Noticias en español
Fast Rates for Unbounded Losses: from ERM to Generalized Bayes
Abstract: I will present new excess risk bounds for randomized and deterministic estimators, discarding boundedness assumptions to handle general unbounded loss functions like log loss and squared loss under heavy tails. These bounds have a PAC-Bayesian flavor in both derivation and form, and their expression in terms of the information complexity forms a natural connection to generalized Bayesian estimators. The bounds hold with high probability and a fast $\tilde{O}(1/n)$ rate in parametric settings, under the recently introduced central’ condition (or various weakenings of this condition...
Read MoreProphet Secretary Through Blind Strategies
Abstract: In the classic prophet inequality, a problem in optimal stopping theory, samples from independent random variables arrive online. A gambler that knows the distributions, but cannot see the future, must decide at each point in time whether to stop and pick the current sample or to continue and lose that sample forever. The goal of the gambler is to maximize the expected value of what she picks and the performance measure is the worst case ratio between the expected value the gambler gets and what a prophet, that sees all the realizations in advance, gets. We study when the samples...
Read MoreA Linear Programming Based Approach to the Steiner Tree Problem with a Fixed Number of Terminals
Abstract: We present a set of integer programs (IPs) for the Steiner tree problem with the property that the best solution obtained by solving all, provides an optimal Steiner tree. Each IP is polynomial in the size of the underlying graph and our main result is that the linear programming (LP) relaxation of each IP is integral so that it can be solved as a linear program. However, the number of IPs grows exponentially with the number of terminals in the Steiner tree. As a consequence, we are able to solve the Steiner tree problem by solving a polynomial number of LPs, when the number of...
Read MoreFair Auctions with Asymmetrically Informed Bidders
Abstract: (With Aranyak Mehta and Uri Nadav) Agents often arrive to auctions with different levels of informations about their own value for the object sold. In such asymmetric settings, it may be optimal to charge different reservation prices to discriminate between bidders. However, it is often infeasible to expressly treat different bidders in the same auction differently, particularly in on-line settings. We characterize optimal nondiscriminatory mechanisms in the presence of informational asymmetries and compares them to the revenue of unconstrained optimal auctions. We find the revenue...
Read MorePreferential Attachment Random graphs with edge-step functions
Abstract: Nowadays, modeling and understanding the evolution and properties of concrete networks are important questions for many areas in the scientific community. The huge amount of data generated these days combined with new computing power allowed us to see concretely how many entities, such as our own society, are organized and connected. These findings naturally motivated the investigation of many models that intended to reproduce the properties observed empirically. In this seminar, in its first moment, we will introduce which kind of properties one desires to see on a random graph...
Read MoreA new method for showing nonexistence of solutions for a generalized Brezis-Nirenberg problem
Abstract: In this talk I will present new results on the nonexistence of solutions for a generalized hyperbolic Brezis-Nirenberg problem. Here we combine a classical Pohozaev argument with a generalized Hardy inequality. This is joint work with Soledad Benguria (U. Wisconsin).
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