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Found 14 papers, 3 papers with code
Separation-Free Spectral Super-Resolution via Convex Optimization
Atomic norm methods have recently been proposed for spectral super-resolution with flexibility in dealing with missing data and miscellaneous noises.
Error Analysis of Tensor-Train Cross Approximation
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.
Distributed Low-rank Matrix Factorization With Exact Consensus
Low-rank matrix factorization is a problem of broad importance, owing to the ubiquity of low-rank models in machine learning contexts.
The Landscape of Non-convex Empirical Risk with Degenerate Population Risk
We also apply the theory to matrix sensing and phase retrieval to demonstrate how to infer the landscape of empirical risk from that of the corresponding population risk.
Provable Bregman-divergence based Methods for Nonconvex and Non-Lipschitz Problems
Therefore, this work not only develops guaranteed optimization methods for non-Lipschitz smooth problems but also solves an open problem of showing the second-order convergence guarantees for these alternating minimization methods.
Spherical Principal Component Analysis
However, most of the studies on PCA aim to minimize the loss after projection, which usually measures the Euclidean distance, though in some fields, angle distance is known to be more important and critical for analysis.
Global Optimality in Distributed Low-rank Matrix Factorization
We study the convergence of a variant of distributed gradient descent (DGD) on a distributed low-rank matrix approximation problem wherein some optimization variables are used for consensus (as in classical DGD) and some optimization variables appear only locally at a single node in the network.
Geometry of Factored Nuclear Norm Regularization
In spite of the nonconvexity of the factored formulation, we prove that when the convex loss function $f(X)$ is $(2r, 4r)$-restricted well-conditioned, each critical point of the factored problem either corresponds to the optimal solution $X^\star$ of the original convex optimization or is a strict saddle point where the Hessian matrix has a strictly negative eigenvalue.
Sparse and Low-Rank Tensor Decomposition
Our method relies on a reduction of the problem to sparse and low-rank matrix decomposition via the notion of tensor contraction.
Experimental robustness of Fourier Ptychography phase retrieval algorithms
Both noise (e. g. Poisson noise) and model mis-match errors are shown to scale with intensity.
Optimal Low-Rank Tensor Recovery from Separable Measurements: Four Contractions Suffice
This motivates us to consider the problem of low rank tensor recovery from a class of linear measurements called separable measurements.
Compressed Sensing Off the Grid
This paper investigates the problem of estimating the frequency components of a mixture of complex sinusoids from a random subset of regularly spaced samples.
The Sample Complexity of Search over Multiple Populations
We consider a large number of populations, each corresponding to either distribution P0 or P1.
Atomic norm denoising with applications to line spectral estimation
Motivated by recent work on atomic norms in inverse problems, we propose a new approach to line spectral estimation that provides theoretical guarantees for the mean-squared-error (MSE) performance in the presence of noise and without knowledge of the model order.
Information Theory Information Theory
