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The estimation of a random vector with independent components passed through a linear transform followed by a componentwise (possibly nonlinear) output map arises in a range of applications. Approximate message passing (AMP) methods, based on Gaussian appr ...

Linear sketching and recovery of sparse vectors with randomly constructed sparse matrices has numerous applications in several areas, including compressive sensing, data stream computing, graph sketching, and combinatorial group testing. This paper conside ...

Sparse matrices are favorable objects in machine learning and optimization. When such matrices are used, in place of dense ones, the overall complexity requirements in optimization can be significantly reduced in practice, both in terms of space and run-ti ...

We study generalization properties of distributed algorithms in the setting of nonparametric regression over a reproducing kernel Hilbert space (RKHS). We first investigate distributed stochastic gradient methods (SGM), with mini-batches and multi-passes o ...

Machine learning promises to accelerate materials discovery by allowing computational efficient property predictions from a small number of reference calculations. As a result, the literature has spent a considerable effort in designing representations tha ...

In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral/regularized algorithms, including ridge regressi ...

This paper argues that randomized linear sketching is a natural tool for on-the-fly compression of data matrices that arise from large-scale scientific simulations and data collection. The technical contribution consists in a new algorithm for constructing ...

Recent studies show that a reproducing kernel Hilbert space (RKHS) is not a suitable space to model functions by neural networks as the curse of dimensionality (CoD) cannot be evaded when trying to approximate even a single ReLU neuron (Bach, 2017). In thi ...

The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings, such as compressive sensing, subset selection in regression, and gro ...

In this paper, we study the {\em pooled data} problem of identifying the labels associated with a large collection of items, based on a sequence of pooled tests revealing the counts of each label within the pool. In the noiseless setting, we identify an ex ...

We propose a new and low per-iteration complexity first-order primal-dual optimization framework for a convex optimization template with broad applications. Our analysis relies on a novel combination of three classic ideas applied to the primal-dual gap fu ...

The problem of approximately computing the

k

dominant Fourier coefficients of a vector

X

quickly, and using few samples in time domain, is known as the Sparse Fourier Transform (sparse FFT) problem. A long line of work on the sparse FFT has resulted in ...

In this paper, we analyze the recently proposed stochastic primal-dual hybrid gradient (SPDHG) algorithm and provide new theoretical results. In particular, we prove almost sure convergence of the iterates to a solution with convexity and linear convergenc ...

Sampling, coding, and streaming even the most essential data, e.g., in medical imaging and weather-monitoring applications, produce a data deluge that severely stresses the avail able analog-to-digital converter, communication bandwidth, and digital-storag ...

While convolution and self-attention mechanisms have dominated architectural design in deep learning, this survey examines a fundamental yet understudied primitive: the Hadamard product. Despite its widespread implementation across various applications, th ...

We study the fundamental problem of learning an unknown, smooth probability function via pointwise Bernoulli tests. We provide a scalable algorithm for efficiently solving this problem with rigorous guarantees. In particular, we prove the convergence rate ...

This work studies the robustness certification problem of neural network models, which aims to find certified adversary-free regions as large as possible around data points. In contrast to the existing approaches that seek regions bounded uniformly along a ...

This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image, or sketch, of the matrix. These methods can preserve structural properties of the input matrix, such as positive-semidefinite ...

We propose a dimensionality reducing matrix design based on training data with constraints on its Frobenius norm and number of rows. Our design criteria is aimed at preserving the distances between the data points in the dimensionality reduced space as muc ...

Volkan Cevher

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Fixed Points of Generalized Approximate Message Passing with Arbitrary Matrices

Model-based Sketching and Recovery with Expanders

Convex block-sparse linear regression with expanders - provably

Optimal Convergence for Distributed Learning with Stochastic Gradient Methods and Spectral Algorithms

Chemical machine learning with kernels: The impact of loss functions

Optimal Rates for Spectral Algorithms with Least-Squares Regression over Hilbert Spaces

Streaming Low-Rank Matrix Approximation With An Application To Scientific Simulation

Learning with Norm Constrained, Over-parameterized, Two-layer Neural Networks

Limits on Support Recovery With Probabilistic Models: An Information-Theoretic Framework

Phase Transitions in the Pooled Data Problem

A Smooth Primal-Dual Optimization Framework for Nonsmooth Composite Convex Minimization

An Adaptive Sublinear-Time Block Sparse Fourier Transform

On The Convergence Of Stochastic Primal-Dual Hybrid Gradient

Learning Low-Dimensional Signal Models

Hadamard product in deep learning: Introduction, Advances and Challenges

Efficient learning of smooth probability functions from Bernoulli tests with guarantees

On Certifying Non-Uniform Bounds against Adversarial Attacks

Optimal Convergence for Distributed Learning with Stochastic Gradient Methods and Spectral Algorithms

Practical Sketching Algorithms For Low-Rank Matrix Approximation

Energy-aware adaptive bi-Lipschitz embeddings