1 / 25

Exact Inference Algorithms for Probabilistic Reasoning;

This document explores exact inference algorithms for probabilistic reasoning, focusing on belief updating, finding most probable explanations (MPE), maximum a-posteriori hypothesis, and maximum-expected-utility (MEU) decision-making. It discusses the use of bucket elimination and the impact of ordering on complexity. The document also provides examples and explanations of induced width, moral graphs, and the impact of observations.

rogersr
Télécharger la présentation

Exact Inference Algorithms for Probabilistic Reasoning;

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. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Exact Inference Algorithms for Probabilistic Reasoning; COMPSCI 276 Fall 2007

  2. Probabilistic Inference Tasks • Belief updating: • Finding most probable explanation (MPE) • Finding maximum a-posteriory hypothesis • Finding maximum-expected-utility (MEU) decision

  3. Example with a chain P(A|D=d)=? P(D)=? P(D|A=a)=? D A B C O(4k^2) instead of O(k^4), k is the domain size

  4. Example of product-sum in a bucket

  5. Elimination operator bucket B: P(b|a) P(d|b,a) P(e|b,c) B bucket C: P(c|a) C bucket D: D bucket E: e=0 E bucket A: P(a) A P(a|e=0) W*=4 ”induced width” (max clique size) Bucket elimination Algorithm elim-bel (Dechter 1996)

  6. B E C D D C E B A A

  7. A B C D E “Moral” graph B E C D D C E B A A Complexity of elimination The effect of the ordering:

  8. Finding small induced-width • NP-complete • A tree has induced-width of ? • Greedy algorithms: • Min width • Min induced-width • Max-cardinality • Fill-in (thought as the best) • See anytime min-width (Gogate and Dechter)

  9. Different Induced graphs

  10. The impact of observations

  11. A B C D E “Moral” graph Theorem: elim-bel is exponential in the adjusted induced-width w*(e,d)

  12. Use the ancestral graph only

  13. BTE in action

More Related