- 97 Views
- Uploaded on

Download Presentation
## 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

Complexity of Variable Elimination

- Start with m factors
- 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*

Complexity of Variable Elimination

- 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*

Complexity of Variable Elimination

- 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

Complexity and Elimination Order

A

A

Eliminate A first:

…

…

B1

B1

B2

B2

B3

B3

Bk

Bk

C

C

Eliminate Bi‘s first:

Summary

- 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

Download Presentation

Connecting to Server..