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Deep neural networks (DNNs) have enabled impressive breakthroughs in various artificial intelligence (AI) applications recently due to its capability of learning high-level features from big data. However, the current demand of DNNs for…
Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…
CP decomposition (CPD) is prevalent in chemometrics, signal processing, data mining and many more fields. While many algorithms have been proposed to compute the CPD, alternating least squares (ALS) remains one of the most widely used…
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…
Accurate cascaded channel state information is pivotal for extremely large-scale intelligent reflecting surfaces (XL-IRS) in next-generation wireless networks. However, the large XL-IRS aperture induces spherical wavefront propagation due…
Stochastic nested optimization, including stochastic compositional, min-max and bilevel optimization, is gaining popularity in many machine learning applications. While the three problems share the nested structure, existing works often…
High-dimensional sparse data emerge in many critical application domains such as healthcare and cybersecurity. To extract meaningful insights from massive volumes of these multi-dimensional data, scientists employ unsupervised analysis…
The family of temporal difference (TD) methods span a spectrum from computationally frugal linear methods like TD({\lambda}) to data efficient least squares methods. Least square methods make the best use of available data directly…
The low multilinear rank approximation, also known as the truncated Tucker decomposition, has been extensively utilized in many applications that involve higher-order tensors. Popular methods for low multilinear rank approximation usually…
Gradient based optimization methods are the established state-of-the-art paradigm to study strongly entangled quantum systems in two dimensions with Projected Entangled Pair States. However, the key ingredient, the gradient itself, has…
An optimization-based approach for the Tucker tensor approximation of parameter-dependent data tensors and solutions of tensor differential equations with low Tucker rank is presented. The problem of updating the tensor decomposition is…
We show how to develop sampling-based alternating least squares (ALS) algorithms for decomposition of tensors into any tensor network (TN) format. Provided the TN format satisfies certain mild assumptions, resulting algorithms will have…
Nesterov's accelerated gradient (AG) is a popular technique to optimize objective functions comprising two components: a convex loss and a penalty function. While AG methods perform well for convex penalties, such as the LASSO, convergence…
We present an algorithm based on the alternating direction method of multipliers (ADMM) for solving nonlinear matrix decompositions (NMD). Given an input matrix $X \in \mathbb{R}^{m \times n}$ and a factorization rank $r \ll \min(m, n)$,…
We introduce a family of numerical algorithms for the solution of linear system in higher dimensions with the matrix and right hand side given and the solution sought in the tensor train format. The proposed methods are rank--adaptive and…
Low-rank plus diagonal (LRPD) decompositions provide a powerful structural model for large covariance matrices, simultaneously capturing global shared factors and localized corrections that arise in covariance estimation, factor analysis,…
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…
Tensor decomposition has proven to be a strong tool in various 3D image processing tasks such as denoising and super-resolution. In this context, we recently proposed a canonical polyadic decomposition (CPD) based algorithm for single image…
Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…
The storage and computation requirements of Convolutional Neural Networks (CNNs) can be prohibitive for exploiting these models over low-power or embedded devices. This paper reduces the computational complexity of the CNNs by minimizing an…