Related papers: SPHERE-JEPA: Spherical Prediction with Homogeneous…
Stochastic gradient descent (SGD) provides a simple and efficient way to solve a broad range of machine learning problems. Here, we focus on distribution regression (DR), involving two stages of sampling: Firstly, we regress from…
We propose a novel approach for pixel classification in hyperspectral images, leveraging on both the spatial and spectral information in the data. The introduced method relies on a recently proposed framework for learning on distributions…
In this work, we revisit the semi-supervised learning (SSL) problem from a new perspective of explicitly reducing empirical distribution mismatch between labeled and unlabeled samples. Benefited from this new perspective, we first propose a…
Most real-world 3D measurements from depth sensors are incomplete, and to address this issue the point cloud completion task aims to predict the complete shapes of objects from partial observations. Previous works often adapt an…
This paper deals with Riemannian optimization on the unit sphere in terms of $p$-norm with general $p > 1$. As a Riemannian submanifold of the Euclidean space, the geometry of the sphere with $p$-norm is investigated, and several geometric…
T-SNE is a well-known approach to embedding high-dimensional data and has been widely used in data visualization. The basic assumption of t-SNE is that the data are non-constrained in the Euclidean space and the local proximity can be…
Graph based semi-supervised learning (GSSL) has intuitive representation and can be improved by exploiting the matrix calculation. However, it has to perform iterative optimization to achieve a preset objective, which usually leads to low…
We present the first iterative spectral algorithm to find near-optimal solutions for a random quadratic objective over the discrete hypercube, resolving a conjecture of Subag [Subag, Communications on Pure and Applied Mathematics, 74(5),…
One of the most popular algorithms for clustering in Euclidean space is the $k$-means algorithm; $k$-means is difficult to analyze mathematically, and few theoretical guarantees are known about it, particularly when the data is {\em…
A PCA-based, machine learning version of the SPH method is proposed. In the present scheme, the smoothing tensor is computed to have their eigenvalues proportional to the covariance's principal components, using a modified octree data…
In supervised learning with distributional inputs in the two-stage sampling setup, relevant to applications like learning-based medical screening or causal learning, the inputs (which are probability distributions) are not accessible in the…
We study the spherical cap packing problem with a probabilistic approach. Such probabilistic considerations result in an asymptotic sharp universal uniform bound on the maximal inner product between any set of unit vectors and a…
We focus on the distribution regression problem: regressing to a real-valued response from a probability distribution. Although there exist a large number of similarity measures between distributions, very little is known about their…
This paper develops a systematic and geometric theory of optimal quantization on the unit sphere $\mathbb S^2$, focusing on finite uniform probability distributions supported on the spherical surface - rather than on lower-dimensional…
Machine learning holds tremendous promise for transforming the fundamental practice of scientific discovery by virtue of its data-driven nature. With the ever-increasing stream of research data collection, it would be appealing to…
The recent emergence of Self-Supervised Learning (SSL) as a fundamental paradigm for learning image representations has, and continues to, demonstrate high empirical success in a variety of tasks. However, most SSL approaches fail to learn…
Gaussian process (GP) regression provides a flexible, nonparametric framework for probabilistic modeling, yet remains computationally demanding in large-scale applications. For one-dimensional data, state space (SS) models achieve…
Machine learning (ML) has shown significant promise in studying complex geophysical dynamical systems, including turbulence and climate processes. Such systems often display sensitive dependence on initial conditions, reflected in positive…
We propose a new Riemannian gradient descent method for computing spherical area-preserving mappings of topological spheres using a Riemannian retraction-based framework with theoretically guaranteed convergence. The objective function is…
Ultrasound (US) imaging poses unique challenges for representation learning due to its inherently noisy acquisition process. The low signal-to-noise ratio and stochastic speckle patterns hinder standard self-supervised learning methods…