- Title Information
- Title
- Message Passing Dynamics of Belief Propagation Algorithms
- Type of Resource (primo)
- dissertations
- Name:
Personal
- Name Part
- Grim, Anna
- Role
- Role Term:
Text
- creator
- Name:
Personal
- Name Part
- Felzenszwalb, Pedro
- Role
- Role Term:
Text
- Advisor
- Name:
Personal
- Name Part
- Harrison, Matt
- Role
- Role Term:
Text
- Reader
- Name:
Personal
- Name Part
- Guzman, Johnny
- Role
- Role Term:
Text
- Reader
- Name:
Corporate
- Name Part
- Brown University. Department of Applied Mathematics
- Role
- Role Term:
Text
- sponsor
- Origin Information
- Copyright Date
- 2022
- Physical Description
- Extent
- xvii, 182 p.
- digitalOrigin
- born digital
- Note:
thesis
- Thesis (Ph. D.)--Brown University, 2022
- Genre (aat)
- theses
- Abstract
- Our work is motivated by the classical belief propagation algorithms which are well-known for obtaining state of the art results in certain settings, but often fail to converge when the underlying graph has complex topology. The main objective of this thesis is to present a two-part solution to this classical problem. First, we describe an algorithm referred to as convex combination belief propagation. This method was developed by modifying the message passing operator in loopy belief propagation so that it's more robust to graphs with cycles. The main advantage of this algorithm is that it's guaranteed to converge on graphs with arbitrary topology. Although this algorithm has good theoretical properties, one disadvantage is that it is generally less accurate than the classical algorithm when both converge.
Second, we build upon this work by incorporating a homotopy operator that gradually deforms the message passing operator from convex combination belief propagation into the operator used in loopy belief propagation. Under this framework, convex combination belief propagation obtains an initial solution. Then we improve the accuracy of the solution by using the homotopy operator in a continuation scheme. The outcome of this work is an approximate inference algorithm that is significantly more accurate than convex combination belief propagation, while also converging at a much higher rate than loopy belief propagation.
Lastly, we demonstrate the usefulness of our approximate inference algorithms by applying them to real-world problems. We discuss medical diagnostic inference on the QMR network which models causal relations between a set of diseases and findings. We use our homotopy continuation algorithm to perform inference in this problem. Our results show that this algorithm always converges and obtains exceptional results on this task.
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/00972355")
- Topic
- Inference
- Subject
- Topic
- Approximation Algorithms
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/00946659")
- Topic
- Graphical modeling (Statistics)
- Subject
- Topic
- Belief Propagation
- Language
- Language Term (ISO639-2B)
- English
- Record Information
- Record Content Source (marcorg)
- RPB
- Record Creation Date
(encoding="iso8601")
- 20220706