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Software systems will eventually contribute to their own maintenance using implementations of self-awareness. Understanding how to specify, model, and implement software with a sense of self is a daunting problem. This research draws inspiration from the automatic functioning of a gimbal---a self-righting mechanical device that supports an object and maintains the orientation of this object with respect to gravity independently of its immediate operating environment. A software gimbal exhibits a self-righting feature that provisions software with two auxiliary mechanisms: a historical mechanism and a reflective mechanism. The historical mechanism consists of behavior classifiers trained on statistical models of data that are collected from executions of the program that exhibit known behaviors of the program. The reflective mechanism uses the historical mechanism to assess an ongoing or selected execution. This dissertation presents techniques for the identification and modeling of program execution features as statistical models. It further demonstrates how statistical machine-learning techniques can be used to manipulate these models and to construct behavior classifiers that can automatically detect and label known program behaviors and detect new unknown behaviors. The thesis is that statistical summaries of data collected from a software program's executions can model and predict external behaviors of the program. This dissertation presents three control-flow features and one value-flow feature of program executions that can be modeled as stochastic processes exhibiting the Markov property. A technique for building automated behavior classifiers from these models is detailed. Empirical studies demonstrating the efficacy of this approach are presented. The use of these techniques in example software engineering applications in the categories of software testing and failure detection are described.

Thesis (Ph. D.)--Rutgers University, 2009. / "Graduate Program in Computer Science." Includes bibliographical references (p. 238-261).

In the last decade Support Vector Machines (SVMs) have emerged as an important learning technique for solving classification and regression problems in various fields, most notably in computational biology, finance and text categorization. This is due in part to built-in mechanisms to ensure good generalization which leads to accurate prediction, the use of kernel functions to model non-linear distributions, the ability to train relatively quickly on large data sets using novel mathematical optimization techniques and most significantly the possibility of theoretical analysis using computational learning theory. In this thesis, we discuss the theoretical basis and computational approaches to Support Vector Machines.

Thesis (Ph. D.)--University of Washington, 2007. / Includes bibliographical references (p. 134-142).

Thesis (Ph.D.)--City University of Hong Kong, 2009. / "Submitted to Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy." Includes bibliographical references (leaves [57]-62)

Thesis (Ph. D.)--University of British Columbia, 2000. / Description based on contents viewed Aug. 16, 2007; title from title screen. Includes bibliographical references (p. 153-157).

A central goal of theoretical computer science is to characterize the limits of efficient computation in a variety of models. We pursue this research objective in the contexts of communication complexity and computational learning theory. In the former case, one seeks to understand which distributed computations require a significant amount of communication among the parties involved. In the latter case, one aims to rigorously explain why computers cannot master some prediction tasks or learn from past experience. While communication and learning may seem to have little in common, they turn out to be closely related, and much insight into both can be gained by studying them jointly. Such is the approach pursued in this thesis. We answer several fundamental questions in communication complexity and learning theory and in so doing discover new relations between the two topics. A consistent theme in our work is the use of analytic methods to solve the problems at hand, such as approximation theory, Fourier analysis, matrix analysis, and duality. We contribute a novel technique, the pattern matrix method, for proving lower bounds on communication. Using our method, we solve an open problem due to Krause and Pudlák (1997) on the comparative power of two well-studied circuit classes: majority circuits and constant-depth AND/OR/NOT circuits. Next, we prove that the pattern matrix method applies not only to classical communication but also to the more powerful quantum model. In particular, we contribute lower bounds for a new class of quantum communication problems, broadly subsuming the celebrated work by Razborov (2002) who used different techniques. In addition, our method has enabled considerable progress by a number of researchers in the area of multiparty communication. Second, we study unbounded-error communication, a natural model with applications to matrix analysis, circuit complexity, and learning. We obtain essentially optimal lower bounds for all symmetric functions, giving the first strong results for unbounded-error communication in years. Next, we resolve a longstanding open problem due to Babai, Frankl, and Simon (1986) on the comparative power of unbounded-error communication and alternation, showing that [mathematical equation]. The latter result also yields an unconditional, exponential lower bound for learning DNF formulas by a large class of algorithms, which explains why this central problem in computational learning theory remains open after more than 20 years of research. We establish the computational intractability of learning intersections of halfspaces, a major unresolved challenge in computational learning theory. Specifically, we obtain the first exponential, near-optimal lower bounds for the learning complexity of this problem in Kearns’ statistical query model, Valiant’s PAC model (under standard cryptographic assumptions), and various analytic models. We also prove that the intersection of even two halfspaces on {0,1}n cannot be sign-represented by a polynomial of degree less than [Theta](square root of n), which is an exponential improvement on previous lower bounds and solves an open problem due to Klivans (2002). We fully determine the relations and gaps among three key complexity measures of a communication problem: product discrepancy, sign-rank, and discrepancy. As an application, we solve an open problem due to Kushilevitz and Nisan (1997) on distributional complexity under product versus nonproduct distributions, as well as separate the communication classes PPcc and UPPcc due to Babai, Frankl, and Simon (1986). We give interpretations of our results in purely learning-theoretic terms. / text

This thesis presents an unsupervised method for discovering and analyzing the different kinds of activities in an active environment. Drawing from natural language processing, a novel representation of activities as bags of event n-grams is introduced, where the global structural information of activities using their local event statistics is analyzed. It is demonstrated how maximal cliques in an undirected edge-weighted graph of activities, can be used in an unsupervised manner, to discover the different activity-classes. Taking on some work done in computer networks and bio-informatics, it is shown how to characterize these discovered activity-classes from a wholestic as well as a by-parts view-point. A definition of anomalous activities is formulated along with a way to detect them based on the difference of an activity instance from each of the discovered activity-classes. Finally, an information theoretic method to explain the detected anomalies in a human-interpretable form is presented. Results over extensive data-sets, collected from multiple active environments are presented, to show the competence and generalizability of the proposed framework.

In this thesis we prove intractability results for well studied problems in computational learning and approximation. Let ε , mu > 0 be arbitrarily small constants and t be an arbitrary constant positive integer. We show an almost optimal hardness factor of d[superscript{1-ε}] for computing an equivalent DNF expression with minimum terms for a boolean function on d variables, given its truth table. In the study of weak learnability, we prove an optimal 1/2 + ε inapproximability for the accuracy of learning an intersection of two halfspaces with an intersection of t halfspaces. Further, we study the learnability of small DNF formulas, and prove optimal 1/2 + ε inapproximability for the accuracy of learning (i) a two term DNF by a t term DNF, and (ii) an AND under adversarial mu-noise by a t-CNF. In addition, we show a 1 - 2[superscript{-d}] + ε inapproximability for accurately learning parities (over GF(2)), under adversarial mu-noise, by degree d polynomials, where d is a constant positive integer. We also provide negative answers to the possibility of stronger semi-definite programming (SDP) relaxations yielding much better approximations for graph partitioning problems such as Maximum Cut and Sparsest Cut by constructing integrality gap examples for them. For Maximum Cut and Sparsest Cut we construct examples -- with gaps alpha[superscript{-1}] - ε (alpha is the Goemans-Williamson constant) and Omega((logloglog n)[superscript{1/13}]) respectively -- for the standard SDP relaxations augmented with O((logloglog n)[superscript{1/6}]) rounds of Sherali-Adams constraints. The construction for Sparsest Cut also implies that an n-point negative type metric may incur a distortion of Omega((logloglog n)[superscript{1/ 13}]) to embed into ell_1 even if the induced submetric on every subset of O((logloglog n)[superscript{1/6}]) points is isometric to ell_1. We also construct an integrality gap of Omega(loglog n) for the SDP relaxation for Uniform Sparsest Cut problem augmented with triangle inequalities, disproving a well known conjecture of Arora, Rao and Vazirani.