arXiv research

The study bounds the stability of Gaussian mixtures under small perturbations.

Revisits Gaussian process model with spherical harmonics for scalable deep learning.

Corrected whitening restores orthogonality in high-dimensional spherical Gaussian mixtures.

Existence and uniqueness of spherical helicoidal surfaces in 3-sphere via spherical curves.

Bayesian approach approximates probability functions of Gaussian mixtures.

New method clusters non-spherical Gaussian mixtures with fewer samples and time.

Researchers found multiple spherical Ricci metrics on tori with rotational symmetry.

Proves a special case of the Gaussian kinematic formula using large sphere limits.

A new GP model uses spherical harmonics for faster inference.

Enhances Gaussian processes with spherical features for better scalability and flexibility.

Bayesian framework for sphere regression using Gaussian fields.

This work provides a computationally efficient and statistically consistent moment-based estimator for mixtures of spherical Gaussians. Under the condition that component means are in general position, a simple spectral decomposition technique yields consistent parameter estimates from low-order observable moments, wit…

We consider the problem of clustering data points in high dimensions, i.e. when the number of data points may be much smaller than the number of dimensions. Specifically, we consider a Gaussian mixture model (GMM) with non-spherical Gaussian components, where the clusters are distinguished by only a few relevant dimens…

In the present study we consider the generalized rotational surfaces in Euclidean spaces. Firstly, we consider generalized spherical curves in Euclidean $(n+1)-$space $\mathbb{E}^{n+1}$. Further, we introduce some kind of generalized spherical surfaces in Euclidean spaces $\mathbb{E}^{3}$ and $$ respect…

Minimal Lagrangian diffeomorphisms between spherical surfaces are rigid.

Study free energy in spherical spin glasses, proving universality dichotomy.

New Fourier features improve high-precision approximation in large-scale problems.

New method uses spherical harmonics to simplify learning single-index models.

Polynomial networks converge to Gaussian processes at a rate of O(n^(-1/2)).

Support Vector Data Description (SVDD) is a machine-learning technique used for single class classification and outlier detection. SVDD formulation with kernel function provides a flexible boundary around data. The value of kernel function parameters affects the nature of the data boundary. For example, it is observed …

Third-order PDEs describe spherical and pseudospherical surfaces.

Developed a diffusion model on spherical data, addressing geometric and stochastic challenges.

Study on spherical conical metrics and their reducibility on compact Riemann surfaces.

Study sharp upper bounds for Aharonov-Bohm eigenvalues on surfaces.

Noise in SGD affects overparameterized models, favoring sparse solutions.

Gradient descent on DDPM objective learns Gaussian mixtures efficiently.

Derives TAP approximation for Bayesian linear regression.

Study spherical convex bodies using $L_p$-floating areas and curvature entropy.

Statistical and machine-learning algorithms are frequently applied to high-dimensional data. In many of these applications data is scarce, and often much more costly than computation time. We provide the first sample-efficient polynomial-time estimator for high-dimensional spherical Gaussian mixtures. For mixtures of a…

In this paper we introduce three methods for re-scaling data sets aiming at improving the likelihood of clustering validity indexes to return the true number of spherical Gaussian clusters with additional noise features. Our method obtains feature re-scaling factors taking into account the structure of a given data set…

Non-asymptotic tail bounds for Kostlan-Shub-Smale field on sphere

Method for factor analysis in short panels without assuming sphericity or Gaussianity.

Study on complexity of random polynomials with deterministic spikes, identifying phase transitions.

A new method using spherical harmonics approximates the Sliced-Wasserstein distance.

Unified analysis simplifies Johnson-Lindenstrauss lemma for data reduction.

Algorithm learns means of spherical Gaussian mixtures efficiently in low dimensions.

We study ruled surfaces in R3 which are obtained from dual spher- ical indicatrix curves of dual Frenet vector fields. We find the Gaussian and mean curvatures of the ruled surfaces and give some results of being Wein- garten surface.

In this paper, we study the spherical indicatrices of W-direction curves in three dimensional Euclidean space which were defined by using the unit Darboux vector field W of a Frenet curve, in [11]. We obtain the Frenet apparatus of these spherical indicatrix curves and the characterizations of being general helix and s…

We study singularities of constant positive Gaussian curvature surfaces and determine the way they bifurcate in generic 1-parameter families of such surfaces. We construct the bifurcations explicitly using loop group methods. Constant Gaussian curvature surfaces correspond to harmonic maps, and we examine the relations…

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 stochastically independent uniformly distributed unit vector. When the set of unit vectors …

This article is concerned with Gaussian process quadratures, which are numerical integration methods based on Gaussian process regression methods, and sigma-point methods, which are used in advanced non-linear Kalman filtering and smoothing algorithms. We show that many sigma-point methods can be interpreted as Gaussia…

Statistical models with constrained probability distributions are abundant in machine learning. Some examples include regression models with norm constraints (e.g., Lasso), probit, many copula models, and latent Dirichlet allocation (LDA). Bayesian inference involving probability distributions confined to constrained d…

Improved sample complexity for Gaussian Mixture Models using Pair Correlation Factor.

Tensor decomposition recovers Gaussian mixtures from moments.

In this paper, we study the problem of learning a mixture of Gaussians with streaming data: given a stream of $N$ points in $d$ dimensions generated by an unknown mixture of $k$ spherical Gaussians, the goal is to estimate the model parameters using a single pass over the data stream. We analyze a streaming version of …

Abstract: Generalizes SGMs to infinite-dimensional Hilbertian setting.

New neural network solves Nirenberg problem for curvature on sphere.

Support Vector Data Description (SVDD) provides a useful approach to construct a description of multivariate data for single-class classification and outlier detection with various practical applications. Gaussian kernel used in SVDD formulation allows flexible data description defined by observations designated as sup…