Understanding Bayes Net Inference Algorithm from Russel & Norvig

  • Thread starter 0rthodontist
  • Start date
  • Tags
    Net
In summary: If the variable Y is not observed (not in the set e), then we sum over all possible values of Y to get the final probability. In summary, Enumerate-All uses Bayes net to compute the probability of a set of variables given observed values by recursively considering each variable and its parents.
  • #1
0rthodontist
Science Advisor
1,231
0
I don't understand this simple algorithm from Russel & Norvig for computing a distribution of X given certain observed values e:

Code:
function Enumeration-Ask(X, e, bn) returns a distribution over X
	inputs: X, the query variable
		e, observed values for variables E
		bn, a Bayes net with variables {X} u E u Y /* Y = hidden variables */
	
	Q(X) <- a distribution over X, initially empty
	for each value xi of X do
		extend e with value xi for X
		Q(xi) <- Enumerate-All(Vars[bn], e)
	return Normalize(Q(X))
	
function Enumerate-All(vars, e) returns a real number
	if Empty?(vars) then return 1.0
	Y <- First(vars)
	if Y has value y in e
		then return P(y | parents(Y)) * Enumerate-All(Rest(vars), e)
		else return the sum over y of P(y | parents(Y)) * Enumerate-All(Rest(vars), ey)
			where ey is e extended with Y = y

I am having trouble understanding exactly what Enumerate-All does. Specifically I do not understand how P(y | parents(Y)) is computed. We don't know the values that the parents of Y take, do we?
 
Technology news on Phys.org
  • #2
Can you explain it in more detail?Enumerate-All is a recursive algorithm that computes the probability of a given set of variables (vars) given certain observed values (e). This is done by recursively considering each variable Y in the set of variables Vars[bn] and computing the probability of Y given its parents. This is done by multiplying P(y | parents(Y)) with the result of Enumerate-All on the rest of the variables, which is the probability of the remaining variables given the same set of observed values. The probability of a variable Y given its parents can be obtained from the Bayes net. Specifically, it is the conditional probability of Y given the values of its parents, which is usually stored in a probability table.
 
  • #3


The Bayes Net Inference Algorithm from Russel & Norvig is a method for calculating a probability distribution over a query variable X, given certain observed values e and a Bayes net bn. The algorithm is based on the principle of enumeration, which involves considering all possible combinations of values for the variables in the Bayes net.

The first step in the algorithm is to define a distribution Q(X) over the query variable X. This distribution is initially empty, and will be filled in by the algorithm.

Next, the algorithm considers each possible value xi for X and extends the observed values e with this value. This means that e now includes the value of X, as well as any other observed values from the variables E. This extended set of values is then used in a function called Enumerate-All.

Enumerate-All is a recursive function that calculates the probability of a particular combination of values for all the variables in the Bayes net. It takes two inputs: a set of variables and a set of observed values. If the set of variables is empty, the function returns 1.0, indicating that the probability of this combination of values is 100%.

The function then takes the first variable Y from the set of variables and checks if it has a value in the observed values e. If it does, then the probability of this value given its parents is calculated using the conditional probability table in the Bayes net. This probability is then multiplied by the result of the function Enumerate-All on the remaining variables and observed values.

If Y does not have a value in e, then the function calculates the sum of probabilities for all possible values of Y given its parents, multiplied by the result of Enumerate-All on the remaining variables and an extended set of observed values e. This extended set of observed values includes the value of Y that is being considered.

The function continues to recursively calculate probabilities for each variable in the set, until all variables have been considered. The result of Enumerate-All is the total probability of the entire combination of values for all variables.

Going back to the original algorithm, after Enumerate-All has been called for each value of X, the distribution Q(X) is normalized, meaning that all the probabilities are scaled so that they sum to 1. This gives us the final probability distribution over X.

In summary, Enumerate-All is a recursive function that calculates the probability of a particular combination of values for all variables in a Bay
 

FAQ: Understanding Bayes Net Inference Algorithm from Russel & Norvig

1. What is a Bayes Net Inference Algorithm?

A Bayes Net Inference Algorithm is a probabilistic graphical model used for making predictions and inferences about a system based on known evidence or observations. It allows for the representation of complex relationships between variables and their probabilities, making it a powerful tool for decision-making and analysis.

2. How does the Bayes Net Inference Algorithm work?

The algorithm works by using Bayes' rule to update the probabilities of variables in the network based on new information or evidence. It uses a process called variable elimination to compute the probability of a specific event occurring, given the available evidence.

3. What are the advantages of using a Bayes Net Inference Algorithm?

One advantage is that it can handle both discrete and continuous variables, making it applicable to a wide range of problems. It also allows for the incorporation of prior knowledge and uncertainty, making it a more realistic model for real-world scenarios. Additionally, it is a computationally efficient method for making inferences in large, complex networks.

4. What are some common applications of the Bayes Net Inference Algorithm?

The algorithm has a wide range of applications in various fields such as medicine, finance, and artificial intelligence. It is commonly used for medical diagnosis, predicting stock market trends, and in natural language processing for tasks such as text classification and sentiment analysis.

5. How can I improve my understanding of the Bayes Net Inference Algorithm?

To improve your understanding, it is helpful to have a strong foundation in probability theory and graphical models. It is also beneficial to practice implementing the algorithm on different problems and datasets. Additionally, reading and understanding articles and research papers on the subject can provide deeper insights and understanding of the algorithm.

Similar threads

Replies
1
Views
651
Replies
9
Views
2K
Replies
15
Views
2K
Replies
8
Views
2K
Replies
3
Views
1K
Replies
1
Views
742
Replies
5
Views
2K
Back
Top