Related papers: Black-Box Approximation and Optimization with Hier…
Big data analysis has become a crucial part of new emerging technologies such as the internet of things, cyber-physical analysis, deep learning, anomaly detection, etc. Among many other techniques, dimensionality reduction plays a key role…
In recent years, low-rank tensor completion (LRTC) has received considerable attention due to its applications in image/video inpainting, hyperspectral data recovery, etc. With different notions of tensor rank (e.g., CP, Tucker, tensor…
Single-objective black box optimization (also known as zeroth-order optimization) is the process of minimizing a scalar objective $f(x)$, given evaluations at adaptively chosen inputs $x$. In this paper, we consider multi-objective…
This paper is devoted to the study (common in many applications) of the black-box optimization problem, where the black-box represents a gradient-free oracle $\tilde{f} = f(x) + \xi$ providing the objective function value with some…
We propose a new cross-conv algorithm for approximate computation of convolution in different low-rank tensor formats (tensor train, Tucker, Hierarchical Tucker). It has better complexity with respect to the tensor rank than previous…
Low-rank tensor approximation techniques attempt to mitigate the overwhelming complexity of linear algebra tasks arising from high-dimensional applications. In this work, we study the low-rank approximability of solutions to linear systems…
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…
Black box variational inference allows researchers to easily prototype and evaluate an array of models. Recent advances allow such algorithms to scale to high dimensions. However, a central question remains: How to specify an expressive…
Multi-dimensional data completion is a critical problem in computational sciences, particularly in domains such as computer vision, signal processing, and scientific computing. Existing methods typically leverage either global low-rank…
Learning decompositions of expensive-to-evaluate black-box functions promises to scale Bayesian optimisation (BO) to high-dimensional problems. However, the success of these techniques depends on finding proper decompositions that…
Black-box alpha (BB-$\alpha$) is a new approximate inference method based on the minimization of $\alpha$-divergences. BB-$\alpha$ scales to large datasets because it can be implemented using stochastic gradient descent. BB-$\alpha$ can be…
Machine learning and data mining algorithms are becoming increasingly important in analyzing large volume, multi-relational and multi--modal datasets, which are often conveniently represented as multiway arrays or tensors. It is therefore…
Low-rank tensor approximation approaches have become an important tool in the scientific computing community. The aim is to enable the simulation and analysis of high-dimensional problems which cannot be solved using conventional methods…
We propose a novel approach for hyperspectral super-resolution, that is based on low-rank tensor approximation for a coupled low-rank multilinear (Tucker) model. We show that the correct recovery holds for a wide range of multilinear ranks.…
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…
New algorithms are proposed for the Tucker approximation of a 3-tensor, that access it using only the tensor-by-vector-by-vector multiplication subroutine. In the matrix case, Krylov methods are methods of choice to approximate the dominant…
In statistics, it is common to encounter multi-modal and non-smooth likelihood (or objective function) maximization problems, where the parameters have known upper and lower bounds. This paper proposes a novel derivative-free global…
Black-box problems are common in real life like structural design, drug experiments, and machine learning. When optimizing black-box systems, decision-makers always consider multiple performances and give the final decision by comprehensive…
We study tensor completion (TC) through the lens of low-rank tensor decomposition (TD). Many TD algorithms use fast alternating minimization methods to solve highly structured linear regression problems at each step (e.g., for CP, Tucker,…
A gradient-enhanced functional tensor train cross approximation method for the resolution of the Hamilton-Jacobi-Bellman (HJB) equations associated to optimal feedback control of nonlinear dynamics is presented. The procedure uses samples…