Related papers: SPHERE-JEPA: Spherical Prediction with Homogeneous…

A major challenge in Semi-Supervised Learning (SSL) is the limited information available about the class distribution in the unlabeled data. In many real-world applications this arises from the prevalence of long-tailed distributions, where…

The existing research on spectral algorithms, applied within a Reproducing Kernel Hilbert Space (RKHS), has primarily focused on general kernel functions, often neglecting the inherent structure of the input feature space. Our paper…

The Stiefel manifold $V_{p,d}$ is the space of all $d \times p$ orthonormal matrices, with the $d-1$ hypersphere and the space of all orthogonal matrices constituting special cases. In modeling data lying on the Stiefel manifold, parametric…

In this paper, we provide $R$-estimators of the location of a rotationally symmetric distribution on the unit sphere of $\R^k$. In order to do so we first prove the local asymptotic normality property of a sequence of rotationally symmetric…

The family of Mat\'ern kernels are often used in spatial statistics, function approximation and Gaussian process methods in machine learning. One reason for their popularity is the presence of a smoothness parameter that controls, for…

This paper addresses the scalability problem of Bayesian deep neural networks. The performance of deep neural networks is undermined by the fact that these algorithms have poorly calibrated measures of uncertainty. This restricts their…

In image segmentation, there is often more than one plausible solution for a given input. In medical imaging, for example, experts will often disagree about the exact location of object boundaries. Estimating this inherent uncertainty and…

Existing self-supervised learning (SSL) methods primarily learn object-invariant representations but often neglect the spatial structure and relationships among object parts. To address this limitation, we introduce Spatial Prediction (SP),…

We present a numerical framework to approximate the $\mu$-domain in the planar Skorokhod embedding problem (PSEP), recently appeared in \cite{gross2019}. Our approach investigates the continuity and convergence properties of the solutions…

Needlets have been recognized as state-of-the-art tools to tackle spherical data, due to their excellent localization properties in both spacial and frequency domains. This paper considers developing kernel methods associated with the…

Diffusion models typically inject isotropic Gaussian noise, disregarding structure in the data. Motivated by the way quantum squeezed states redistribute uncertainty according to the Heisenberg uncertainty principle, we introduce Squeezed…

We initiate a study of the following problem: Given a continuous domain $\Omega$ along with its convex hull $\mathcal{K}$, a point $A \in \mathcal{K}$ and a prior measure $\mu$ on $\Omega$, find the probability density over $\Omega$ whose…

We propose a generic spatiotemporal event forecasting method, which we developed for the National Institute of Justice's (NIJ) Real-Time Crime Forecasting Challenge. Our method is a spatiotemporal forecasting model combining scalable…

Gaussian processes (GPs) stand as crucial tools in machine learning and signal processing, with their effectiveness hinging on kernel design and hyper-parameter optimization. This paper presents a novel GP linear multiple kernel (LMK) and a…

Score-based methods, such as diffusion models and Bayesian inverse problems, are often interpreted as learning the data distribution in the low-noise limit ($\sigma \to 0$). In this work, we propose an alternative perspective: their success…

Remote sensing data has been widely used for various Earth Observation (EO) missions such as land use and cover classification, weather forecasting, agricultural management, and environmental monitoring. Most existing remote sensing…

Probability measures on the sphere form an important class of statistical models and are used, for example, in modeling directional data or shapes. Due to their widespread use, but also as an algorithmic building block, efficient sampling…

We introduce persistence spheres, a novel functional representation of persistence diagrams. Unlike existing embeddings (such as persistence images, landscapes, or kernel methods), persistence spheres provide a bi-continuous mapping: they…

Self-supervised learning (SSL) has recently achieved tremendous empirical advancements in learning image representation. However, our understanding of the principle behind learning such a representation is still limited. This work shows…

We derive concentration inequalities for the supremum norm of the difference between a kernel density estimator (KDE) and its point-wise expectation that hold uniformly over the selection of the bandwidth and under weaker conditions on the…