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# Upcoming Seminars

We present novel oblivious routing algorithms for the splittable and the unsplittable multicommodity flow settings. Our algorithms for both models improve upon the state-of-the-art, in terms of running time and performance with respect to graphs that exhibit good expansion guarantees. As an intermediate step towards the unsplittable setting, we present a novel generalization of Valiant's classical load balancing scheme for packet-switched networks to arbitrary graphs, which is of independent interest. Our approach relies on diffusing traffic throughout the network and then regathering it to its destination, via iterative applications of the random walk operator. Consequently, the performance guarantees of our algorithms are derived from the convergence of the random walk operator to the stationary distribution and are expressed in terms of the spectral gap of the graph (which dominates the mixing time).

Image restoration algorithms are typically evaluated by some distortion measure (e.g. PSNR, SSIM, IFC, VIF) or by human opinion scores that quantify perceived perceptual quality. In this work, we prove mathematically that distortion and perceptual quality are at odds with each other. Specifically, we study the optimal probability for correctly discriminating the outputs of an image restoration algorithm from real images. We show that as the mean distortion decreases, this probability must increase (indicating worse perceptual quality). As opposed to the common belief, this result holds true for any distortion measure, and is not only a problem of the PSNR or SSIM criteria. However, as we show experimentally, for some measures it is less severe (e.g. distance between VGG features). We also show that generative-adversarial-nets (GANs) provide a principled way to approach the perception-distortion bound. This constitutes theoretical support to their observed success in low-level vision tasks. Based on our analysis, we propose a new methodology for evaluating image restoration methods, and use it to perform an extensive comparison between recent super-resolution algorithms. Our study reveals which methods are currently closest to the theoretical perception-distortion bound.

* Joint work with Yochai Blau.

We study the problem of identifying correlations in multivariate data, under information constraints:

Either on the amount of memory that can be used by the algorithm, or the amount of communi- cation when the data is distributed across several machines. We prove a tight trade-off between the memory/communication complexity and the sample complexity, implying (for example) that to detect pairwise correlations with optimal sample complexity, the number of required mem-ory/communication bits is at least quadratic in the dimension. Our results substantially improve those of Shamir (2014), which studied a similar question in a much more restricted setting. To the best of our knowledge, these are the first provable sample/memory/communication trade-offs for a practical estimation problem, using standard distributions, and in the natural regime where the memory/communication budget is larger than the size of a single data point. To derive our theorems, we prove a new information-theoretic result, which may be relevant for studying other information-constrained learning problems.

Joint work with Ohad Shamir