10 accepted papers
Tensor train decomposition is widely used in machine learning and quantum physics due to its concise representation of high-dimensional tensors, overcoming the curse of dimensionality. Cross approximation---originally developed for representing a matrix from a set of selected rows and columns---is a…
This work studies the second-order convergence for both standard alternating minimization and proximal alternating minimization. We show that under mild assumptions on the (nonconvex) objective function, both algorithms avoid strict saddles almost surely from random initialization. Together with kno…
Low-rank matrix factorization is a problem of broad importance, owing to the ubiquity of low-rank models in machine learning contexts. In spite of its non- convexity, this problem has a well-behaved geometric landscape, permitting local search algorithms such as gradient descent to converge to globa…
Blind deconvolution and phase retrieval are both fundamental problems with a growing interest in signal processing and communications. In this work, we consider the task of simultaneous blind deconvolution and phase retrieval. We show that this non-linear problem can be reformulated as a low-rank te…
In this paper, we consider a general sparse recovery and blind demodulation model. Different from the ones in the literature, in our general model, each dictionary atom undergoes a distinct modulation process; we refer to this as non-stationary modulation. We also assume that the modulation matrices…
A variety of unconstrained nonconvex optimization problems have been shown to have benign geometric landscapes that satisfy the strict saddle property and have no spurious local minima. We present a general result relating the geometry of an unconstrained centralized problem to its equality-constrai…
The landscape of empirical risk has been widely studied in a series of machine learning problems, including low-rank matrix factorization, matrix sensing, matrix completion, and phase retrieval. In this work, we focus on the situation where the corresponding population risk is a degenerate non-conve…
In this paper, we propose a new framework for parameter estimation of complex exponentials from their modulations with unknown waveforms via convex programming. Our model generalizes the recently developed blind sparse spike deconvolution framework by Y. Chi [1] to the non-stationary scenario and en…
We develop a theoretical and computational framework to perform guaranteed tensor decomposition, which also has the potential to accomplish other tensor tasks such as tensor completion and denoising. We formulate tensor decomposition as a problem of measure estimation from moments. By constructing a…
Motivated by the problem of robust factorization of a low-rank tensor, we study the question of sparse and low-rank tensor decomposition. We present an efficient computational algorithm that modifies Leurgans' algoirthm for tensor factorization. Our method relies on a reduction of the problem to spa…