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Message Passing Approaches to Compressive Inference Under Structured Signal Priors

Ziniel, Justin A
http://rave.ohiolink.edu/etdc/view?acc_num=osu1408713337

Abstract Details

2014, Doctor of Philosophy, Ohio State University, Electrical and Computer Engineering.
Across numerous disciplines, the ability to generate high-dimensional datasets is driving an enormous demand for increasingly efficient ways of both capturing and processing this data. A promising recent trend for addressing these needs has developed from the recognition that, despite living in high-dimensional ambient spaces, many datasets have vastly smaller intrinsic dimensionality. When capturing (sampling) such datasets, exploiting this realization permits one to dramatically reduce the number of samples that must be acquired without losing the salient features of the data. When processing such datasets, the reduced intrinsic dimensionality can be leveraged to allow reliable inferences to be made in scenarios where it is infeasible to collect the amount of data that would be required for inference using classical techniques. To date, most approaches for taking advantage of the low intrinsic dimensionality inherent in many datasets have focused on identifying succinct (i.e., sparse) representations of the data, seeking to represent the data using only a handful of "significant" elements from an appropriately chosen dictionary. While powerful in their own right, such approaches make no additional assumptions regarding possible relationships between the significant elements of the dictionary. In this dissertation, we examine ways of incorporating knowledge of such relationships into our sampling and processing schemes. One setting in which it is possible to dramatically improve the efficiency of sampling schemes concerns the recovery of temporally correlated, sparse time series, and in the first part of this dissertation we summarize our work on this important problem. Central to our approach is a Bayesian formulation of the recovery problem, which allows us to access richly expressive models of signal structure. While Bayesian sparse linear regression algorithms have often been shown to outperform their non-Bayesian counterparts, this frequently comes at the cost of substantially increased computational complexity. We demonstrate that, by leveraging recent advances in the field of probabilistic graphical models and message passing algorithms, we are able to dramatically reduce the computational complexity of Bayesian inference on structured sparse regression problems without sacrificing performance. A complementary problem to that of efficient sampling entails making the most of the data that is available, particularly when such data is extremely scarce. Motivated by an application from the field of cognitive neuroscience, we consider the problem of binary classification in a setting where one has many possible predictive features, but only a small number of training examples. We build on the mathematical and software tools developed in the aforementioned regression setting, showing how these tools may be applied to classification problems. Specifically, we describe how inference on a generalized linear model can be conducted through our previously developed message passing framework, suitably modified to account for categorical response variables.
Philip Schniter, PhD (Advisor)
Lee Potter, PhD (Committee Member)
Per Sederberg, PhD (Committee Member)
198 p.
Computer Science; Electrical Engineering
compressive sensing; compressed sensing; message passing; approximate message passing; AMP; GAMP; generalized approximate message passing; belief propagation; dynamic compressed sensing

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Citations

  • Ziniel, J. A. (2014). Message Passing Approaches to Compressive Inference Under Structured Signal Priors [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1408713337

    APA Style (7th edition)

  • Ziniel, Justin. Message Passing Approaches to Compressive Inference Under Structured Signal Priors. 2014. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1408713337.

    MLA Style (8th edition)

  • Ziniel, Justin. "Message Passing Approaches to Compressive Inference Under Structured Signal Priors." Doctoral dissertation, Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1408713337

    Chicago Manual of Style (17th edition)

osu1408713337
530
© 2014, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.