1 / 12

# Complexity Analysis - PowerPoint PPT Presentation

Inference. Probabilistic Graphical Models. Variable Elimination. Complexity Analysis. Eliminating Z. Reminder: Factor Product. N k =|Val( X k )|. Cost: (m k -1) N k multiplications. Reminder: Factor Marginalization. N k =|Val( X k )|. Cost: ~ N k additions.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' Complexity Analysis' - apollo

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Probabilistic

Graphical

Models

Variable Elimination

### Complexity Analysis

Nk=|Val(Xk)|

Cost: (mk-1)Nk multiplications

Nk=|Val(Xk)|

• m  n for Bayesian networks

• can be larger for Markov networks

• At each elimination step generate

• At most elimination steps

• Total number of factors: m*

• N = max(Nk) = size of the largest factor

• Product operations: k(mk-1)Nk

• Sum operations: kNk

• Total work is linear in N and m*

• Total work is linear in N and m

• Nk=|Val(Xk)|=O(drk) where

• d = max(|Val(Xi)|)

• rk = |Xk| = cardinality of the scope of the kth factor

C

I

D

D

G

S

L

J

H

C

• Eliminate: G

I

D

D

G

S

L

J

H

A

A

Eliminate A first:

B1

B1

B2

B2

B3

B3

Bk

Bk

C

C

Eliminate Bi‘s first:

• Complexity of variable elimination linear in

• size of the model (# factors, # variables)

• size of the largest factor generated

• Size of factor is exponential in its scope

• Complexity of algorithm depends heavily on elimination ordering