36 citations · 61 across the 23 of their papers we have counts for
11 papers · 1 filter
Stochastic Optimization of Tree Tensor Networks
Marius Willner, Maximilian Scharf, André Uschmajew +2
Tensor networks, originally developed for quantum many-body physics, are promising models for machine learning. We derive stochastic Riemannian optimizers for tree tensor networks…
Natural Riemannian gradient for learning functional tensor networks
Nikolas Klug, Michael Ulbrich, André Uschmajew +1
We consider machine learning tasks with low-rank functional tree tensor networks (TTN) as the learning model. While in the case of least-squares regression, low-rank functional TTN…
Numerically stable variants of overrelaxation for operator Sinkhorn iteration
Henrik Eisenmann, Tasuku Soma, Xun Tang +1
We consider accelerated versions of the operator Sinkhorn iteration (OSI) for solving scaling problems for completely positive maps. Based on the interpretation of OSI as alternati…
Gauss-Southwell type descent methods for low-rank matrix optimization
Guillaume Olikier, André Uschmajew, Bart Vandereycken
We consider gradient-related methods for low-rank matrix optimization with a smooth cost function. The methods operate on single factors of the low-rank factorization and share asp…
Time-Varying Semidefinite Programming: Path Following a Burer-Monteiro Factorization
Antonio Bellon, Mareike Dressler, Vyacheslav Kungurtsev +2
We present an online algorithm for time-varying semidefinite programs (TV-SDPs), based on the tracking of the solution trajectory of a low-rank matrix factorization, also known as…
Kronecker Product Approximation of Operators in Spectral Norm via Alternating SDP
Mareike Dressler, André Uschmajew, Venkat Chandrasekaran
The decomposition or approximation of a linear operator on a matrix space as a sum of Kronecker products plays an important role in matrix equations and low-rank modeling. The appr…
A note on the optimal convergence rate of descent methods with fixed step sizes for smooth strongly convex functions
André Uschmajew, Bart Vandereycken
Based on a result by Taylor, Hendrickx, and Glineur (J. Optim. Theory Appl., 178(2):455--476, 2018) on the attainable convergence rate of gradient descent for smooth and strongly c…
Riemannian thresholding methods for row-sparse and low-rank matrix recovery
Henrik Eisenmann, Felix Krahmer, Max Pfeffer +1
In this paper, we present modifications of the iterative hard thresholding (IHT) method for recovery of jointly row-sparse and low-rank matrices. In particular a Riemannian version…
A note on overrelaxation in the Sinkhorn algorithm
Tobias Lehmann, Max-K. von Renesse, Alexander Sambale +1
We derive an a priori parameter range for overrelaxation of the Sinkhorn algorithm, which guarantees global convergence and a strictly faster asymptotic local convergence. Guided b…
A new convergence proof for the higher-order power method and generalizations
André Uschmajew
A proof for the point-wise convergence of the factors in the higher-order power method for tensors towards a critical point is given. It is obtained by applying established results…
Convergence results for projected line-search methods on varieties of low-rank matrices via Łojasiewicz inequality
Reinhold Schneider, André Uschmajew
The aim of this paper is to derive convergence results for projected line-search methods on the real-algebraic variety of real matrices of rank a…