Lifted probabilistic relational inference for uncertain networks

Probabilistic Relational Graphical Model (PRGM) is a popular tool for modeling uncertain relational knowledge, of which the set of uncertain relational knowledge is usually assumed to be independent with the domain of the application. One common application of PRGM is to model complex networks using structural features. Efficient and accurate inference algorithms that can handle models with non-trivial structural features (e.g., transitive relations) are important for applications of this kind. In this thesis, (1) we provide new algorithm for efficient and accurate inference on PRGMs with structural features; (2) we show a counter example to the domain-independence assumption of PRGM. A PRGM is a set of uncertain relational knowledge, which translates to Probabilistic Graphical Models (PGM) on different domains of discourse. Lifted inference and domain-independence assumption are two important concepts for PRGM. Domain-independence assumption separates the uncertain relational knowledge of a PRGM from its domains of application, therefore distinguishes PRGM from propositional PGM. Lifted inference techniques try to speedup inference on PRGM by lifting the computation from propositional level to relational level. However, these techniques are not designed to handle complex structural features, therefore lack efficiency and accuracy in the presence of these features. In this thesis, we propose a deterministic approximate inference algorithm for Exponential Random Graph Model (ERGM) -- a family of statistical models, which are closely related to PRGM. An ERGM defines a probabilistic distribution of all graphs of $n$ nodes using a set of subgraph statistics. The main insight enabling this advance is that subgraph statistics are sufficient to derive a lower bound for partition functions of ERGM when the model of interests is not dominated by a few graphs. We then show that a class of PRGMs with structural features can be converted to ERGM, which leads to an approximate lifted inference algorithm for PRGM. Theoretical and experimental results show that the proposed algorithms are scalable, stable, and precise enough for inference tasks. Lastly, we show a counter example of the domain-independence assumption. In general, PRGM parameters fitted to one network data cannot be extrapolated to other networks of different sizes.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Pu, Wen

Contributors dc:contributor

• Amir, Eyal
• Roth, Dan
• DeJong, Gerald F.
• Hunter, David

• Exponential Random Graph Model
• Markov Logic Network
• Lifted Inference
• Approximate Probabilistic Inference

Statement dc:rights

• Copyright 2014 Wen Pu

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/49470

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/49470