Related papers: Christoffel Adaptive Sampling for Sparse Random Fe…

The random feature method (RFM) has demonstrated great potential in bridging traditional numerical methods and machine learning techniques for solving partial differential equations (PDEs). It retains the advantages of mesh-free approaches…

In this paper we propose an algorithm for recovering sparse orthogonal polynomials using stochastic collocation. Our approach is motivated by the desire to use generalized polynomial chaos expansions (PCE) to quantify uncertainty in models…

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…

Slow feature analysis (SFA), as a method for learning slowly varying features in classification and signal analysis, has attracted increasing attention in recent years. Recent probabilistic extensions to SFA learn effective representations…

Unlike traditional statistical methods, Conformal Prediction (CP) allows for the determination of valid and accurate confidence levels associated with individual predictions based only on exchangeability of the data. We here introduce a new…

This paper introduces the Asymptotic-Preserving Random Feature Method (APRFM) for the efficient resolution of multiscale radiative transfer equations. The APRFM effectively addresses the challenges posed by stiffness and multiscale…

Covariance function estimation is a fundamental task in multivariate functional data analysis and arises in many applications. In this paper, we consider estimating sparse covariance functions for high-dimensional functional data, where the…

Random feature (RF) method is a powerful kernel approximation technique, but is typically equipped with fixed activation functions, limiting its adaptability across diverse tasks. To overcome this limitation, we introduce the Random Feature…

Sparse support vector machine (SVM) is a popular classification technique that can simultaneously learn a small set of the most interpretable features and identify the support vectors. It has achieved great successes in many real-world…

We consider learning a sparse pairwise Markov Random Field (MRF) with continuous-valued variables from i.i.d samples. We adapt the algorithm of Vuffray et al. (2019) to this setting and provide finite-sample analysis revealing sample…

Continual learning in natural language processing plays a crucial role in adapting to evolving data and preventing catastrophic forgetting. Despite significant progress, existing methods still face challenges, such as inefficient parameter…

In the second part of the series papers, we set out to study the algorithmic efficiency of sparse sensing. Stemmed from co-prime sensing, we propose a generalized framework, termed Diophantine sensing, which utilizes generic Diophantine…

Sampling-based motion planners perform exceptionally well in robotic applications that operate in high-dimensional space. However, most works often constrain the planning workspace rooted at some fixed locations, do not adaptively reason on…

We study distributed optimization algorithms for minimizing the average of \emph{heterogeneous} functions distributed across several machines with a focus on communication efficiency. In such settings, naively using the classical stochastic…

This paper presents an adaptive and intelligent sparse model for digital image sampling and recovery. In the proposed sampler, we adaptively determine the number of required samples for retrieving image based on space-frequency-gradient…

In this work, we propose an adaptive sparse learning algorithm that can be applied to learn the physical processes and obtain a sparse representation of the solution given a large snapshot space. Assume that there is a rich class of…

We study linear function approximation in a finite basis under finite-precision arithmetic. In a highly non-orthogonal basis, certain directions are only weakly represented, so that rounding errors can significantly distort the effectively…

The randomized-feature approach has been successfully employed in large-scale kernel approximation and supervised learning. The distribution from which the random features are drawn impacts the number of features required to efficiently…

Adaptive sampling algorithms are modern and efficient methods that dynamically adjust the sample size throughout the optimization process. However, they may encounter difficulties in risk-averse settings, particularly due to the challenge…

We introduce adaptive sampling methods for stochastic programs with deterministic constraints. First, we propose and analyze a variant of the stochastic projected gradient method where the sample size used to approximate the reduced…