Which algorithm suits for classification of multivariate time series data?

I have multivariate time series data, where the goal is to predict a binary label, which is changing in time. For illustration: there are 20 individuals, for each of them I measure 50 values (...
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Is it possible to create a binary classifier from bayesian network?

I have a labeled data set consisting of longitudinal data and I would like to train a dynamic bayesian network. The output should be probability of the observation being 1 in a selected step given the ...
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How to report the parameter learning results from dynamic Bayesian network for test and control groups in a research paper?

I have a Dynamic Bayesian Network which I used in my research. Network is shown below: It was employed in an educational video game and I ran the experiment for test and control groups separately. ...
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Why prior distribution is not conditioned on X?

I would like to know why in the below formula the prior distribution of theta is not conditioned on X (observations): $$P(\theta|X, y)=\frac{P(y|X, \theta)P(\theta)}{P(y|X)}$$ In my understanding, the ...
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Do-calculus example from PGM Book by Daphne Koller

Consider the last line of this example. The relevant DAG is shown here. Clearly, $G$ is d-separated from $\hat{S}$ given S, J because the path $G-J-S-\hat{S}$ is blocked by S since arrows meet at S ...
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Should I report credible intervals based on HDI or QI?

I have highly positively skewed outcome variable. I need to publish my results in an academic journal. tidybayes allows calculating credible intervals (CI) using median or mean with high density ...
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Assessing impact of concurrent interventions on time series data

I am hoping to assess which interventions create the most change in multiple response variables. What makes this problem more complicated than typical intervention analysis is the concurrent nature of ...
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Training a Bernoulli model using probabilities as inputs

I'm using two methods to train a Bernoulli model, and am trying to understand why they are not yielding similar results. For both methods, I have a length $N$ array of probabilities $\{\hat{y}^{(n)}\}...
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Bayesian neural network with delta variational distribution (Stochastic Variational Inference)

Is doing the stochastic variational inference (SVI) with the delta variational distribution on a Bayesian neural network the same as doing the frequentist inference, or is it still a Bayesian ...
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Graphic model factorizing, marginalization

This is actually a probability marginalization question that I encountered in graphic models section of PRML by Bishop (question about equation 8.26 page 391). Assume I have the following graphic ...
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Packages for autoregressive HMM?

I have data I'd like to fit a generalized HMM on: my observations $\{Y_t\}_{t=1}^N$ and my states $\{X_t\}_{t=1}^N$ are both time series. The specific task I'd like to do is decoding the states given ...
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How do we generate the samples of hidden root nodes in the Bayes network (Sigmoid Belief Networks) of a generative model

Following is a Sigmoid Belief Networks where we can only observe the bottom observable layer $v.$ Usually we use ...
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Why did the inclusion of random effect drastically change the parameter estimates

I working on a project using Poisson model with an offset term. Points to note: The structure of the data is such that; data were collected at state level for each year starting from 2010 to 2015. ...
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Do variational approximations capture the flow of influence or “conditional independence” relationships in graphical models?

Probabilistic Graphical Models (PGMs) are used to model all sorts of complex decision processes, such as medical diagnoses or robot positions, etc. In common machine learning textbooks, like ...
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What is the benefit of adding control flow to probabilistic programming?

I was watching an interesting video on the Pyro package in Pytorch for probabilistic programming. One of the things that they ...
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Are nodes outside the markov blanket unconditionally independent?

Apologies if my question is deeply flawed, I've been working through a lot of material in the past few weeks and have a few blind spots here and there. On one level my question is this - given a ...
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Multi-object counting under uncertainty

I am interested in learning about different ways to model ones beliefs about hearing related sounds under uncertainty. Specifically, how might I model the following: There is a finite set of possible ...
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how to find a better bayesian networks structure for large-scale dataset

The data set we hold is related to the after-sales service of a factory, which has about one million records, 8 variables, and a large number of different modes in these variables, (for example, one ...
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Question about Marginalizing Distributions from CMU 10-701, HWK3, Problem #3

I have a question about a pseudocode write-up from an online course that I've been following. Currently I am going over the Bayes Nets section. Here are the links to the homework and it's solution key:...
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Bayesian estimation for analysing project evaluation

Using Bayesian estimation how can we assess the group projects given that different members in the group may have performed differently?
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Messages to parents in variational message passing

I am trying to understand the message passing algorithm in Variational approximation from this and this paper. It all makes sense to me until they explain the message from children to parents. More ...
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Chain rule for Bayesian Networks posterior probability

suppose there are 3 independent binary variables: a1,a2,a3 and there is one variable: c = a1+a2+a3 ...
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Epistemic and Aleatoric uncertainty formula for regression tasks

I read this smart github repo with paper : https://github.com/kumar-shridhar/PyTorch-BayesianCNN! And they are capable of computing the aleatoric and the epistemic uncertainties for a classification ...
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Probability of an event in bayes network

I am a second year grad student who was recently accepted in a PhD program. My professor wants me familiar with networks and network modeling. My professor has some large data of geographic, ...

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