Concentration Inequalities in the Wild: Case Studies in Blockchain & Reinforcement Learning

Concentration inequalities (CIs) are a powerful tool that provide probability bounds on how a random variable deviates from its expectation. In this dissertation, first I describe a blockchain protocol that I have developed, called Graphene, which uses CIs to provide probabilistic guarantees on performance. Second, I analyze the extent to which CIs are robust when the assumptions they require are violated, using Reinforcement Learning (RL) as the domain. Graphene is a method for interactive set reconciliation among peers in blockchains and related distributed systems. Through the novel combination of a Bloom filter and an Invertible Bloom Lookup Table, Graphene uses a fraction of the network bandwidth used by deployed work for one- and two-way synchronization. It is a fast and implementation-independent algorithm that uses CIs for parameterizing an IBLT so that it is optimal in size for a given desired decode rate. I characterize performance improvements through analysis, detailed simulation, and deployment results for Bitcoin Cash, a prominent cryptocurrency. Implementations of Graphene, IBLTs, and the IBLT optimization algorithm are all open-source code. Second, I analyze the extent to which existing methods rely on accurate training data for a specific class of RL algorithms, known as Safe and Seldonian RL. Several Seldonian RL algorithms have a component called the safety test, which uses CIs to lower bound the performance of a new policy with training data collected from another policy. I introduce a new measure of security to quantify the susceptibility to corruptions in training data, and show that a couple of Seldonian RL methods are extremely sensitive to even a few data corruptions, completely breaking the probability bounds guaranteed by CIs. I then introduce a new algorithm, called Panacea, that is more robust against data corruptions, and demonstrate its usage in practice on some RL problems, including a grid-world and diabetes treatment simulation

Statistical Analysis and Spectral Methods for Signal-Plus-Noise Matrix Models

The singular value matrix decomposition plays a ubiquitous role in statistics and related fields. Myriad applications including clustering, classification, and dimensionality reduction involve studying and understanding the geometric structure of singular values and singular vectors. Chapter 2 of this dissertation presents an initial analysis of local (e.g., entrywise) singular vector (resp., eigenvector) perturbations for signal-plus-noise matrix models. We obtain both deterministic and probabilistic upper bounds on singular vector perturbations that complement and in certain settings improve upon classical, well-established benchmark bounds in the literature. We then apply our tools and methods of analysis to problems involving (spike) principal subspace estimation for high-dimensional covariance matrices and network models exhibiting community structure. Subsequently, Chapter 3 obtains precise local eigenvector estimation results under stronger assumptions involving signal strength, probabilistic concentration, and homogeneity. We provide in silico simulation examples to illustrate our theoretical bounds and distributional limit theory. Chapter 4 transitions to the investigation of singular value (resp., eigenvalue) perturbations, still in the signal-plus-noise matrix model framework. There, our results are leveraged for the purpose of better understanding hypothesis testing and change-point detection in statistical random graph analysis. Chapter 5 builds upon recent joint analysis of singular (resp., eigen) values and vectors in order to investigate the asymptotic relationship between spectral embedding performance and underlying network structure for stochastic block model graphs

Dynamics and collective phenomena of social systems

This thesis focuses on the study of social systems through methods of theoretical physics, in particular proceedings of statistical physics and complex systems, as well as mathematical tools like game theory and complex networks. There already ex- ists predictive and analysis methods to address these problems in sociology, but the contribution of physics provides new perspectives and complementary and powerful tools. This approach is particularly useful in problems involving stochastic aspects and nonlinear dynamics. The contribution of physics to social systems provides not only prediction procedures, but new insights, especially in the study of emergent properties that arise from holistic approaches. We study social systems by introducing different agent-based models (ABM). When possible, the models are analyzed using mathematical methods of physics, in order to achieve analytical solutions. In addition to a theoretical approach, experi- mental treatment is performed via computer simulations both through Monte Carlo methods and deterministic or mixed procedures. This working method has proved very fruitful for the study of several open problems. The book is structured as follows. This introduction presents the mathematical formalisms used in the investigations, which are structured in two parts: in part I we deal with the emergence of cooperation, while in part II we analyze cultural dynamics under the perspective of tolerance

Network information theory for classical-quantum channels

Network information theory is the study of communication problems involving multiple senders, multiple receivers and intermediate relay stations. The purpose of this thesis is to extend the main ideas of classical network information theory to the study of classical-quantum channels. We prove coding theorems for quantum multiple access channels, quantum interference channels, quantum broadcast channels and quantum relay channels. A quantum model for a communication channel describes more accurately the channel's ability to transmit information. By using physically faithful models for the channel outputs and the detection procedure, we obtain better communication rates than would be possible using a classical strategy. In this thesis, we are interested in the transmission of classical information, so we restrict our attention to the study of classical-quantum channels. These are channels with classical inputs and quantum outputs, and so the coding theorems we present will use classical encoding and quantum decoding. We study the asymptotic regime where many copies of the channel are used in parallel, and the uses are assumed to be independent. In this context, we can exploit information-theoretic techniques to calculate the maximum rates for error-free communication for any channel, given the statistics of the noise on that channel. These theoretical bounds can be used as a benchmark to evaluate the rates achieved by practical communication protocols. Most of the results in this thesis consider classical-quantum channels with finite dimensional output systems, which are analogous to classical discrete memoryless channels. In the last chapter, we will show some applications of our results to a practical optical communication scenario, in which the information is encoded in continuous quantum degrees of freedom, which are analogous to classical channels with Gaussian noise.Comment: Ph.D. Thesis, McGill University, School of Computer Science, July 2012, 223 pages, 18 figures, 36 TikZ diagram

TOWARDS SCALABLE GRADIENT-BASED HYPERPARAMETER OPTIMIZATION IN DEEP NEURAL NETWORKS

Ph.DDOCTOR OF PHILOSOPH

Hardware-Conscious Wireless Communication System Design

The work at hand is a selection of topics in efficient wireless communication system design, with topics logically divided into two groups.One group can be described as hardware designs conscious of their possibilities and limitations. In other words, it is about hardware that chooses its configuration and properties depending on the performance that needs to be delivered and the influence of external factors, with the goal of keeping the energy consumption as low as possible. Design parameters that trade off power with complexity are identified for analog, mixed signal and digital circuits, and implications of these tradeoffs are analyzed in detail. An analog front end and an LDPC channel decoder that adapt their parameters to the environment (e.g. fluctuating power level due to fading) are proposed, and it is analyzed how much power/energy these environment-adaptive structures save compared to non-adaptive designs made for the worst-case scenario. Additionally, the impact of ADC bit resolution on the energy efficiency of a massive MIMO system is examined in detail, with the goal of finding bit resolutions that maximize the energy efficiency under various system setups.In another group of themes, one can recognize systems where the system architect was conscious of fundamental limitations stemming from hardware.Put in another way, in these designs there is no attempt of tweaking or tuning the hardware. On the contrary, system design is performed so as to work around an existing and unchangeable hardware limitation. As a workaround for the problematic centralized topology, a massive MIMO base station based on the daisy chain topology is proposed and a method for signal processing tailored to the daisy chain setup is designed. In another example, a large group of cooperating relays is split into several smaller groups, each cooperatively performing relaying independently of the others. As cooperation consumes resources (such as bandwidth), splitting the system into smaller, independent cooperative parts helps save resources and is again an example of a workaround for an inherent limitation.From the analyses performed in this thesis, promising observations about hardware consciousness can be made. Adapting the structure of a hardware block to the environment can bring massive savings in energy, and simple workarounds prove to perform almost as good as the inherently limited designs, but with the limitation being successfully bypassed. As a general observation, it can be concluded that hardware consciousness pays off

2020-2021, University of Memphis bulletin

University of Memphis bulletin containing the graduate catalog for 2020-2021.https://digitalcommons.memphis.edu/speccoll-ua-pub-bulletins/1440/thumbnail.jp

2010-2011, University of Memphis bulletin

University of Memphis bulletin containing the graduate catalog for 2010-2011.https://digitalcommons.memphis.edu/speccoll-ua-pub-bulletins/1430/thumbnail.jp

2021-2022, University of Memphis bulletin

University of Memphis bulletin containing the graduate catalog for 2021-2022.https://digitalcommons.memphis.edu/speccoll-ua-pub-bulletins/1441/thumbnail.jp