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University of Illinois – Urbana-Champaign

1.
Choi, Jaesik.
*Lifted**Inference* for Relational Hybrid Models.

Degree: PhD, 0112, 2012, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/32004

Probabilistic Graphical Models (PGMs) promise to play a prominent role in many complex real-world systems. Probabilistic Relational Graphical Models (PRGMs) scale the representation and learning of PGMs. Answering questions using PRGMs enables many current and future applications, such as medical informatics, environmental engineering, financial forecasting and robot localizations. Scaling inference algorithms for large models is a key challenge for scaling up current applications and enabling future ones.
This thesis presents new insights into large-scale probabilistic graphical models. It provides fresh ideas for maintaining a compact structure when answering questions or inferences about large, continuous models. The insights result in a key contribution, the Lifted Relational Kalman filter (LRKF), an efficient estimation algorithm for large-scale linear dynamic systems. It shows that the new relational Kalman filter enables scaling the exact vanilla Kalman filter from 1,000 to 1,000,000,000 variables. Another key contribution of this thesis is that it proves that typically used probabilistic first-order languages, including Markov Logic Networks (MLNs) and First-Order Probabilistic Models (FOPMs), can be reduced to compact probabilistic graphical representations under reasonable conditions. Specifically, this thesis shows that aggregate operators and the existential quantification in the languages are accurately approximated by linear constraints in the Gaussian distribution. In general, probabilistic first-order languages are transformed into nonparametric variational models where lifted inference algorithms can efficiently solve inference problems.
*Advisors/Committee Members: Amir, Eyal (advisor), Amir, Eyal (Committee Chair), Roth, Dan (committee member), LaValle, Steven M. (committee member), Poole, David (committee member).*

Subjects/Keywords: Probabilistic Graphical Models; Relational Hybrid Models; Lifted Inference; First-Order Probabilistic Models; Probabilistic Logic; Kalman filter; Relational Kalman filter; Variational Learning, Markov Logic Networks

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Choi, J. (2012). Lifted Inference for Relational Hybrid Models. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/32004

Chicago Manual of Style (16^{th} Edition):

Choi, Jaesik. “Lifted Inference for Relational Hybrid Models.” 2012. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed March 28, 2020. http://hdl.handle.net/2142/32004.

MLA Handbook (7^{th} Edition):

Choi, Jaesik. “Lifted Inference for Relational Hybrid Models.” 2012. Web. 28 Mar 2020.

Vancouver:

Choi J. Lifted Inference for Relational Hybrid Models. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2012. [cited 2020 Mar 28]. Available from: http://hdl.handle.net/2142/32004.

Council of Science Editors:

Choi J. Lifted Inference for Relational Hybrid Models. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2012. Available from: http://hdl.handle.net/2142/32004

2.
Pu, Wen.
* Lifted* probabilistic relational

Degree: PhD, 0112, 2014, University of Illinois – Urbana-Champaign

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

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.
*Advisors/Committee Members: Amir, Eyal (advisor), Amir, Eyal (Committee Chair), Roth, Dan (committee member), DeJong, Gerald F. (committee member), Hunter, David (committee member).*

Subjects/Keywords: Exponential Random Graph Model; Markov Logic Network; Lifted Inference; Approximate Probabilistic Inference

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2.2.2 *Lifted* *Inference* . . . . . . . . . . . . . . . . . .
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applicability and efficiency of *lifted* *inference* algorithms usually depend on… …However, besides extensive study on *lifted* *inference* algorithms, the liftability
for PRGMs with… …Although general-purpose approximate *lifted*
*inference* algorithms [Niepert, 2012b; Singla and…

Record Details Similar Records

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Pu, W. (2014). Lifted probabilistic relational inference for uncertain networks. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/49470

Chicago Manual of Style (16^{th} Edition):

Pu, Wen. “Lifted probabilistic relational inference for uncertain networks.” 2014. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed March 28, 2020. http://hdl.handle.net/2142/49470.

MLA Handbook (7^{th} Edition):

Pu, Wen. “Lifted probabilistic relational inference for uncertain networks.” 2014. Web. 28 Mar 2020.

Vancouver:

Pu W. Lifted probabilistic relational inference for uncertain networks. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2014. [cited 2020 Mar 28]. Available from: http://hdl.handle.net/2142/49470.

Council of Science Editors:

Pu W. Lifted probabilistic relational inference for uncertain networks. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2014. Available from: http://hdl.handle.net/2142/49470