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We introduce a sampling theoretic framework for the recovery of smooth surfaces and functions living on smooth surfaces from few samples. The proposed approach can be thought of as a nonlinear generalization of union of subspace models…

In this paper, we leverage over-parameterization to design regularization-free algorithms for the high-dimensional single index model and provide theoretical guarantees for the induced implicit regularization phenomenon. Specifically, we…

Low-rank matrix regression is a fundamental problem in data science with various applications in systems and control. Nuclear norm regularization has been widely applied to solve this problem due to its convexity. However, it suffers from…

The paper addresses the problem of low-rank trace norm minimization. We propose an algorithm that alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is characterized by an efficient factorization…

We propose a low-rank method for solving the Helmholtz equation. Our approach is based on the WaveHoltz method, which computes Helmholtz solutions by applying a time-domain filter to the solution of a related wave equation. The wave…

Deconvolution is a statistical inverse problem to estimate the distribution of a random variable based on its noisy observations. Despite the extensive studies on the topic, deconvolution with unknown noise distribution remains as a…

The problem of recovering a signal from its low frequency components occurs often in practical applications due to the lowpass behavior of many physical systems. Here we study in detail conditions under which a signal can be determined from…

This paper tackles the problem of recovering a low-rank signal tensor with possibly correlated components from a random noisy tensor, or so-called spiked tensor model. When the underlying components are orthogonal, they can be recovered…

Matrix learning is at the core of many machine learning problems. A number of real-world applications such as collaborative filtering and text mining can be formulated as a low-rank matrix completion problem, which recovers incomplete…

With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing techniques that incorporate known physical constraints into the learned…

Deep neuroevolution is a highly scalable alternative to reinforcement learning due to its unique ability to encode network updates in a small number of bytes. Recent insights from traditional deep learning indicate high-dimensional models…

Low-rank regularization (LRR) has been widely applied in various machine learning tasks, but the associated optimization is challenging. Directly optimizing the rank function under constraints is NP-hard in general. To overcome this…

Tensor Ring (TR) decomposition is a powerful tool for high-order data modeling, but is inherently restricted to discrete forms defined on fixed meshgrids. In this work, we propose a TR functional decomposition for both meshgrid and…

Multitask learning, i.e. taking advantage of the relatedness of individual tasks in order to improve performance on all of them, is a core challenge in the field of machine learning. We focus on matrix regression tasks where the rank of the…

The low-rank matrix approximation problems within a threshold are widely applied in information retrieval, image processing, background estimation of the video sequence problems and so on. This paper presents an adaptive randomized…

Random Fourier features provide a way to tackle large-scale machine learning problems with kernel methods. Their slow Monte Carlo convergence rate has motivated the research of deterministic Fourier features whose approximation error can…

We study the problem of learning mixtures of low-rank models, i.e. reconstructing multiple low-rank matrices from unlabelled linear measurements of each. This problem enriches two widely studied settings -- low-rank matrix sensing and mixed…

Factor Analysis (FA) is a technique of fundamental importance that is widely used in classical and modern multivariate statistics, psychometrics and econometrics. In this paper, we revisit the classical rank-constrained FA problem, which…

We consider the problem of learning a low-rank matrix, constrained to lie in a linear subspace, and introduce a novel factorization for modeling such matrices. A salient feature of the proposed factorization scheme is it decouples the…

Trace norm regularization is a widely used approach for learning low rank matrices. A standard optimization strategy is based on formulating the problem as one of low rank matrix factorization which, however, leads to a non-convex problem.…