Related papers: Consistency of functional learning methods based o…

Many real-world optimization problems contain parameters that are unknown before deployment time, either due to stochasticity or to lack of information (e.g., demand or travel times in delivery problems). A common strategy in such cases is…

We introduce a neural implicit framework that exploits the differentiable properties of neural networks and the discrete geometry of point-sampled surfaces to approximate them as the level sets of neural implicit functions. To train a…

Due to developments in instruments and computers, functional observations are increasingly popular. However, effective methodologies for flexibly estimating the underlying trends with valid uncertainty quantification for a sequence of…

Smoothing of noisy sample covariances is an important component in functional data analysis. We propose a novel covariance smoothing method based on penalized splines and associated software. The proposed method is a bivariate spline…

Based on the continuous interpretation of deep learning cast as an optimal control problem, this paper investigates the benefits of employing B-spline basis functions to parameterize neural network controls across the layers. Rather than…

Functional data analysis finds widespread application across various fields. While functional data are intrinsically infinite-dimensional, in practice, they are observed only at a finite set of points, typically over a dense grid. As a…

In this paper, a method is proposed to solve the problem of monotone smoothing splines using general linear systems. This problem, also called monotone control theoretic splines, has been solved only when the curve generator is modeled by…

This paper develops a smooth model identification and self-learning strategy for dynamic systems taking into account possible parameter variations and uncertainties. We have tried to solve the problem such that the model follows the changes…

This paper is concerned with the problem of sampling and interpolation involving derivatives in shift-invariant spaces and the error analysis of the derivative sampling expansions for fundamentally large classes of functions. A new type of…

Uncertainty sampling, a popular active learning algorithm, is used to reduce the amount of data required to learn a classifier, but it has been observed in practice to converge to different parameters depending on the initialization and…

Forecast verification plays a crucial role in the development cycle of operational numerical weather prediction models. At the same time, verification remains a challenge as the traditionally used non-spatial forecast quality metrics…

Deep learning-based methods have become the de facto standard for industrial defect detection. However, their data-hungry nature and inherent "black-box" characteristics often lead to performance bottlenecks and limited trustworthiness in…

Statistical shape modeling (SSM) is an enabling quantitative tool to study anatomical shapes in various medical applications. However, directly using 3D images in these applications still has a long way to go. Recent deep learning methods…

In a world where Machine Learning (ML) is increasingly deployed to support decision-making in critical domains, providing decision-makers with explainable, stable, and relevant inputs becomes fundamental. Understanding how machine learning…

In implementations of the functional data methods, the effect of the initial choice of an orthonormal basis has not gained much attention in the past. Typically, several standard bases such as Fourier, wavelets, splines, etc. are considered…

The spatial random-effects model is flexible in modeling spatial covariance functions, and is computationally efficient for spatial prediction via fixed rank kriging. However, the success of this model depends on an appropriate set of basis…

Recently, there has been a growing interest in the problem of learning rich implicit models - those from which we can sample, but can not evaluate their density. These models apply some parametric function, such as a deep network, to a base…

The paradigm of differentiable programming has significantly enhanced the scope of machine learning via the judicious use of gradient-based optimization. However, standard differentiable programming methods (such as autodiff) typically…

In areas such as kernel smoothing and non-parametric regression there is emphasis on smooth interpolation and smooth statistical models. Splines are known to have optimal smoothness properties in one and higher dimensions. It is shown, with…

Many imputation methods are based on statistical models that assume that the variable of interest is a noisy observation of a function of the auxiliary variables or covariates. Misspecification of this model may lead to severe errors in…