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Inference in Generalized Linear Models with Applications

Byrne, Evan
http://rave.ohiolink.edu/etdc/view?acc_num=osu1555152640361367

Abstract Details

2019, Doctor of Philosophy, Ohio State University, Electrical and Computer Engineering.
In this dissertation, we first consider two problems involving the generalized linear model: sparse multinomial logistic regression (SMLR) and sketched clustering, which in the context of machine learning are forms of supervised and unsupervised learning, respectively. Conventional approaches to these problems fit the parameters of the model to the data by minimizing some regularized loss function between the model and data with an iterative gradient-based algorithm, which may suffer from various issues such as slow convergence or finding a sub-optimal solution. Slow convergence is particularly detrimental when applied to modern datasets, which may contain upwards of millions of sample points. We take an alternate inference approach based on approximate message passing, rather than optimization. In particular, we apply the hybrid generalized approximate message passing (HyGAMP) algorithm to both of these problems in order to learn the underlying parameters of interest. The HyGAMP algorithm approximates the sum-product or min-sum loopy belief propagation algorithms, which approximate minimum mean squared error (MMSE) or maximum a posteriori (MAP) estimation, respectively, of the unknown parameters of interest. We apply a simplified form of HyGAMP (SHyGAMP) to SMLR, where we show through numerical experiments that our approach meets or exceeds the performance of state-of-the-art SMLR algorithms with respect to classification accuracy and algorithm training time. We then apply the MMSE-SHyGAMP algorithm to the sketched clustering problem, where we also show through numerical experiments that our approach exceeds the performance of other state-of-the-art sketched clustering algorithms with respect to clustering accuracy and computational efficiency, as well as the widely used K-means++ algorithm in some regimes. Finally, we study the problem of adaptive detection from quantized measurements. We focus on the case of strong, but low-rank interference, which is motivated by wireless communications applications for the military, where the receiver is experiencing strong jamming from a small number of sources in a time-invariant channel. In this scenario, the receiver requires many antennas to effectively null out the interference, but at the cost of increased hardware complexity, and total volume of data to be processed. Using highly quantized measurements is one method of reducing the amount of data to be processed, but it is unknown how this affects detection performance. We first investigate the effect of quantized measurements on existing unquantized detection algorithms. We observe that unquantized detection algorithms applied to quantized measurements lack the ability to null arbitrarily large interference, despite being able to null arbitrarily large interference when applied to unquantized measurements. We then derive a generalized likelihood ratio test for the quantized measurement model, which gives rise to a generalized bilinear model. Via simulation, we empirically observe the quantized algorithm only offers a fraction of a decibel improvement in equivalent SNR relative to unquantized algorithms. We then evaluate alternative techniques to address the performance loss due to quantized measurements, including a novel analog pre-whitening using digitally controlled phase-shifters. In simulation, we observe that the new technique shows up to 8 dB improvement in equivalent SNR.
Philip Schniter (Advisor)
Lee Potter (Committee Member)
Kiryung Lee (Committee Member)
162 p.
Electrical Engineering
generalized linear model; multinomial logistic regression; sketched clustering; classification; approximate message passing; adaptive detection; quantization

Recommended Citations

Citations

  • Byrne, E. (2019). Inference in Generalized Linear Models with Applications [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1555152640361367

    APA Style (7th edition)

  • Byrne, Evan. Inference in Generalized Linear Models with Applications . 2019. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1555152640361367.

    MLA Style (8th edition)

  • Byrne, Evan. "Inference in Generalized Linear Models with Applications ." Doctoral dissertation, Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1555152640361367

    Chicago Manual of Style (17th edition)

osu1555152640361367
259
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This open access ETD is published by The Ohio State University and OhioLINK.