Related papers: Tensor Methods for Generating Compact Uncertainty …
Tensor networks developed in the context of condensed matter physics try to approximate order-$N$ tensors with a reduced number of degrees of freedom that is only polynomial in $N$ and arranged as a network of partially contracted smaller…
Random Fourier features provide a way to tackle large-scale machine learning problems with kernel methods. Their slow Monte Carlo convergence rate has motivated the research of deterministic Fourier features whose approximation error can…
The advancement of sensing technology has driven the widespread application of high-dimensional data. However, issues such as missing entries during acquisition and transmission negatively impact the accuracy of subsequent tasks. Tensor…
Density based representations of atomic environments that are invariant under Euclidean symmetries have become a widely used tool in the machine learning of interatomic potentials, broader data-driven atomistic modelling and the…
Dynamic mode decomposition (DMD) has become a powerful data-driven method for analyzing the spatiotemporal dynamics of complex, high-dimensional systems. However, conventional DMD methods are limited to matrix-based formulations, which…
Option pricing is a significant problem for option risk management and trading. In this article, we utilize a framework to present financial data from different sources. The data is processed and represented in a form of 2D tensors in three…
For minimization problems without 2nd derivative information, methods that estimate Hessian matrices can be very effective. However, conventional techniques generate dense matrices that are prohibitive for large problems. Limited-memory…
Tensor-valued data benefits greatly from dimension reduction as the reduction in size is exponential in the number of modes. To achieve maximal reduction without loss in information, our objective in this work is to give an automated…
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…
Machine learning is a promising application of quantum computing, but challenges remain as near-term devices will have a limited number of physical qubits and high error rates. Motivated by the usefulness of tensor networks for machine…
What learning algorithms can be run directly on compressively-sensed data? In this work, we consider the question of accurately and efficiently computing low-rank matrix or tensor factorizations given data compressed via random projections.…
Tensor networks are a popular and computationally efficient approach to simulate general quantum systems on classical computers and, in a broader sense, a framework for dealing with high-dimensional numerical problems. This paper presents a…
Deep Learning is a consolidated, state-of-the-art Machine Learning tool to fit a function when provided with large data sets of examples. However, in regression tasks, the straightforward application of Deep Learning models provides a point…
The widespread use of multi-sensor technology and the emergence of big datasets has highlighted the limitations of standard flat-view matrix models and the necessity to move towards more versatile data analysis tools. We show that…
Fabrication process variations are a major source of yield degradation in the nano-scale design of integrated circuits (IC), microelectromechanical systems (MEMS) and photonic circuits. Stochastic spectral methods are a promising technique…
Tensor network methods have been a key ingredient of advances in condensed matter physics and have recently sparked interest in the machine learning community for their ability to compactly represent very high-dimensional objects. Tensor…
Tensors play a pivotal role in the realms of science and engineering, particularly in the realms of data analysis, machine learning, and computational mathematics. The process of unfolding a tensor into matrices, commonly known as tensor…
Deep neural networks have seen enormous success in various real-world applications. Beyond their predictions as point estimates, increasing attention has been focused on quantifying the uncertainty of their predictions. In this review, we…
The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…
When the cost of misclassifying a sample is high, it is useful to have an accurate estimate of uncertainty in the prediction for that sample. There are also multiple types of uncertainty which are best estimated in different ways, for…