Download presentation

Presentation is loading. Please wait.

Published byJaida Brich Modified over 2 years ago

1
CSCE 582 Computation of the Most Probable Explanation in Bayesian Networks using Bucket Elimination -Hareesh Lingareddy University of South Carolina

2
Bucket Elimination -Algorithmic framework that generalizes dynamic programming to accommodate algorithms for many complex problem solving and reasoning activities. -Uses “buckets” to mimic the algebraic manipulations involved in each of these problems resulting in an easily expressible algorithmic formulation

3
Bucket Elimination Algorithm -Partition functions on the graph into “buckets” in backwards relative to the given node order -In the bucket of variable X we put all functions that mention X but do not mention any variable having a higher index -Process buckets backwards relative to the node order -The computed function after elimination is placed in the bucket of the ‘highest’ variable in its scope

4
Algorithms using Bucket Elimination -Belief Assessment -Most Probable Estimation(MPE) -Maximum A Posteriori Hypothesis(MAP) -Maximum Expected Utility(MEU)

5
Belief Assessment Definition - Given a set of evidence compute the posterior probability of all the variables – The belief assessment task of X k = x k is to find In the Visit to Asia example, the belief assessment problem answers questions like – What is the probability that a person has tuberculosis, given that he/she has dyspnoea and has visited Asia recently ? where k – normalizing constant

6
Belief Assessment Overview In reverse Node Ordering: – Create bucket function by multiplying all functions (given as tables) containing the current node – Perform variable elimination using Summation over the current node – Place the new created function table into the appropriate bucket

7
Most Probable Explanation (MPE) Definition – Given evidence find the maximum probability assignment to the remaining variables – The MPE task is to find an assignment x o = (x o 1, …, x o n ) such that

8
Differences from Belief Assessment – Replace Sums With Max – Keep track of maximizing value at each stage – “Forward Step” to determine what is the maximizing assignment tuple

9
Elimination Algorithm for Most Probable Explanation Bucket : Bucket : Bucket : Bucket : Bucket : Bucket : Bucket : Bucket : P( | ) P( | )*P( ) P( | , ) P( | , ), =“no” MPE= MAX { , , , ,, , , } (P( | )* P( | )* P( | , )* P( | , )* P( )*P( | )*P( | )*P( )) P( | ) P( | )*P( ) H()H() H()H() H(,)H(,) H ( ,, ) H ( , , ) H()H() H(,)H(,) MPE probability Finding MPE = max , , , ,, , , P( , , , ,, , , ) H n (u)=max xn ( П xn Fn C(x n |x pa ))

10
Elimination Algorithm for Most Probable Explanation Bucket : Bucket : Bucket : Bucket : Bucket : Bucket : Bucket : Bucket : P( | ) P( | )*P( ) P( | , ) P( | , ), =“no” P( | ) P( | )*P( ) H()H() H()H() H(,)H(,) H ( ,, ) H ( , , ) H()H() H(,)H(,) Forward part ’ = arg max H ( )* H ( ) ’ = arg max H ( ’, ) ’ = arg max P( ’| )*P( )* H ( ’, ’, ) ’ = arg max P( | ’)*H ( ’,, ’) ’ = arg max P( | ’, ’)*H ( , ’)*H ( ) ’ = “no” ’ = arg max P( | ’) ’ = arg max P( ’| )*P( ) Return: ( ’, ’, ’, ’, ’, ’, ’, ’)

11
MPE Overview In reverse node Ordering – Create bucket function by multiplying all functions (given as tables) containing the current node – Perform variable elimination using the Maximization operation over the current node (recording the maximizing state function) – Place the new created function table into the appropriate bucket In forward node ordering – Calculate the maximum probability using maximizing state functions

12
Maximum Aposteriori Hypothesis (MAP) Definition – Given evidence find an assignment to a subset of “hypothesis” variables that maximizes their probability – Given a set of hypothesis variables A = {A 1, …, A k },,the MAP task is to find an assignment a o = (a o 1, …, a o k ) such that

Similar presentations

OK

Daphne Koller Overview Conditional Probability Queries Probabilistic Graphical Models Inference.

Daphne Koller Overview Conditional Probability Queries Probabilistic Graphical Models Inference.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on company act 1956 provisions Ppt on nature and human development Ppt on op amp circuits Ppt on andrew file system Ppt on etiquettes meaning Ppt on building brand equity Ppt on different dances of india Ppt on waves tides and ocean currents maps Ppt on sources of energy for class 8th science Ppt on conservation of matter