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Title

INDEX CODING VIA RANK MINIMIZATION

Creator

Huang, Xiao

Date

2015, 2015-07

Description

Index codes reduce the number of bits broadcast by a wireless transmitter to a number of receivers with different demands and with side...
Show moreIndex codes reduce the number of bits broadcast by a wireless transmitter to a number of receivers with different demands and with side information. It is known that the problem of finding optimal linear index codes is NP-hard (a worst-case result). Many heuristic solutions based on graph coloring have been proposed. However, graph coloring is also a NP-hard problem, and it only gives an upper bound of the index coding. Motivated by a connection between index coding and rank minimization, this thesis investigates the performance of different heuristics based on rank minimization and matrix completion methods, such as alternating projections and alternating minimization, for constructing linear index codes over the reals. The underlying matrices representing an index coding problem have a special structure that makes celebrated methods, such as nuclear norm minimization, perform badly. The performance of different methods, such as alternating projections, directional alternating projections and alternating minimization are presented, through extensive simulation results on random instances of the index coding problem. This thesis makes the following contributions: 1) The proposed alternating projections method gives the best performance compared to other graph based algorithms in the literature. 2) This proposed method leads to up to 13% savings on average communication cost compared to the well know greedy graph coloring algorithm. 3) The thesis describes how the proposed methods can be used to construct linear network codes for non-multicast networks. Our computer code is available online.
M.S. in Electrical Engineering, July 2015
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Title

Statistical Experimental Design and Modeling for Complex Data

Creator

Huang, Xiao

Date

2018

Description

The ability to handle complex data is essential for new research findings and business success today. With increased complexity, data can...
Show moreThe ability to handle complex data is essential for new research findings and business success today. With increased complexity, data can either be difficult to collect with designed experiments or be difficult to analyze with statistical models. Both kinds of difficulties are addressed in this dissertation.The first part of this dissertation (Chapter 2 and 3) addresses the issue of complex data collection by considering two design of experiment problems. In chapter 2, we consider Bayesian A-optimal design problem under a hierarchical probabilistic model involving both quantitative and qualitative response variables. The objective function was derived and an efficient optimization algorithm was developed. In chapter 3, we consider the A/B-testing problem and propose a novel discrepancy-based approach for designing such an experiment. As the numerical examples show, the A/B-testing experiments designed in this way achieve better group balance and parametric estimation results.In the second part of this dissertation (Chapter 4 and 5), we focus on analyzing complex data with Gaussian process (GP) models. Gaussian process model is widely used for analyzing data with highly nonlinear relationships and emulating complex systems. In Chapter 4, we apply and extend GP model to analyze the in-cylinder pressure data resulted from experiments on a newly-developed dual fuel engine. The resulted model incorporates different data types and achieves good prediction accuracy. In Chapter 5, a generalized functional ANOVA GP model is proposed to tackle the difficulty resulted from high-dimensional feature space, and we develop an efficient algorithm for building such a model from the perspective of multiple kernel learning. The proposed approach outperforms traditional MLE-based GP models on both computational efficiency and prediction accuracy.
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