61 research outputs found

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    LIPIcs, Volume 274, ESA 2023, Complete Volume

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    LIPIcs, Volume 274, ESA 2023, Complete Volum

    Theoretical Foundations of Adversarially Robust Learning

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    Despite extraordinary progress, current machine learning systems have been shown to be brittle against adversarial examples: seemingly innocuous but carefully crafted perturbations of test examples that cause machine learning predictors to misclassify. Can we learn predictors robust to adversarial examples? and how? There has been much empirical interest in this contemporary challenge in machine learning, and in this thesis, we address it from a theoretical perspective. In this thesis, we explore what robustness properties can we hope to guarantee against adversarial examples and develop an understanding of how to algorithmically guarantee them. We illustrate the need to go beyond traditional approaches and principles such as empirical risk minimization and uniform convergence, and make contributions that can be categorized as follows: (1) introducing problem formulations capturing aspects of emerging practical challenges in robust learning, (2) designing new learning algorithms with provable robustness guarantees, and (3) characterizing the complexity of robust learning and fundamental limitations on the performance of any algorithm.Comment: PhD Thesi

    LIPIcs, Volume 244, ESA 2022, Complete Volume

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    LIPIcs, Volume 244, ESA 2022, Complete Volum

    Testing, Learning, Sampling, Sketching

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    We study several problems about sublinear algorithms, presented in two parts. Part I: Property testing and learning. There are two main goals of research in property testing and learning theory. The first is to understand the relationship between testing and learning, and the second is to develop efficient testing and learning algorithms. We present results towards both goals. - An oft-repeated motivation for property testing algorithms is to help with model selection in learning: to efficiently check whether the chosen hypothesis class (i.e. learning model) will successfully learn the target function. We present in this thesis a proof that, for many of the most useful and natural hypothesis classes (including halfspaces, polynomial threshold functions, intersections of halfspaces, etc.), the sample complexity of testing in the distribution-free model is nearly equal to that of learning. This shows that testing does not give a significant advantage in model selection in this setting. - We present a simple and general technique for transforming testing and learning algorithms designed for the uniform distribution over {0, 1}^d or [n]^d into algorithms that work for arbitrary product distributions over R d . This leads to an improvement and simplification of state-of-the-art results for testing monotonicity, learning intersections of halfspaces, learning polynomial threshold functions, and others. Part II. Adjacency and distance sketching for graphs. We initiate the thorough study of adjacency and distance sketching for classes of graphs. Two open problems in sublinear algorithms are: 1) to understand the power of randomization in communication; and 2) to characterize the sketchable distance metrics. We observe that constant-cost randomized communication is equivalent to adjacency sketching in a hereditary graph class, which in turn implies the existence of an efficient adjacency labeling scheme, the subject of a major open problem in structural graph theory. Therefore characterizing the adjacency sketchable graph classes (i.e. the constant-cost communication problems) is the probabilistic equivalent of this open problem, and an essential step towards understanding the power of randomization in communication. This thesis gives the first results towards a combined theory of these problems and uses this connection to obtain optimal adjacency labels for subgraphs of Cartesian products, resolving some questions from the literature. More generally, we begin to develop a theory of graph sketching for problems that generalize adjacency, including different notions of distance sketching. This connects the well-studied areas of distance sketching in sublinear algorithms, and distance labeling in structural graph theory

    LIPIcs, Volume 248, ISAAC 2022, Complete Volume

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    LIPIcs, Volume 248, ISAAC 2022, Complete Volum

    Beyond Statistical Fairness

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    In recent years, a great deal of fairness notions has been proposed. Yet, most of them take a reductionist approach by indirectly viewing fairness as equalizing some error statistic across pre-defined groups. This thesis aims to explore some ideas as to how to go beyond such statistical fairness frameworks. First, we consider settings in which the right notion of fairness may not be captured by simple mathematical definitions but might be more complex and nuanced and thus require elicitation from individual or collective stakeholders. By asking stakeholders to make pairwise comparisons to learn which pair of individuals should be treated similarly, we show how to approximately learn the most accurate classifier or converge to such one subject to the elicited fairness constraints. We consider an offline setting where the pairwise comparisons must be made prior to training a model and an online setting where one can continually provide fairness feedback to the deployed model in each round. We also report preliminary findings of a behavioral study of our framework using human-subject fairness constraints elicited on the COMPAS criminal recidivism dataset. Second, unlike most of the statistical fairness framework that promises fairness for pre-defined and often coarse groups, we provide fairness guarantees for finer subgroups, such as all possible intersections of the pre-defined groups, in the context of uncertainty estimation in both offline and online setting. Our framework gives uncertainty guarantees that are more locally sensible than the ones given by conformal prediction techniques; our uncertainty estimates are valid even when averaged over any subgroup, but uncertainty estimates in conformal predictions are usually only valid when averaged over the entire population

    Computer Aided Verification

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    This open access two-volume set LNCS 10980 and 10981 constitutes the refereed proceedings of the 30th International Conference on Computer Aided Verification, CAV 2018, held in Oxford, UK, in July 2018. The 52 full and 13 tool papers presented together with 3 invited papers and 2 tutorials were carefully reviewed and selected from 215 submissions. The papers cover a wide range of topics and techniques, from algorithmic and logical foundations of verification to practical applications in distributed, networked, cyber-physical, and autonomous systems. They are organized in topical sections on model checking, program analysis using polyhedra, synthesis, learning, runtime verification, hybrid and timed systems, tools, probabilistic systems, static analysis, theory and security, SAT, SMT and decisions procedures, concurrency, and CPS, hardware, industrial applications

    Statistical Query Algorithms for Mean Vector Estimation and Stochastic Convex Optimization

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    Stochastic convex optimization, by which the objective is the expectation of a random convex function, is an important and widely used method with numerous applications in machine learning, statistics, operations research, and other areas. We study the complexity of stochastic convex optimization given only statistical query (SQ) access to the objective function. We show that well-known and popular first-order iterative methods can be implemented using only statistical queries. For many cases of interest, we derive nearly matching upper and lower bounds on the estimation (sample) complexity, including linear optimization in the most general setting. We then present several consequences for machine learning, differential privacy, and proving concrete lower bounds on the power of convex optimization–based methods. The key ingredient of our work is SQ algorithms and lower bounds for estimating the mean vector of a distribution over vectors supported on a convex body in Rd. This natural problem has not been previously studied, and we show that our solutions can be used to get substantially improved SQ versions of Perceptron and other online algorithms for learning halfspaces
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