A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study quantifies performance gap between tensor and matrix-based approaches in nested matrix-tensor model.
The tensor-tensor product (t-product) [M. E. Kilmer and C. D. Martin, 2011] is a natural generalization of matrix multiplication. Based on t-product, many operations on matrix can be extended to tensor cases, including tensor SVD, tensor spectral norm, tensor nuclear norm [C. Lu, et al., 2018] and many others. The line…
Tensor factorization arises in many machine learning applications, such knowledge base modeling and parameter estimation in latent variable models. However, numerical methods for tensor factorization have not reached the level of maturity of matrix factorization methods. In this paper, we propose a new method for CP te…
New method for multiway clustering of 3rd order tensors.
Alexandrov spaces with non-negative curvature are characterized by the matrix displacement convexity of an entropy tensor.
Robust tensor CP decomposition involves decomposing a tensor into low rank and sparse components. We propose a novel non-convex iterative algorithm with guaranteed recovery. It alternates between low-rank CP decomposition through gradient ascent (a variant of the tensor power method), and hard thresholding of the resid…
Study reveals efficient recovery of multi-modal signals via Bayesian methods and sequential learning.
Efficiently factorizes coupled matrix tensor data for better accuracy and speed.
Graphical notation simplifies tensor operations and decompositions.
This paper introduces matrix product state (MPS) decomposition as a new and systematic method to compress multidimensional data represented by higher-order tensors. It solves two major bottlenecks in tensor compression: computation and compression quality. Regardless of tensor order, MPS compresses tensors to matrices …
New estimator reduces bias and variance in tensor and matrix denoising.
Unified framework for non-negative matrices and tensors using Wasserstein loss.
In this paper, we study robust tensor completion by using transformed tensor singular value decomposition (SVD), which employs unitary transform matrices instead of discrete Fourier transform matrix that is used in the traditional tensor SVD. The main motivation is that a lower tubal rank tensor can be obtained by usin…
Paper proposes an algorithm for PARAFAC2-based CMTF models with various constraints.
We study low rank matrix and tensor completion and propose novel algorithms that employ adaptive sampling schemes to obtain strong performance guarantees. Our algorithms exploit adaptivity to identify entries that are highly informative for learning the column space of the matrix (tensor) and consequently, our results …
Theoretical studies have proven that the Hilbert space has remarkable performance in many fields of applications. Frames in tensor product of Hilbert spaces were introduced to generalize the inner product to high-order tensors. However, these techniques require tensor decomposition which could lead to the loss of infor…
In the low-rank matrix completion (LRMC) problem, the low-rank assumption means that the columns (or rows) of the matrix to be completed are points on a low-dimensional linear algebraic variety. This paper extends this thinking to cases where the columns are points on a low-dimensional nonlinear algebraic variety, a pr…
Paper proposes a new method to improve clustering ensemble performance.
Minimizing the nuclear norm of a matrix has been shown to be very efficient in reconstructing a low-rank sampled matrix. Furthermore, minimizing the sum of nuclear norms of matricizations of a tensor has been shown to be very efficient in recovering a low-Tucker-rank sampled tensor. In this paper, we propose to recover…
Deep tensor factorization benefits from implicit regularization with polynomial growth.
New methods solve tensor-on-tensor regression with unknown rank, revealing benefits of over-parameterization.
Automates supervised learning pipeline design with matrix and tensor factorization.
In this paper, we consider the Tensor Robust Principal Component Analysis (TRPCA) problem, which aims to exactly recover the low-rank and sparse components from their sum. Our model is based on the recently proposed tensor-tensor product (or t-product). Induced by the t-product, we first rigorously deduce the tensor sp…
Study on tensor signal estimation from incomplete data.
We obtain the first polynomial-time algorithm for exact tensor completion that improves over the bound implied by reduction to matrix completion. The algorithm recovers an unknown 3-tensor with incoherent, orthogonal components in from randomly observed entries of the tensor…
Tensor completion estimates missing components by exploiting the low-rank structure of multi-way data. The recently proposed methods based on tensor train (TT) and tensor ring (TR) show better performance in image recovery than classical ones. Compared with TT and TR, the projected entangled pair state (PEPS), which is…
We propose a general algorithmic framework for constrained matrix and tensor factorization, which is widely used in signal processing and machine learning. The new framework is a hybrid between alternating optimization (AO) and the alternating direction method of multipliers (ADMM): each matrix factor is updated in tur…
Introduces nondecreasing rank for matrices and tensors, developing methods and applications.
New method models matrix time series using tensor CP-decomposition.
Paper proposes a tensor model for clustering noisy multi-view data.
A low-rank tensor model simplifies multi-dimensional Markov chains.
Unified model for tensor completion using low-rank and sparse Tucker decomposition.
In many problems of supervised tensor learning (STL), real world data such as face images or MRI scans are naturally represented as matrices, which are also called as second order tensors. Most existing classifiers based on tensor representation, such as support tensor machine (STM) need to solve iteratively which occu…
Paper studies tensor models using random matrix theory.
Paper proposes C-STM for multimodal neuroimaging data classification.
Portfolio allocation and risk management make use of correlation matrices and heavily rely on the choice of a proper correlation matrix to be used. In this regard, one important question is related to the choice of the proper sample period to be used to estimate a stable correlation matrix. This paper addresses this qu…
Recently, fundamental conditions on the sampling patterns have been obtained for finite completability of low-rank matrices or tensors given the corresponding ranks. In this paper, we consider the scenario where the rank is not given and we aim to approximate the unknown rank based on the location of sampled entries an…
AMP algorithm for matrix tensor product model provides recovery conditions.
In many signal processing and machine learning applications, datasets containing private information are held at different locations, requiring the development of distributed privacy-preserving algorithms. Tensor and matrix factorizations are key components of many processing pipelines. In the distributed setting, diff…
We want to construct a homological link invariant whose Euler characteristic is MOY polynomial as Khovanov and Rozansky constructed a categorification of HOMFLY polynomial. The present paper gives the first step to construct a categorification of MOY polynomial. For the essential colored planar diagrams with additional…
A new method for traffic data imputation considering spatiotemporal correlations.
We propose a tensor neural network (-NN) framework that offers an exciting new paradigm for designing neural networks with multidimensional (tensor) data. Our network architecture is based on the -product (Kilmer and Martin, 2011), an algebraic formulation to multiply tensors via circulant convolution. In this $t…
We study the problem of learning a distribution from samples, when the underlying distribution is a mixture of product distributions over discrete domains. This problem is motivated by several practical applications such as crowd-sourcing, recommendation systems, and learning Boolean functions. The existing solutions e…
Proposes a method to recover sparse tensors with covariate info.
The paper studies phase transitions in random matrices and tensor unfolding for detecting signals.
Paper finds formulas for mutual information and MMSE in matrix tensor product problems.
Tensor networks improve unsupervised learning performance.
Paper studies nonnegative Tucker decomposition identifiability with sparsity conditions.