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How can researchers use sensitive data for statistical estimation without compromising the privacy of the individuals who contributed their data? In this talk, I will describe my work on the foundations of statistical estimation in a rigorous privacy framework called differential privacy. Using fundamental examples like mean and covariance estimation, I'll discuss a range of issues like the minimax error rate of private estimation and practical tools for achieving differential privacy.
Contextual search is a generalization of binary search in higher dimensions, which captures settings such as feature-based dynamic pricing. Standard game-theoretic formulations of this problem assume that agents act in accordance with a specific behavioral model. In practice, however, some agents may not follow the dominant behavioral model or they may act in ways that seem to be arbitrarily irrational. Existing algorithms heavily depend on the behavioral model being (approximately) accurate for all agents and have poor performance in the presence of even a few such arbitrarily irrational agents. In this talk, I provide a framework for studying contextual search when some of the agents can behave in ways inconsistent with the underlying behavioral model. The algorithms that I will present attain near-optimal regret guarantees in the absence of irrational agents and their performance degrades gracefully with the number of such agents.
The talk will be based on joint works with Thodoris Lykouris, Akshay Krishnamurthy, Robert Schapire, Renato Paes Leme, and Jon Schneider.
In this talk I will describe some simple average-case reduction techniques and use these techniques to connect several statistical problems with widely varying structures. These reduction techniques transform the probability distribution defining a problem in an algorithmically efficient way while preserving the strength of the underlying signal, thereby transferring the computational phase transitions from one problem to another. We'll focus especially on the mixtures of linear regressions problem, and show how this supervised learning problem over continuous variables can be precisely related to the planted clique problem, a combinatorial unsupervised learning problem. Along the way we'll see a method for turning positive correlations into negative correlations amongst a subset of variables without knowing which subset is the correlated one, as well as a clean but non-obvious way to turn a supervised learning problem into an unsupervised one. The talk is based on joint work with Matthew Brennan (https://arxiv.org/abs/2005.08099).
Join us for coffee and snacks at 3:30pm in the Grove outside Packard (near Bytes' outdoor seating). This week's speaker will join us via Zoom, which will be screened in Packard 101, and streamed for those unable to attend in person.
Complexity analysis in optimization seeks upper bounds on the amount of work required to find approximate solutions of problems in a given class with a given algorithm, and also lower bounds, usually in the form of a worst-case example from a given problem class. The relationship between theoretical complexity bounds and practical performance of algorithms on "typical" problems varies widely across problem and algorithm classes, and relative interest among researchers between the theoretical and practical aspects of algorithm design and analysis has waxed and waned over the years. This talk surveys complexity analysis and its relationship to practical algorithms in optimization, with an emphasis on linear programming and convex and nonconvex nonlinear optimization, providing historical (and cultural) perspectives on research in these areas.
I will present a single idea about representation which allows advances made by several different groups to be combined into an imaginary system called GLOM. The advances include transformers, neural fields, contrastive representation learning, distillation and capsules. GLOM answers the question: How can a neural network with a fixed architecture parse an image into a part-whole hierarchy which has a different structure for each image? The idea is simply to use islands of identical vectors to represent the nodes in the parse tree. The talk will discuss the many ramifications of this idea. If GLOM can be made to work, it should significantly improve the interpretability of the representations produced by transformer-like systems when applied to vision or language.