7 accepted papers
A promising trend in deep learning replaces traditional feedforward networks with implicit networks. Unlike traditional networks, implicit networks solve a fixed point equation to compute inferences. Solving for the fixed point varies in complexity, depending on provided data and an error tolerance.…
Tensor optimization is crucial to massive machine learning and signal processing tasks. In this paper, we consider tensor optimization with a convex and well-conditioned objective function and reformulate it into a nonconvex optimization using the Burer-Monteiro type parameterization. We analyze the…
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…
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…
Symmetric nonnegative matrix factorization (NMF)---a special but important class of the general NMF---is demonstrated to be useful for data analysis and in particular for various clustering tasks. Unfortunately, designing fast algorithms for Symmetric NMF is not as easy as for the nonsymmetric count…
Frequency estimation is a classical problem in signal processing, with applications ranging from sensor array processing to wireless communications and structural health monitoring. Modern algorithms based on atomic norm minimization can cope with missing data but incur a high computational cost. To…