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Mutual information for low-rank even-order symmetric tensor estimation

Publications associées (32)

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A key challenge across many disciplines is to extract meaningful information from data which is often obscured by noise. These datasets are typically represented as large matrices. Given the current trend of ever-increasing data volumes, with datasets grow ...

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COMMUNICATION LOWER BOUNDS AND OPTIMAL ALGORITHMS FOR MULTIPLE TENSOR-TIMES-MATRIX COMPUTATION

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Multiple tensor-times-matrix (Multi-TTM) is a key computation in algorithms for computing and operating with the Tucker tensor decomposition, which is frequently used in multidimensional data analysis. We establish communication lower bounds that determine ...

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Rank-Adaptive Time Integration Of Tree Tensor Networks

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A rank-adaptive integrator for the approximate solution of high-order tensor differential equations by tree tensor networks is proposed and analyzed. In a recursion from the leaves to the root, the integrator updates bases and then evolves connection tenso ...

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Spectral Estimators for High-Dimensional Matrix Inference

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COMMUNICATION LOWER BOUNDS AND OPTIMAL ALGORITHMS FOR MULTIPLE TENSOR-TIMES-MATRIX COMPUTATION

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Low-Rank Tensor Methods for High-Dimensional Problems

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In this thesis, we propose and analyze novel numerical algorithms for solving three different high-dimensional problems involving tensors. The commonality of these problems is that the tensors can potentially be well approximated in low-rank formats. Ident ...

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STREAMING TENSOR TRAIN APPROXIMATION

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Tensor trains are a versatile tool to compress and work with high-dimensional data and functions. In this work we introduce the streaming tensor train approximation (STTA), a new class of algorithms for approximating a given tensor ' in the tensor train fo ...

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Preserving the positivity of the deformation gradient determinant in intergrid interpolation by combining RBFs and SVD: Application to cardiac electromechanics

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The accurate, robust and efficient transfer of the deformation gradient tensor between meshes of different resolution is crucial in cardiac electromechanics simulations. This paper presents a novel method that combines rescaled localized Radial Basis Funct ...

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Measuring bathymetry has always been a major scientific and technological challenge. In this work, we used a deep learning technique for inferring bathymetry from the depth-averaged velocity field. The training of the neural network is based on 5742 labora ...

2023

Higher Order Asymptotics: Applications to Satellite Conjunction and Boundary Problems

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Higher-order asymptotics provide accurate approximations for use in parametric statistical modelling. In this thesis, we investigate using higher-order approximations in two-specific settings, with a particular emphasis on the tangent exponential model. ...

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Impact of phylogeny on structural contact inference from protein sequence data

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Local and global inference methods have been developed to infer structural contacts from multiple sequence alignments of homologous proteins. They rely on correlations in amino acid usage at contacting sites. Because homologous proteins share a common ance ...

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Adaptive isogeometric methods with C-1 (truncated) hierarchical splines on planar multi-patch domains

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Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline models is not well s ...

WORLD SCIENTIFIC PUBL CO PTE LTD2023

Page 1 sur 4

Low-Rank Tensor Methods for High-Dimensional Problems

Christoph Max Strössner

EPFL2023

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Daniel Kressner

Siam Publications2023

Preserving the positivity of the deformation gradient determinant in intergrid interpolation by combining RBFs and SVD: Application to cardiac electromechanics

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Elsevier Science Sa2023