We study implicit regularization when optimizing an underdetermined quadratic objective
over a matrix $ X $ with gradient descent on a factorization of X. We conjecture and provide …

Compressed sensing is an alternative to Shannon/Nyquist sampling for acquiring sparse or
compressible signals. Sparse coding represents a signal as a sparse linear combination of …

We improve a recent gurantee of Bach and Moulines on the linear convergence of SGD for
smooth and strongly convex objectives, reducing a quadratic dependence on the strong …

We establish theoretical results concerning all local optima of various regularized M-
estimators, where both loss and penalty functions are allowed to be nonconvex. Our results …

The R package partykit provides a flexible toolkit for learning, representing, summarizing,
and visualizing a wide range of tree-structured regression and classification models. The …

Noisy matrix completion aims at estimating a low-rank matrix given only partial and
corrupted entries. Despite remarkable progress in designing efficient estimation algorithms …

Matrix approximation is a common tool in recommendation systems, text mining, and
computer vision. A prevalent assumption in constructing matrix approximations is that the …

We address the rectangular matrix completion problem by lifting the unknown matrix to a
positive semidefinite matrix in higher dimension, and optimizing a nonconvex objective over …

In the present paper, we consider the problem of matrix completion with noise. Unlike
previous works, we consider quite general sampling distribution and we do not need to …

We study a localized notion of uniform convergence known as an “optimistic rate”[,] for linear
regression with Gaussian data. Our refined analysis avoids the hidden constant and …