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This paper is concerned with the analysis of the average error in approximating the global minimum of a 1-dimensional, time-homogeneous diffusion by non-adaptive methods. We derive the limiting distri...
This paper presents several strategies for spectral de-noising of hyperspectral images and hypercube reconstruction from a limited number of tomographic measurements. In particular we show that the no...
In this paper we analyze the randomized block-coordinate descent (RBCD) methods proposed in [8,11] for minimizing the sum of a smooth convex function and a block-separable convex function. In particul...
In this paper we present a novel technique for micro-seismic localization using a group sparse penalization that is robust to the focal mechanism of the source and requires only a velocity model of th...
We consider the fundamental question of learnability of a hypotheses class in the supervised learning setting and in the general learning setting introduced by Vladimir Vapnik. We survey classic resul...
The problem of stochastic convex optimization with bandit feedback (in the learning community) or without knowledge of gradients (in the optimization community) has received much attention in recent y...
This paper studies the sample complexity of searching over multiple populations. We consider a large number of populations, each corresponding to either distribution P0 or P1. The goal of the search p...
This paper provides lower bounds on the convergence rate of Derivative Free Optimization (DFO) with noisy function evaluations, exposing a fundamental and unavoidable gap between the performance of al...
In this thesis we study adaptive nonparametric regression with noise misspecifi-cation and the complexity of approximation of random fields in dependence of the dimension. First, we consider the prob...
In this paper we develop a randomized block-coordinate descent method for minimizing the sum of a smooth and a simple nonsmooth block-separable convex function and prove that it obtains an $\epsilon$-...
The paper introduces the recent results related to an entropy functional on trajectories of a controlled diffusion process, and the information path functional (IPF), analyzing their connections to th...
We consider the unconstrained L2-Lp minimization: find a minimizer of kAx−bk2 2+λkxkp p for given A ∈ Rm×n, b ∈ Rm and parameters λ > 0, p ∈ [0, 1). This problem has been studied extensively...
We give an exponential lower bound for the Graver complexity of the incidence matrix of a complete bipartite graph of arbitrary size. Our result is a generalization of the result by Berstein and Onn (...
We introduce an information theoretic measure of statistical structure, called 'binding information', for sets of random variables, and compare it with several previously proposed measures including e...
We tackle the problem of building adaptive estimation procedures for ill-posed inverse problems. For general regularization methods depending on tuning parameters, we construct a penalized method that...

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