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We introduce a computationally efficient method for the automation of inverse design in science and engineering. Based on simple least-square regression, the underlying dynamic mode decomposition algorithm can be used to construct a…

Adaptive intelligence aims at empowering machine learning techniques with the additional use of domain knowledge. In this work, we present the application of adaptive intelligence to accelerate MR acquisition. Starting from undersampled…

In this paper we propose an enhanced version of the residual sub-sampling method (RSM) in [9] for adaptive interpolation by radial basis functions (RBFs). More precisely, we introduce in the context of sub-sampling methods a maximum profile…

We analyze the parallel performance of randomized interpolative decomposition by decomposing low rank complex-valued Gaussian random matrices up to 64 GB. We chose a Cray XMT supercomputer as it provides an almost ideal PRAM model…

Robust PCA is a widely used statistical procedure to recover a underlying low-rank matrix with grossly corrupted observations. This work considers the problem of robust PCA as a nonconvex optimization problem on the manifold of low-rank…

Deep learning for recommendation data is one of the most pervasive and challenging AI workload in recent times. State-of-the-art recommendation models are one of the largest models matching the likes of GPT-3 and Switch Transformer.…

Kernel method has been developed as one of the standard approaches for nonlinear learning, which however, does not scale to large data set due to its quadratic complexity in the number of samples. A number of kernel approximation methods…

We consider the informative path planning ($\mathtt{IPP}$) problem in which a robot interacts with an uncertain environment and gathers information by visiting locations. The goal is to minimize its expected travel cost to cover a given…

Spectral clustering is one of the most effective clustering approaches that capture hidden cluster structures in the data. However, it does not scale well to large-scale problems due to its quadratic complexity in constructing similarity…

The irregular strip-packing problem consists of the computation of a non-overlapping placement of a set of polygons onto a rectangular strip of fixed width and the minimal length possible. Recent performance gains of the Mixed-Integer…

Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…

This paper considers the robust phase retrieval, which can be cast as a nonsmooth and nonconvex composite optimization problem. We propose two first-order algorithms with adaptive step sizes: the subgradient algorithm (AdaSubGrad) and the…

This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). Searching this approximation in a data-driven approach is formalised as attempting to solve a low-rank…

To enable DNNs on edge devices like mobile phones, low-rank approximation has been widely adopted because of its solid theoretical rationale and efficient implementations. Several previous works attempted to directly approximate a…

Randomized algorithms for low-rank matrix approximation are investigated, with the emphasis on the fixed-precision problem and computational efficiency for handling large matrices. The algorithms are based on the so-called QB factorization,…

In this paper, we consider the problem of Robust Matrix Completion (RMC) where the goal is to recover a low-rank matrix by observing a small number of its entries out of which a few can be arbitrarily corrupted. We propose a simple…

Randomization has emerged as a powerful set of tools for large-scale matrix and tensor decompositions. Randomized algorithms involve computing sketches with random matrices. A prevalent approach is to take the random matrix as a standard…

Generative retrieval (GR) has emerged as a promising paradigm in recommendation systems by autoregressively decoding identifiers of target items. Despite its potential, current approaches typically rely on the next-token prediction schema,…

This paper is concerned with the problem of low rank plus sparse matrix decomposition for big data. Conventional algorithms for matrix decomposition use the entire data to extract the low-rank and sparse components, and are based on…

Robust matrix completion (RMC) is a widely used machine learning tool that simultaneously tackles two critical issues in low-rank data analysis: missing data entries and extreme outliers. This paper proposes a novel scalable and learnable…