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In this paper, we consider the nonparametric least square regression in a Reproducing Kernel Hilbert Space (RKHS). We propose a new randomized algorithm that has optimal generalization error bounds with respect to the square loss, closing a…

We propose a novel explicit dense 3D reconstruction approach that processes a set of images of a scene with sensor poses and calibrations and estimates a photo-real digital model. One of the key innovations is that the underlying volumetric…

We propose to learn deep undirected graphical models (i.e., MRFs) with a non-ELBO objective for which we can calculate exact gradients. In particular, we optimize a saddle-point objective deriving from the Bethe free energy approximation to…

We propose a data-driven approach to quantify the uncertainty of models constructed by kernel methods. Our approach minimizes the needed distributional assumptions, hence, instead of working with, for example, Gaussian processes or…

We introduce a numerical method for reconstructing a multidimensional surface using the gradient of the surface measured at some values of the coordinates. The method consists of defining a multidimensional spline function and minimizing…

Fitting statistical models to spatiotemporal data requires finding the right balance between imposing smoothness and following the data. In the context of p-splines, we propose a Bayesian framework for choosing the smoothing parameter which…

Fast, autonomous flight in unstructured, cluttered environments such as forests is challenging because it requires the robot to compute new plans in realtime on a computationally-constrained platform. In this paper, we enable this…

Synthesizing information from multiple data sources is crucial for constructing accurate individualized treatment rules (ITRs). However, privacy concerns often present significant barriers to the integrative analysis of such multi-source…

A new projection method based on radial basis functions (RBFs) is presented for discretizing the incompressible unsteady Stokes equations in irregular geometries. The novelty of the method comes from the application of a new technique for…

Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…

We propose and analyze a novel framework for learning sparse representations, based on two statistical techniques: kernel smoothing and marginal regression. The proposed approach provides a flexible framework for incorporating feature…

This paper is concerned with inverse scattering of plane waves by a locally perturbed infinite plane (which is called a locally rough surface) with the modulus of the total-field data (also called the phaseless near-field data) at a fixed…

We investigate statistical properties for a broad class of modern kernel-based regression (KBR) methods. These kernel methods were developed during the last decade and are inspired by convex risk minimization in infinite-dimensional Hilbert…

Data depth is a statistical function that generalizes order and quantiles to the multivariate setting and beyond, with applications spanning over descriptive and visual statistics, anomaly detection, testing, etc. The celebrated halfspace…

Efficient tools for predicting the drag of rough walls in turbulent flows would have a tremendous impact. However, methods for drag prediction rely on experiments or numerical simulations which are costly and time-consuming. Data-driven…

This paper presents a new methodology, called AFSSEN, to simultaneously select significant predictors and produce smooth estimates in a high-dimensional function-on-scalar linear model with a sub-Gaussian errors. Outcomes are assumed to lie…

Research on differentiable scene representations is consistently moving towards more efficient, real-time models. Recently, this has led to the popularization of splatting methods, which eschew the traditional ray-based rendering of…

This paper presents a machine learning methodology to improve the predictions of traditional RANS turbulence models in channel flows subject to strong variations in their thermophysical properties. The developed formulation contains several…

A physics assisted deep learning framework to perform accurate indoor imaging using phaseless Wi-Fi measurements is proposed. It is able to image objects that are large (compared to wavelength) and have high permittivity values, that…

Diffusion-based remote sensing (RS) generative foundation models are cruial for downstream tasks. However, these models rely on large amounts of globally representative data, which often contain redundancy, noise, and class imbalance,…