arXiv research

Study relates Gaussian curvature signs to cuspidal edge types and geometric invariants.

Study invariant connections on multivariate Gaussian distributions.

New sampling methods improve statistical efficiency for intractable targets.

New approach to quantum knot invariants using perturbed Gaussian generating functions.

This work preserves linear invariants in ensemble filters for non-Gaussian data assimilation.

We study pathwise invariances of centred random fields that can be controlled through the covariance. A result involving composition operators is obtained in second-order settings, and we show that various path properties including additivity boil down to invariances of the covariance kernel. These results are extended…

Study curvature and torsion in Gaussian distribution's dual coordinate system.

This paper studies gradient flows for sampling using various metrics and their affine invariance.

The paper models financial correlation matrices using permutation invariant Gaussian models and predicts market anomalies.

Modified Wasserstein metric for Gaussian distributions, invariant to isometries.

Random Gaussian fields on 4D Riemannian manifolds with conformal invariance.

Study non-asymptotic bounds on correlation in high-dimensional linear systems, revealing invariant subspaces and bottlenecks.

Wavelet scattering spectra model non-Gaussian time-series, proving scale invariance for self-similar processes.

The paper develops GPR models for hyperelastic materials, improving accuracy and rotational invariance.

Scales attention for long contexts in LLMs.

Extracts invariant features to predict Y without confounding by Z, using conditional independence and optimal transport.

Spectral clustering performance depends on eigenvector fluctuations, shown to be Gaussian.

Develops a Gaussian model to compute the Alexander polynomial of knots.

In this paper we consider the Gaussian thermostat ray transform on both closed Riemannian surfaces and compact Riemannian surfaces with boundary. We establish certain results on the injectivity of the thermostat ray transform and the surjectivity of its adjoint.

SGD converges to an invariant distribution with sub-Gaussian or sub-exponential properties.

Generalising well in supervised learning tasks relies on correctly extrapolating the training data to a large region of the input space. One way to achieve this is to constrain the predictions to be invariant to transformations on the input that are known to be irrelevant (e.g. translation). Commonly, this is done thro…

We prove that the default times (or any of their minima) in the dynamic Gaussian copula model of Cr{é}pey, Jeanblanc, and Wu (2013) are invariance times in the sense of Cr{é}pey and Song (2017), with related invariance probability measures different from the pricing measure. This reflects a departure from the immersion…

Develops Gaussian processes on non-Euclidean spaces with symmetries.

Develops Gaussian processes on non-compact Lie groups.

A surface in homogenous space Sol is said to be an invariant surface if it is invariant under some of the two 1-parameter groups of isometries of the ambient space whose fix point sets are totally geodesic surfaces. In this work we study invariant surfaces that satisfy a certain condition on their curvatures. We classi…

New AMP algorithms improve multi-layer signal reconstruction.

Researchers study the conformal geometry of bivariate Gaussian manifolds.

Study on curvature invariants near singularities of wavefronts.

Flat surfaces in Lie groups with constant curvature are flat.

SGD with constant stepsize converges to a non-Gaussian limit near flat minima.

Paper introduces new Gromov-type distances for comparing Gaussian mixture models.

In nonlinear latent variable models or dynamic models, if we consider the latent variables as confounders (common causes), the noise dependencies imply further relations between the observed variables. Such models are then closely related to causal discovery in the presence of nonlinear confounders, which is a challeng…

In this thesis we deal with spectral invariants for polygons and closed orbisurfaces of constant Gaussian curvature. In each case our method is to study the heat kernel and the asymptotic expansion of the heat trace. First, we investigate hyperbolic polygons, i.e. relatively compact domains in the hyperbolic plane with…

The Gaussian kernel is never positive-definite on Riemannian symmetric spaces.

New approach learns image transformations directly for clustering.

We propose a novel Bayesian nonparametric method to learn translation-invariant relationships on non-Euclidean domains. The resulting graph convolutional Gaussian processes can be applied to problems in machine learning for which the input observations are functions with domains on general graphs. The structure of thes…

Study analyzes perturbations in singular subspaces under random noise.

We develop Fourier methods to expand translation-invariant kernels.

New framework uses dynamics to justify Gaussian process for turbulent flows.

Novel knot polynomials from Gaussian calculus show half vanish and determine Jones polynomials.

New method for spatiotemporal data regression using Gaussian processes.

Using one of the key property of copulas that they remain invariant under an arbitrary monotonous change of variable, we investigate the null hypothesis that the dependence between financial assets can be modeled by the Gaussian copula. We find that most pairs of currencies and pairs of major stocks are compatible with…

dynoGP uses deep Gaussian processes for dynamic system identification.

New kernels on symmetric groups enable efficient Gaussian process sampling.

We define cuspidal curvature $κ_c$ (resp. normalized cuspidal curvature $μ_c$) along cuspidal edges (resp. at swallowtail singularity) in Riemannian $3$-manifolds, and show that it gives a coefficient of the divergent term of the mean curvature function. Moreover, we show that the product $κ_Π$ called the product curva…

New theory allows ICA without assuming non-Gaussian sources.

Develops intrinsic Gaussian process regression for manifold-valued data.

Estimating signals with linear recurrence relations under Gaussian noise is nearly as hard as sparse signals.