Implicit regularization in nonconvex statistical estimation: Gradient descent converges linearly for phase retrieval and matrix completion
Recent years have seen a flurry of activities in designing provably efficient nonconvex
optimization procedures for solving statistical estimation problems. For various problems like …
optimization procedures for solving statistical estimation problems. For various problems like …
The global optimization geometry of low-rank matrix optimization
This paper considers general rank-constrained optimization problems that minimize a
general objective function over the set of rectangular matrices that have rank at most r. To …
general objective function over the set of rectangular matrices that have rank at most r. To …
A nonconvex approach for exact and efficient multichannel sparse blind deconvolution
We study the multi-channel sparse blind deconvolution (MCS-BD) problem, whose task is to
simultaneously recover a kernel $\mathbf a $ and multiple sparse inputs $\{\mathbf x_i\} _ {i …
simultaneously recover a kernel $\mathbf a $ and multiple sparse inputs $\{\mathbf x_i\} _ {i …
Manifold gradient descent solves multi-channel sparse blind deconvolution provably and efficiently
Multi-channel sparse blind deconvolution, or convolutional sparse coding, refers to the
problem of learning an unknown filter by observing its circulant convolutions with multiple …
problem of learning an unknown filter by observing its circulant convolutions with multiple …
Convex and nonconvex optimization are both minimax-optimal for noisy blind deconvolution under random designs
We investigate the effectiveness of convex relaxation and nonconvex optimization in solving
bilinear systems of equations under two different designs (ie, a sort of random Fourier …
bilinear systems of equations under two different designs (ie, a sort of random Fourier …
Convolutional phase retrieval via gradient descent
We study the convolutional phase retrieval problem, of recovering an unknown signal x∈ C
n from m measurements consisting of the magnitude of its cyclic convolution with a given …
n from m measurements consisting of the magnitude of its cyclic convolution with a given …
Recursive generalized extended least squares and RML algorithms for identification of bilinear systems with ARMA noise
Bilinear systems are considered as a particular class of nonlinear systems including the
state variables which are typically used for online identification. By using a recursive …
state variables which are typically used for online identification. By using a recursive …
Modified log-Sobolev inequalities, Beckner inequalities and moment estimates
We prove that in the context of general Markov semigroups Beckner inequalities with
constants separated from zero as p→ 1+ are equivalent to the modified log Sobolev …
constants separated from zero as p→ 1+ are equivalent to the modified log Sobolev …
Multi-Antenna ISAC Receiver with n-Tuple Blind Deconvolution
Recent developments in spectrum-sharing technologies include integrated sensing and
communications (ISAC) systems to save resources, cost, and power. In this paper, we …
communications (ISAC) systems to save resources, cost, and power. In this paper, we …
Finding the sparsest vectors in a subspace: Theory, algorithms, and applications
The problem of finding the sparsest vector (direction) in a low dimensional subspace can be
considered as a homogeneous variant of the sparse recovery problem, which finds …
considered as a homogeneous variant of the sparse recovery problem, which finds …