Machine learning, data mining, and statistical methods work by representing real-world objects in terms of feature sets that best describe them. This thesis addresses problems related to inferring and analyzing correlations among such features. The contributions of this thesis are two-fold: we develop formulations and algorithms for addressing correlation mining problems, and we also provide novel applications of our methods to statistical software analysis domains. We consider problems related to analyzing correlations via unsupervised approaches, as well as algorithms that infer correlations using fully-supervised or semi-supervised information. In the context of correlation analysis, we propose the problem of correlation matrix clustering which employs a k-means style algorithm to group sets of correlations in an unsupervised manner. Fundamental to this algorithm is a measure for comparing correlations called the log-determinant (LogDet) divergence, and a primary contribution of this thesis is that of interpreting and analyzing this measure in the context of information theory and statistics. Additionally based on the LogDet divergence, we present a metric learning problem called Information-Theoretic Metric Learning which uses semi-supervised or fully-supervised data to infer correlations for parametrization of a Mahalanobis distance metric. We also consider the problem of learning Mahalanobis correlation matrices in the presence of high dimensions when the number of pairwise correlations can grow very large. In validating our correlation mining methods, we consider two in-depth and real-world statistical software analysis problems: software error reporting and unit test prioritization. In the context of Clarify, we investigate two types of correlation mining applications: metric learning for nearest neighbor software support, and decision trees for error classification. We show that our metric learning algorithms can learn program-specific similarity models for more accurate nearest neighbor comparisons. In the context of decision tree learning, we address the problem of learning correlations with associated feature costs, in particular, the overhead costs of software instrumentation. As our second application, we present a unit test ordering algorithm which uses clustering and nearest neighbor algorithms, along with a metric learning component, to efficiently search and execute large unit test suites. / text

published_or_final_version / Industrial and Manufacturing Systems Engineering / Doctoral / Doctor of Philosophy

The task of multi-body motion segmentation refers to segmenting feature trajectories in a sequence of images according to their 3D motion affinity without knowing the number of motions in advance. It is critical for understanding and reconstructing a dynamic scene. This problem essentially consists of two subproblems, segmenting features and detecting the number of motions. While the state-of-the-art LBF algorithm achieves segmentation accuracy as high as 96.5%, it is still disturbed by a phenomenon called over-locality. A novel mode seeking algorithm with an adaptive distance measure is proposed to avoid this problem, and improves the accuracy to 98.1%. The LBF algorithm is incapable of detecting the number of motions itself. A randomized version of the mode seeking algorithm is presented, which could detect the number as well as preserve satisfactory segmentation accuracy. To detect the number of motions, a kernel optimization method locates it via kernel alignment. However, it suffers from over-locality and over-detects the number of motions. An intersection measure and two mutual information measures are presented to solve this problem. Using these measures, the proposed clustering consensus framework recasts the motion number detection problem to a clustering consensus problem. It extends the kernel optimization method from two-clustering consensus to multiple-clustering consensus. A large number of experiments and comparisons have been done, and convincing results are obtained. / published_or_final_version / Computer Science / Doctoral / Doctor of Philosophy

We study algorithms and models for several economics-related problems from the perspective of linear programming. In network bargaining games, stable and balanced outcomes have been investigated in previous work. However, existence of such outcomes requires that the linear program relaxation of a certain maximum matching problem has integral optimal solution. We propose an alternative model for network bargaining games in which each edge acts as a player, who proposes how to split the weight of the edge among the two incident nodes. We show that the distributed protocol by Kanoria et. al can be modified to be run by the edge players such that the configuration of proposals will converge to a pure Nash Equilibrium, without the linear program integrality gap assumption. Moreover, ambiguous choices can be resolved in a way such that there exists a Nash Equilibrium that will not hurt the social welfare too much. In the oblivious matching problem, an algorithm aims to find a maximum matching while it can only makes (random) decisions that are essentially oblivious to the input graph. Any greedy algorithm can achieve performance ratio 0:5, which is the expected number of matched nodes to the number of nodes in a maximum matching. We revisit the Ranking algorithm using the linear programming framework, where the constraints of the linear program are given by the structural properties of Ranking. We use continuous linear program relaxation to analyze the limiting behavior as the finite linear program grows. Of particular interest are new duality and complementary slackness characterizations that can handle monotone constraints and mixed evolving and boundary constraints in continuous linear program, which enable us to achieve a theoretical ratio of 0:523 on arbitrary graphs. The J-choice K-best secretary problem, also known as the (J;K)-secretary problem, is a generalization of the classical secretary problem. An algorithm for the (J;K)-secretary problem is allowed to make J choices and the payoff to be maximized is the expected number of items chosen among the K best items. We use primal-dual continuous linear program techniques to analyze a class of infinite algorithms, which are general enough to capture the asymptotic behavior of the finite model with large number of items. Our techniques allow us to prove that the optimal solution can be achieved by a (J;K)-threshold algorithm, which has a nice \rational description" for the case K = 1. / published_or_final_version / Computer Science / Doctoral / Doctor of Philosophy

abstract / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

Not available / text

Not available / text

published_or_final_version / abstract / toc / Computer Science and Information Systems / Master / Master of Philosophy

published_or_final_version / abstract / toc / Electrical and Electronic Engineering / Master / Master of Philosophy

published_or_final_version / abstract / toc / Computer Science and Information Systems / Doctoral / Doctor of Philosophy