What is "Bayes' rule" in Bayesian Networks?
P(A|B)=P(B|A)*P(A)/P(B)
P(A|B)=P(B|A)*P(A)
P(A|B)=P(B|A)*P(B)
P(A|B)=P(A)/P(B)
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Which of the following is NOT a use case for Bayesian Networks?
Predictive modeling
Classification
Feature selection
Time series forecasting
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Suppose we have a Bayesian Network with a plate (i.e., a set of nodes that share a common probability distribution). How does the plate affect the computation of the posterior probability distribution?
It reduces the number of nodes in the network
It increases the number of nodes in the network
It has no effect on the number of nodes in the network
It depends on the specific plate and nodes
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Suppose we have a Bayesian Network with a noisy-OR gate as its conditional probability distribution. How does this gate affect the behavior of the network?
It reduces the probability of the output node
It increases the probability of the output node
It has no effect on the probability of the output node
It depends on the specific noisy-OR gate
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Suppose we have a Bayesian Network with a cycle (i.e., a node that points back to itself). Which algorithm can be used to perform inference on this network?
Exact inference
Approximate inference
Belief propagation
Gibbs sampling
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Which of the following is a characteristic of a Bayesian Network?
It is a directed acyclic graph (DAG)
It is an undirected graph
It is a probabilistic graphical model
It is a neural network
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Consider a Bayesian Network with three variables A, B, and 𝐶 where

A→B and B→C. How would you marginalize B out from the joint distribution

P(A,B,C)?

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In the variable elimination algorithm, when eliminating a variable XXX, which of the following operations is required on the factors that depend on XXX?
Marginalization
Normalization
Multiplication
Addition
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When performing Gibbs sampling, which of the following is the key challenge in achieving convergence to the correct distribution?
Ensuring the variables are conditionally independent.
Sampling from the exact marginal distribution
Dealing with variables that have complex conditional distributions.
Handling high-dimensional joint distributions.
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Suppose you have a Bayesian Network with two variables X and

Y, where X→Y. If you are given P(X)=0.3 and P(Y=1∣X=0)=0.2, P(Y=1∣X=1)=0.8, what is

P(Y=1)? (Upto 2 decimals)

0.56
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What is the purpose of hybrid MCMC in Gibbs Sampling?
To reduce computational complexity
To improve convergence rate
To reduce variance of estimates
To increase precision of estimates
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What is the purpose of importance sampling in Gibbs Sampling?
To reduce computational complexity
To improve convergence rate
To reduce variance of estimates
To increase precision of estimates
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Which of the following is a common technique used in Gibbs Sampling to improve convergence?
Tempering
Annealing
Adaptive MCMC
Importance sampling
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What is the purpose of the Metropolis-Hastings algorithm in Gibbs Sampling?
To propose new values for each variable
To accept or reject proposed values for each variable
To compute the exact posterior distribution
To eliminate variables from the network
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What is the purpose of the burn-in period in Gibbs Sampling?
To discard initial samples that are not representative of the target distribution
To compute the exact posterior distribution
To eliminate variables from the network
To compute the joint probability distribution of a Bayesian Network
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Positive Marks: 2.00
Negative Marks: 0.66