Related papers: Adaptive hp-Polynomial Based Sparse Grid Collocati…

We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…

In this paper we introduce an algorithm based on a sparse grid adaptive refinement, for the approximation of the eigensolutions to parametric problems arising from elliptic partial differential equations. In particular, we are interested in…

High-dimensional sparse data present computational and statistical challenges for supervised learning. We propose compact linear sketches for reducing the dimensionality of the input, followed by a single layer neural network. We show that…

We present and analyze a novel sparse polynomial technique for approximating high-dimensional Hilbert-valued functions, with application to parameterized partial differential equations (PDEs) with deterministic and stochastic inputs. Our…

When uncertainty meets costly information gathering, a fundamental question emerges: which data points should we probe to unlock near-optimal solutions? Sparsification of stochastic packing problems addresses this trade-off. The existing…

Adaptive gradient methods are typically used for training over-parameterized models. To better understand their behaviour, we study a simplistic setting -- smooth, convex losses with models over-parameterized enough to interpolate the data.…

Many applications in machine learning or signal processing involve nonsmooth optimization problems. This nonsmoothness brings a low-dimensional structure to the optimal solutions. In this paper, we propose a randomized proximal gradient…

Forward uncertainty quantification in dynamical systems is challenging due to non-smooth or locally oscillating nonlinear behaviors. Spline dimensional decomposition (SDD) addresses such nonlinearity by partitioning input coordinates via…

Incorporating sparsity priors in learning tasks can give rise to simple, and interpretable models for complex high dimensional data. Sparse models have found widespread use in structure discovery, recovering data from corruptions, and a…

GraphSPME is an open source Python, R and C++ header-only package implement-ing non-parametric sparse precision matrix estimation along with asymptotic Stein-type shrinkage estimation of the covariance matrix. The user defines a potential…

Motivated by extreme multi-label classification applications, we consider training deep learning models over sparse data in multi-GPU servers. The variance in the number of non-zero features across training batches and the intrinsic GPU…

We propose and analyze a variant of Sparse Polyak for high dimensional M-estimation problems. Sparse Polyak proposes a novel adaptive step-size rule tailored to suitably estimate the problem's curvature in the high-dimensional setting,…

We present a novel approach for the construction of basis functions to be employed in selective or adaptive h-refined finite element applications with arbitrary-level hanging node configurations. Our analysis is not restricted to…

We investigate the sparse spikes deconvolution problem onto spaces of algebraic polynomials. Our framework encompasses the measure reconstruction problem from a combination of noiseless and noisy moment measurements. We study a TV-norm…

Stochastic gradient methods are dominant in nonconvex optimization especially for deep models but have low asymptotical convergence due to the fixed smoothness. To address this problem, we propose a simple yet effective method for improving…

Using neural networks to solve variational problems, and other scientific machine learning tasks, has been limited by a lack of consistency and an inability to exactly integrate expressions involving neural network architectures. We address…

Space filling curves are widely used in Computer Science. In particular Hilbert curves and their generalisations to higher dimension are used as an indexing method because of their nice locality properties. This article generalises this…

In the present work we introduce a complete set of algorithms to efficiently perform adaptive refinement and coarsening by exploiting truncated hierarchical B-splines (THB-splines) defined on suitably graded isogeometric meshes, that are…

Estimation techniques to precisely localize a kinematic platform with GNSS observables can be broadly partitioned into two categories: differential, or undifferenced. The differential techniques (e.g., real-time kinematic (RTK)) have…

Sparse polynomial approximation has become indispensable for approximating smooth, high- or infinite-dimensional functions from limited samples. This is a key task in computational science and engineering, e.g., surrogate modelling in…