Related papers: Uncertainty principles and optimally sparse wavele…
In stochastic simulation, input uncertainty refers to the output variability arising from the statistical noise in specifying the input models. This uncertainty can be measured by a variance contribution in the output, which, in the…
In this article, we construct discrete tight frames for $L^2(\mathbb{S}^{d-1})$, $d\geq3$, which consist of localized polynomial wavelets with adjustable degrees of directionality. In contrast to the well studied isotropic case, these…
Inverse problems defined naturally on the sphere are becoming increasingly of interest. In this article we provide a general framework for evaluation of inverse problems on the sphere, with a strong emphasis on flexibility and scalability.…
We establish a general form of explicit, input-dependent, measure-valued warpings for learning nonstationary kernels. While stationary kernels are ubiquitous and simple to use, they struggle to adapt to functions that vary in smoothness…
This paper presents a novel machine-learning framework for reconstructing low-order gust-encounter flow field and lift coefficients from sparse, noisy surface pressure measurements. Our study thoroughly investigates the time-varying…
Uncertainty quantification, once a singular task, has evolved into a spectrum of tasks, including abstained prediction, out-of-distribution detection, and aleatoric uncertainty quantification. The latest goal is disentanglement: the…
The celebrated sparse representation model has led to remarkable results in various signal processing tasks in the last decade. However, despite its initial purpose of serving as a global prior for entire signals, it has been commonly used…
In this article, we investigate the application of wavelet packet transform as a novel spectrum sensing approach. The main attraction for wavelet packets is the tradeoffs they offer in terms of satisfying various performance metrics such as…
Transfer learning aims to improve performance on a target task by leveraging information from related source tasks. We propose a nonparametric regression transfer learning framework that explicitly models heterogeneity in the source-target…
The construction of optimally localized Wannier functions (and Wannier functions in general) for a Chern insulator has been considered to be impossible owing to the fact that the second moment of such functions is generally infinite. In…
As machine learning systems get widely adopted for high-stake decisions, quantifying uncertainty over predictions becomes crucial. While modern neural networks are making remarkable gains in terms of predictive accuracy, characterizing…
Better representation of the uncertainty in a data visualisation is a focus of recent research activity. A problem with the current literature is that there is a lack of clarity about the definition of uncertainty and what it means to…
Image-based environment perception is an important component especially for driver assistance systems or autonomous driving. In this scope, modern neuronal networks are used to identify multiple objects as well as the according position and…
Segmentation plays an important role in many preprocessing stages in image processing. Recently, convex relaxation methods for image multi-labeling were proposed in the literature. Often these models involve the total variation (TV)…
We present two methods for detecting patterns and clusters in high dimensional time-dependent functional data. Our methods are based on wavelet-based similarity measures, since wavelets are well suited for identifying highly discriminant…
We develop a method to estimate the power spectrum of a stochastic process on the sphere from data of limited geographical coverage. Our approach can be interpreted either as estimating the global power spectrum of a stationary process when…
The problem of detecting and quantifying the presence of symmetries in datasets is useful for model selection, generative modeling, and data analysis, amongst others. While existing methods for hard-coding transformations in neural networks…
Prediction deviations of different uncertainties have varying impacts on downstream decision-making. Improving the prediction accuracy of critical uncertainties with significant impacts on decision-making quality yields better optimization…
Many existing approaches for estimating parameters in settings with distributional shifts operate under an invariance assumption. For example, under covariate shift, it is assumed that $p(y|x)$ remains invariant. We refer to such…
Data following an interval structure are increasingly prevalent in many scientific applications. In medicine, clinical events are often monitored between two clinical visits, making the exact time of the event unknown and generating…