On the complexity of finding a local minimizer of a quadratic function over a polytope

We show that unless P=NP, there cannot be a polynomial-time algorithm that finds a point within Euclidean distance $c^n$ (for any constant $c \ge 0$) of a local minimizer of an $n$-variate quadratic function over a polytope. This result (even with $c=0$) answers a question of Pardalos and Vavasis that appeared in 1992 on a list of seven open problems in complexity theory for numerical optimization. Our proof technique also implies that the problem of deciding whether a quadratic function has a local minimizer over an (unbounded) polyhedron, and that of deciding if a quartic polynomial has a local minimizer are NP-hard.Comment: 9 page

Combining Treewidth and Backdoors for CSP

We show that CSP is fixed-parameter tractable when parameterized by the treewidth of a backdoor into any tractable CSP problem over a finite constraint language. This result combines the two prominent approaches for achieving tractability for CSP: (i) structural restrictions on the interaction between the variables and the constraints and (ii) language restrictions on the relations that can be used inside the constraints. Apart from defining the notion of backdoor-treewidth and showing how backdoors of small treewidth can be used to efficiently solve CSP, our main technical contribution is a fixed-parameter algorithm that finds a backdoor of small treewidth

Enhancing Usability and Explainability of Data Systems

The recent growth of data science expanded its reach to an ever-growing user base of nonexperts, increasing the need for usability, understandability, and explainability in these systems. Enhancing usability makes data systems accessible to people with different skills and backgrounds alike, leading to democratization of data systems. Furthermore, proper understanding of data and data-driven systems is necessary for the users to trust the function of the systems that learn from data. Finally, data systems should be transparent: when a data system behaves unexpectedly or malfunctions, the users deserve proper explanation of what caused the observed incident. Unfortunately, most existing data systems offer limited usability and support for explanations: these systems are usable only by experts with sound technical skills, and even expert users are hindered by the lack of transparency into the systems\u27 inner workings and functions. The aim of my thesis is to bridge the usability gap between nonexpert users and complex data systems, aid all sort of users, including the expert ones, in data and system understanding, and provide explanations that help reason about unexpected outcomes involving data systems. Specifically, my thesis has the following three goals: (1) enhancing usability of data systems for nonexperts, (2) enable data understanding that can assist users in a variety of tasks such as achieving trust in data-driven machine learning, gaining data understanding, and data cleaning, and (3) explaining causes of unexpected outcomes involving data and data systems. For enhancing usability, we focus on example-driven user intent discovery. We develop systems based on example-driven interactions in two different settings: querying relational databases and personalized document summarization. Towards data understanding, we develop a new data-profiling primitive that can characterize tuples for which a machine-learned model is likely to produce untrustworthy predictions. We also develop an explanation framework to explain causes of such untrustworthy predictions. Additionally, this new data-profiling primitive enables interactive data cleaning. Finally, we develop two explanation frameworks, tailored to provide explanations in debugging data system components, including the data itself. The explanation frameworks focus on explaining the root cause of a concurrent application\u27s intermittent failure and exposing issues in the data that cause a data-driven system to malfunction

Fundamentals

Volume 1 establishes the foundations of this new field. It goes through all the steps from data collection, their summary and clustering, to different aspects of resource-aware learning, i.e., hardware, memory, energy, and communication awareness. Machine learning methods are inspected with respect to resource requirements and how to enhance scalability on diverse computing architectures ranging from embedded systems to large computing clusters

Fundamentals

Volume 1 establishes the foundations of this new field. It goes through all the steps from data collection, their summary and clustering, to different aspects of resource-aware learning, i.e., hardware, memory, energy, and communication awareness. Machine learning methods are inspected with respect to resource requirements and how to enhance scalability on diverse computing architectures ranging from embedded systems to large computing clusters