Related papers: Tensor Balancing on Statistical Manifold
We consider the problem of solving mixed random linear equations with $k$ components. This is the noiseless setting of mixed linear regression. The goal is to estimate multiple linear models from mixed samples in the case where the labels…
Tensor decompositions, which represent an $N$-order tensor using approximately $N$ factors of much smaller dimensions, can significantly reduce the number of parameters. This is particularly beneficial for high-order tensors, as the number…
We consider supervised learning (regression/classification) problems with tensor-valued input. We derive multi-linear sufficient reductions for the regression or classification problem by modeling the conditional distribution of the…
Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. In a recent paper [arXiv:0907.2994v1] we discussed how to…
We study a statistical model for the tensor principal component analysis problem introduced by Montanari and Richard: Given a order-$3$ tensor $T$ of the form $T = \tau \cdot v_0^{\otimes 3} + A$, where $\tau \geq 0$ is a signal-to-noise…
The Symmetric Tensor Approximation problem (STA) consists of approximating a symmetric tensor or a homogeneous polynomial by a linear combination of symmetric rank-1 tensors or powers of linear forms of low symmetric rank. We present two…
In distributed optimization and distributed numerical linear algebra, we often encounter an inversion bias: if we want to compute a quantity that depends on the inverse of a sum of distributed matrices, then the sum of the inverses does not…
In this paper, we investigate a second-order stochastic algorithm for solving large-scale binary classification problems. We propose to make use of a new hybrid stochastic Newton algorithm that includes two weighted components in the…
Matrix completion, the problem of completing missing entries in a data matrix with low dimensional structure (such as rank), has seen many fruitful approaches and analyses. Tensor completion is the tensor analog, that attempts to impute…
The development of efficient machine learning models for molecular systems representation is becoming crucial in scientific research. We introduce TensorNet, an innovative O(3)-equivariant message-passing neural network architecture that…
Tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems in classical statistical mechanics. While tensor networks can now be seen as becoming standard tools in the…
Modern scientific studies often collect data sets in the forms of tensors, which call for innovative statistical analysis methods. In particular, there is a pressing need for tensor clustering methods to understand the heterogeneity in the…
In this work, we present a globalized stochastic semismooth Newton method for solving stochastic optimization problems involving smooth nonconvex and nonsmooth convex terms in the objective function. We assume that only noisy gradient and…
Tensor regression is an important tool for tensor data analysis, but existing works have not considered the impact of outliers, making them potentially sensitive to such data points. This paper proposes a low tubal rank robust regression…
We give a description of numerical Newton algorithm on a constraint manifold using only the ambient coordinates (usually Euclidean coordinates) and the geometry of the constraint manifold. We apply the numerical Newton algorithm on a sphere…
The goal of tensor completion is to fill in missing entries of a partially known tensor under a low-rank constraint. In this paper, we mainly study low rank third-order tensor completion problems by using Riemannian optimization methods on…
Real eigenpairs of symmetric tensors play an important role in multiple applications. In this paper we propose and analyze a fast iterative Newton-based method to compute real eigenpairs of symmetric tensors. We derive sufficient conditions…
We propose a new numerical algorithm for computing the tensor rank decomposition or canonical polyadic decomposition of higher-order tensors subject to a rank and genericity constraint. Reformulating this computational problem as a system…
In this paper, we propose a novel model to recover a low-rank tensor by simultaneously performing double nuclear norm regularized low-rank matrix factorizations to the all-mode matricizations of the underlying tensor. An block successive…
This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…