Related papers: An algorithm for online tensor prediction
We introduce a new, quadratically convergent algorithm for finding maximum absolute value entries of tensors represented in the canonical format. The computational complexity of the algorithm is linear in the dimension of the tensor. We…
We incorporate future information in the form of the estimated value of future gradients in online convex optimization. This is motivated by demand response in power systems, where forecasts about the current round, e.g., the weather or the…
A numerical algorithm to decompose an exact low-rank skew-symmetric tensor into a sum of elementary (rank-$1$) skew-symmetric tensors is introduced. The algorithm uncovers this Grassmann decomposition based on linear relations that are…
In this study, we present a tensor--train framework for nonintrusive operator inference aimed at learning discrete operators and using them to predict solutions of physical governing equations. Our framework comprises three approaches:…
Tensor classification has become increasingly crucial in statistics and machine learning, with applications spanning neuroimaging, computer vision, and recommendation systems. However, the high dimensionality of tensors presents significant…
Recently, there has been a growing interest in efficient numerical algorithms based on tensor networks and low-rank techniques to approximate high-dimensional functions and solutions to high-dimensional PDEs. In this paper, we propose a new…
Assume that f is a strict convex function with a unique minimum in R^n. We divide the vector of n-variables to d groups of vector subvariables with d at least two. We assume that we can find the partial minimum of f with respect to each…
In this paper, we propose new learning algorithms for approximating high-dimensional functions using tree tensor networks in a least-squares setting. Given a dimension tree or architecture of the tensor network, we provide an algorithm that…
The use of network Newton methods for the decentralized optimization of a sum cost distributed through agents of a network is considered. Network Newton methods reinterpret distributed gradient descent as a penalty method, observe that the…
This article introduces a novel approach to the mathematical development of Ordinary Least Squares and Neural Network regression models, diverging from traditional methods in current Machine Learning literature. By leveraging Tensor…
We develop the first fast spectral algorithm to decompose a random third-order tensor over $\mathbb{R}^d$ of rank up to $O(d^{3/2}/\text{polylog}(d))$. Our algorithm only involves simple linear algebra operations and can recover all…
We propose a novel online learning paradigm for nonlinear-function estimation tasks based on the iterative projections in the L2 space with probability measure reflecting the stochastic property of input signals. The proposed learning…
Tensor train decomposition is widely used in machine learning and quantum physics due to its concise representation of high-dimensional tensors, overcoming the curse of dimensionality. Cross approximation-originally developed for…
This paper is concerned with the approximation of tensors using tree-based tensor formats, which are tensor networks whose graphs are dimension partition trees. We consider Hilbert tensor spaces of multivariate functions defined on a…
The tensor train (TT) format enjoys appealing advantages in handling structural high-order tensors. The recent decade has witnessed the wide applications of TT-format tensors from diverse disciplines, among which tensor completion has drawn…
In the tensor completion problem, one seeks to estimate a low-rank tensor based on a random sample of revealed entries. In terms of the required sample size, earlier work revealed a large gap between estimation with unbounded computational…
This work considers the problem of estimating the parameters of negative mixture models, i.e. mixture models that possibly involve negative weights. The contributions of this paper are as follows. (i) We show that every rational probability…
Dimensionality reduction for high-order tensors is a challenging problem. In conventional approaches, higher order tensors are `vectorized` via Tucker decomposition to obtain lower order tensors. This will destroy the inherent high-order…
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…
This paper presents new projection-free algorithms for Online Convex Optimization (OCO) over a convex domain $\mathcal{K} \subset \mathbb{R}^d$. Classical OCO algorithms (such as Online Gradient Descent) typically need to perform Euclidean…