15. Bayesian Networks 1 Flashcards
What is a Bayesian Network?
A Bayesian Network is a graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). It is used to describe joint probabilities and allows for the calculation of complex joint distributions using local conditional probabilities.
What are the key components of a Bayesian Network?
The key components are: 1. Nodes: Represent variables with their domains. 2. Edges: Encode interactions or conditional probabilities between variables. 3. Nodes not directly connected: Represent independent random variables.
What is the difference between a directed and an undirected graph?
In a directed graph, edges have a direction (from one node to another), while in an undirected graph, edges have no direction and represent mutual relationships.
What is a DAG (Directed Acyclic Graph)?
A DAG is a directed graph with no directed cycles. It is used in Bayesian Networks to represent conditional dependencies without any loops.
What is the Common Cause Principle?
The Common Cause Principle states that if two variables appear to be correlated but are not directly causally related, there may be a common cause that explains the correlation. For example, ice cream sales and shark attacks may both increase due to warm weather.
What is conditional independence in Bayesian Networks?
Two variables A and B are conditionally independent given a third variable C if: P(A,B∣C)=P(A∣C)P(B∣C). This means that knowing C makes A and B independent
What is the D-separation algorithm?
The D-separation algorithm is used to determine if two sets of variables in a Bayesian Network are conditionally independent given a set of evidence variables. It checks if all paths between the two sets are blocked by the evidence.
What is the Indirect Causal Effect?
The Indirect Causal Effect occurs when two variables I and L are correlated through an intermediate variable G. If G is known, I and L become conditionally independent: L⊥I∣G
What is the Common Effect in Bayesian Networks?
The Common Effect occurs when two independent causes T and B influence a common effect S. If S is observed, T and B become dependent, even if they were independent before.
How do you calculate the joint probability in a Bayesian Network?
The joint probability is calculated using the product of conditional probabilities: P(X_1,…,X_n)=∏_{i=1}^{n}P(X_i ∣ parents(X_i))
What is the role of evidence variables in Bayesian Networks?
Evidence variables are observed variables that are used to update the probabilities of other variables in the network through conditional probability queries.
What is the difference between a joint distribution query and a conditional distribution query?
A joint distribution query asks for the probability of a set of variables, while a conditional distribution query asks for the probability of a set of variables given evidence (i.e., other variables are observed).
What is the Law of Total Probability?
The Law of Total Probability states that the total probability of an event A can be calculated by summing over all possible conditions Bn: P(A)=∑_{n}P(A∣Bn)P(B_n).
What is Bayes’ Rule?
Bayes’ Rule relates the conditional and marginal probabilities of random events: P(C∣E)=\frac{P(E)P(E∣C)}{P(C)}. It is used to update the probability of a hypothesis C given evidence E.
What is a parent node in a Bayesian Network?
A node that directly influences another node via an edge.
What is a descendant node in a Bayesian Network?
A node that is influenced by another node through direct or indirect edges
What is Exact Inference in Bayesian Networks?
A method to compute probabilities using joint distribution queries and conditional probability queries.
What is Inference by Enumeration?
A method to compute probabilities by summing over all possible values of hidden variables.
What is an example of the Common Cause Principle?
Ice cream sales and shark attacks both increase in summer, but one does not cause the other. The common cause is warm weather.
What is the Indirect Evidential Effect?
If I and L are correlated through a common cause G, then knowing G makes I and L independent.
What is an example of the Indirect Evidential Effect?
A professor’s recommendation (L) is based on a student’s grades (G). Given G, the recommendation does not provide additional evidence about intelligence (I).
What is an example of the Common Effect Principle?
A car does not start (S) due to either an empty tank (T) or a dead battery (B). If we observe that the car won’t start, then knowing T influences our belief about B.
How does d-separation block influence?
If all paths between two variables are blocked by observed variables, then they are independent.
What are the two conditions that block a path in d-separation?
- The path contains a tail-to-tail or head-to-tail structure with an observed variable. 2. The path contains a head-to-head structure (collider), and neither the collider nor its descendants are observed.
What is a joint probability query in Bayesian Networks?
A query that asks for the probability of multiple variables occurring together, computed using the network structure.
What is a conditional probability query?
A query that asks for the probability of a variable given evidence (e.g., P(A∣B)).
How is inference performed in Bayesian Networks?
By using probabilistic rules like marginalization, Bayes’ Rule, and conditional probability updates.
