Related papers: Optimization Landscape of Tucker Decomposition

This paper tackles the problem of recovering a low-rank signal tensor with possibly correlated components from a random noisy tensor, or so-called spiked tensor model. When the underlying components are orthogonal, they can be recovered…

Optimization of non-convex loss surfaces containing many local minima remains a critical problem in a variety of domains, including operations research, informatics, and material design. Yet, current techniques either require extremely high…

Tensor networks provide a powerful framework for compressing multi-dimensional data. The optimal tensor network structure for a given data tensor depends on both data characteristics and specific optimality criteria, making tensor network…

The traditional way of tackling discrete optimization problems is by using local search on suitably defined cost or fitness landscapes. Such approaches are however limited by the slowing down that occurs when the local minima that are a…

Identifying locally optimal solutions is an important issue given an optimization model. In this paper, we focus on a special class of symmetric tensors termed regular simplex tensors, which is a newly-emerging concept, and investigate its…

The TREX is a recently introduced method for performing sparse high-dimensional regression. Despite its statistical promise as an alternative to the lasso, square-root lasso, and scaled lasso, the TREX is computationally challenging in that…

We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…

In many high-dimensional estimation problems the main task consists in minimizing a cost function, which is often strongly non-convex when scanned in the space of parameters to be estimated. A standard solution to flatten the corresponding…

Reducing parameter redundancies in neural network architectures is crucial for achieving feasible computational and memory requirements during training and inference phases. Given its easy implementation and flexibility, one promising…

Tensor decomposition is a powerful computational tool for multiway data analysis. Many popular tensor decomposition approaches---such as the Tucker decomposition and CANDECOMP/PARAFAC (CP)---amount to multi-linear factorization. They are…

Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with…

In all but the most trivial optimization problems, the structure of the solutions exhibit complex interdependencies between the input parameters. Decades of research with stochastic search techniques has shown the benefit of explicitly…

Nonparametric extension of tensor regression is proposed. Nonlinearity in a high-dimensional tensor space is broken into simple local functions by incorporating low-rank tensor decomposition. Compared to naive nonparametric approaches, our…

We propose a novel rank-adaptive higher-order orthogonal iteration (HOOI) algorithm to compute the truncated Tucker decomposition of higher-order tensors with a given error tolerance, and prove that the method is locally optimal and…

Tensor clustering has become an important topic, specifically in spatio-temporal modeling, due to its ability to cluster spatial modes (e.g., stations or road segments) and temporal modes (e.g., time of the day or day of the week). Our…

Nearest-neighbor search in large vector databases is crucial for various machine learning applications. This paper introduces a novel method using tensor-train (TT) low-rank tensor decomposition to efficiently represent point clouds and…

Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. These methods exploit the tensor structure of function spaces and apply…

We address the computational barrier of deploying advanced deep learning segmentation models in clinical settings by studying the efficacy of network compression through tensor decomposition. We propose a post-training Tucker factorization…

Low-rank Tucker and CP tensor decompositions are powerful tools in data analytics. The widely used alternating least squares (ALS) method, which solves a sequence of over-determined least squares subproblems, is costly for large and sparse…

Distributed optimization utilizes local computation and communication to realize a global aim of optimizing the sum of local objective functions. This article addresses a class of constrained distributed nonconvex optimization problems…