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We propose a general framework for reconstructing and denoising single entries of incomplete and noisy entries. We describe: effective algorithms for deciding if and entry can be reconstructed and, if so, for reconstructing and denoising…
Many real optimisation problems lead to multimodal domains and so require the identification of multiple optima. Niching methods have been developed to maintain the population diversity, to investigate many peaks in parallel and to reduce…
We develop and analyze stochastic optimization algorithms for problems in which the expected loss is strongly convex, and the optimum is (approximately) sparse. Previous approaches are able to exploit only one of these two structures,…
Composite convex optimization problems which include both a nonsmooth term and a low-rank promoting term have important applications in machine learning and signal processing, such as when one wishes to recover an unknown matrix that is…
Collecting the most informative data from a large dataset distributed over a network is a fundamental problem in many fields, including control, signal processing and machine learning. In this paper, we establish a connection between…
In this paper, we study the form over the minimum spanning tree problem (MST) from which we will derive an intuitively generalized model and new methods with the upper bound of runtimes of logarithm. The new pattern we made has taken…
We consider the problem of static assortment optimization, where the goal is to find the assortment of size at most $C$ that maximizes revenues. This is a fundamental decision problem in the area of Operations Management. It has been shown…
In this work, we consider the matrix completion problem, where the objective is to reconstruct a low-rank matrix from a few observed entries. A commonly employed approach involves nuclear norm minimization. For this method to succeed, the…
Consider a collection of competing machine learning algorithms. Given their performance on a benchmark of datasets, we would like to identify the best performing algorithm. Specifically, which algorithm is most likely to rank highest on a…
In the setting of nonparametric regression, we propose and study a combination of stochastic gradient methods with Nystr\"om subsampling, allowing multiple passes over the data and mini-batches. Generalization error bounds for the studied…
The problem we concentrate on is as follows: given (1) a convex compact set $X$ in ${\mathbb{R}}^n$, an affine mapping $x\mapsto A(x)$, a parametric family $\{p_{\mu}(\cdot)\}$ of probability densities and (2) $N$ i.i.d. observations of the…
We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…
Early stopping of iterative algorithms is an algorithmic regularization method to avoid over-fitting in estimation and classification. In this paper, we show that early stopping can also be applied to obtain the minimax optimal testing in a…
The scaling of Large Multimodal Models (LMMs) is constrained by the quality-quantity trade-off inherent in synthetic data. Previous approaches, such as LLM-as-a-Judge, have proven their effectiveness in addressing this but suffer from…
In the submodular ranking (SR) problem, the input consists of a set of submodular functions defined on a ground set of elements. The goal is to order elements for all the functions to have value above a certain threshold as soon on average…
Two widely used randomized algorithms are the sketch-and-solve method for least-squares regression and the randomized SVD for low-rank approximation. These algorithms apply a random embedding to compress a target matrix, and they perform…
Consider the problem of minimizing the expected value of a (possibly nonconvex) cost function parameterized by a random (vector) variable, when the expectation cannot be computed accurately (e.g., because the statistics of the random…
We consider the nonparametric regression estimation problem of recovering an unknown response function f on the basis of spatially inhomogeneous data when the design points follow a known compactly supported density g with a finite number…
We consider the problem of inference in a linear regression model in which the relative ordering of the input features and output labels is not known. Such datasets naturally arise from experiments in which the samples are shuffled or…
The exponential growth of volume, variety and velocity of data is raising the need for investigations of automated or semi-automated ways to extract useful patterns from the data. It requires deep expert knowledge and extensive…