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Modeling inverse dynamics is crucial for accurate feedforward robot control. The model computes the necessary joint torques, to perform a desired movement. The highly non-linear inverse function of the dynamical system can be approximated…

Machine Learning · Computer Science 2017-11-15 Stephan Baier , Volker Tresp

We consider the problem of estimating high-dimensional covariance matrices of a particular structure, which is a summation of low rank and sparse matrices. This covariance structure has a wide range of applications including factor analysis…

Methodology · Statistics 2013-10-17 Lin Zhang , Abhra Sarkar , Bani K. Mallick

Low-rank tensor approximations have shown great potential for uncertainty quantification in high dimensions, for example, to build surrogate models that can be used to speed up large-scale inference problems (Eigel et al., Inverse Problems…

Numerical Analysis · Mathematics 2020-11-30 Paul B. Rohrbach , Sergey Dolgov , Lars Grasedyck , Robert Scheichl

We consider the problem of designing sparse sampling strategies for multidomain signals, which can be represented using tensors that admit a known multilinear decomposition. We leverage the multidomain structure of tensor signals and…

Information Theory · Computer Science 2019-06-26 Guillermo Ortiz-Jiménez , Mario Coutino , Sundeep Prabhakar Chepuri , Geert Leus

What learning algorithms can be run directly on compressively-sensed data? In this work, we consider the question of accurately and efficiently computing low-rank matrix or tensor factorizations given data compressed via random projections.…

Machine Learning · Computer Science 2019-05-28 Vatsal Sharan , Kai Sheng Tai , Peter Bailis , Gregory Valiant

In this manuscript a unified framework for conducting inference on complex aggregated data in high dimensional settings is proposed. The data are assumed to be a collection of multiple non-Gaussian realizations with underlying undirected…

Applications · Statistics 2013-10-14 Fang Han , Han Liu , Brian Caffo

We present a scalable Bayesian model for low-rank factorization of massive tensors with binary observations. The proposed model has the following key properties: (1) in contrast to the models based on the logistic or probit likelihood,…

Machine Learning · Statistics 2015-08-19 Changwei Hu , Piyush Rai , Lawrence Carin

Finding "densely connected clusters" in a graph is in general an important and well studied problem in the literature \cite{Schaeffer}. It has various applications in pattern recognition, social networking and data mining…

Machine Learning · Statistics 2011-04-28 Samet Oymak , Babak Hassibi

A tensor network is a type of decomposition used to express and approximate large arrays of data. A given data-set, quantum state or higher dimensional multi-linear map is factored and approximated by a composition of smaller multi-linear…

Quantum Physics · Physics 2022-07-08 Richik Sengupta , Soumik Adhikary , Ivan Oseledets , Jacob Biamonte

When studying interacting systems, computing their statistical properties is a fundamental problem in various fields such as physics, applied mathematics, and machine learning. However, this task can be quite challenging due to the…

Statistical Mechanics · Physics 2023-05-04 Yijia Wang , Yuwen Ebony Zhang , Feng Pan , Pan Zhang

We develop a formalism to compute the statistics of the top eigenpair of weighted sparse graphs with finite mean connectivity and bounded maximal degree. Framing the problem in terms of optimisation of a quadratic form on the sphere and…

Statistical Mechanics · Physics 2019-10-28 Vito Antonio Rocco Susca , Pierpaolo Vivo , Reimer Kuehn

The problem of identifying sparse solutions for the link structure and dynamics of an unknown linear, time-invariant network is posed as finding sparse solutions x to Ax=b. If the sensing matrix A satisfies a rank condition, this problem…

Dynamical Systems · Mathematics 2014-11-18 David Hayden , Young Hwan Chang , Jorge Goncalves , Claire Tomlin

We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…

Optimization and Control · Mathematics 2025-01-13 David A. R. Robin , Kevin Scaman , Marc Lelarge

Tensor completion refers to the problem of recovering the missing, corrupted or unobserved entries in data represented by tensors. In this paper, we tackle the tensor completion problem in the scenario in which multiple tensor acquisitions…

Signal Processing · Electrical Eng. & Systems 2023-12-07 Iain Rolland , Sivasakthy Selvakumaran , Andrea Marinoni

Probabilistic approaches for tensor factorization aim to extract meaningful structure from incomplete data by postulating low rank constraints. Recently, variational Bayesian (VB) inference techniques have successfully been applied to large…

Machine Learning · Computer Science 2014-10-01 Beyza Ermis , A. Taylan Cemgil

The goal of this paper is to find a low-rank approximation for a given tensor. Specifically, we give a computable strategy on calculating the rank of a given tensor, based on approximating the solution to an NP-hard problem. In this paper,…

Numerical Analysis · Mathematics 2016-10-20 Xiaofei Wang , Carmeliza Navasca

Node classification is an important problem in graph data management. It is commonly solved by various label propagation methods that work iteratively starting from a few labeled seed nodes. For graphs with arbitrary compatibilities between…

Machine Learning · Computer Science 2020-03-06 Krishna Kumar P. , Paul Langton , Wolfgang Gatterbauer

In this paper, we investigate the statistical convergence rate of a Bayesian low-rank tensor estimator. Our problem setting is the regression problem where a tensor structure underlying the data is estimated. This problem setting occurs in…

Machine Learning · Statistics 2014-08-14 Taiji Suzuki

Tensor completion refers to the task of estimating the missing data from an incomplete measurement or observation, which is a core problem frequently arising from the areas of big data analysis, computer vision, and network engineering. Due…

Machine Learning · Computer Science 2021-05-21 Chenjian Pan , Chen Ling , Hongjin He , Liqun Qi , Yanwei Xu

We study the statistical limits of both detecting and estimating a rank-one deformation of a symmetric random Gaussian tensor. We establish upper and lower bounds on the critical signal-to-noise ratio, under a variety of priors for the…

Probability · Mathematics 2017-01-25 Amelia Perry , Alexander S. Wein , Afonso S. Bandeira