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We develop and analyze a set of new sequential simulation-optimization algorithms for large-scale multi-dimensional discrete optimization via simulation problems with a convexity structure. The "large-scale" notion refers to that the…
The first order derivative of a data density can be estimated efficiently by denoising score matching, and has become an important component in many applications, such as image generation and audio synthesis. Higher order derivatives…
We consider the problem of estimating the factors of a rank-$1$ matrix with i.i.d. Gaussian, rank-$1$ measurements that are nonlinearly transformed and corrupted by noise. Considering two prototypical choices for the nonlinearity, we study…
Rational approximation schemes for reconstructing periodic signals from samples with poorly separated spectral content are described. These methods are automatic and adaptive, requiring no tuning or manual parameter selection. Collectively,…
We introduce an ordinate method for noisy data analysis, based solely on rank information and thus insensitive to outliers. The method is nonparametric, objective, and the required data processing is parsimonious. Main ingredients are a…
In this paper, we present a data-driven controller design method for continuous-time nonlinear systems, using no model knowledge but only measured data affected by noise. While most existing approaches focus on systems with polynomial…
With recent deep learning based approaches showing promising results in removing noise from images, the best denoising performance has been reported in a supervised learning setup that requires a large set of paired noisy images and ground…
We develop a data-driven approach for signal denoising that utilizes variational mode decomposition (VMD) algorithm and Cramer Von Misses (CVM) statistic. In comparison with the classical empirical mode decomposition (EMD), VMD enjoys…
Although the standard formulations of prediction problems involve fully-observed and noiseless data drawn in an i.i.d. manner, many applications involve noisy and/or missing data, possibly involving dependence, as well. We study these…
In the study of condensed matter physics, spectral information plays an important role for understand the mechanism of materials. However, it is difficult to obtain the spectrum directly through experiments or simulation. For example, the…
In this work we construct an optimal linear shrinkage estimator for the covariance matrix in high dimensions. The recent results from the random matrix theory allow us to find the asymptotic deterministic equivalents of the optimal…
This paper develops a unified analytical framework for determinant identities under finite-rank perturbations of square matrices that remains valid without invertibility assumptions. In contrast to classical inverse-based formulations, the…
In this work, we address the problem of Hessian inversion bias in distributed second-order optimization algorithms. We introduce a novel shrinkage-based estimator for the resolvent of gram matrices which is asymptotically unbiased, and…
We introduce a novel approach for discriminative classification using evolutionary algorithms. We first propose an algorithm to optimize the total loss value using a modified 0-1 loss function in a one-dimensional space for classification.…
We conjecture that the inherent difference in generalisation between adaptive and non-adaptive gradient methods in deep learning stems from the increased estimation noise in the flattest directions of the true loss surface. We demonstrate…
Classical Kullback-Leibler or entropic distances are known to enjoy certain desirable statistical properties in the context of decision-making with noiseless data. However, in most practical situations the data available to a decision maker…
Motivated by the poor performance of cross-validation in settings where data are scarce, we propose a novel estimator of the out-of-sample performance of a policy in data-driven optimization.Our approach exploits the optimization problem's…
We consider the problem of reconstructing a discrete-time signal (sequence) with continuous-valued components corrupted by a known memoryless channel. When performance is measured using a per-symbol loss function satisfying mild regularity…
Self-supervised learning for image denoising problems in the presence of denaturation for noisy data is a crucial approach in machine learning. However, theoretical understanding of the performance of the approach that uses denatured data…
In this paper we estimate the mean-variance portfolio in the high-dimensional case using the recent results from the theory of random matrices. We construct a linear shrinkage estimator which is distribution-free and is optimal in the sense…