arXiv research

Bayesian approach approximates probability functions of Gaussian mixtures.

Generalizes randomized SVD for better matrix approximations using Gaussian vectors.

Orthogonal random features approximate a Bessel kernel, offering sharper bounds than random Fourier features.

Bounds on Gaussian approximation for neural networks with novel smoothing techniques.

Gradient span algorithms show consistent progress in high dimensions.

Proves new concentration inequalities for sub-gaussian and sub-exponential variables.

We study random Morse functions on a Riemann manifold $(M^m,g)$ defined as a random Gaussian weighted superpositions of eigenfunctions of the Laplacian of the metric $g$. The randomness is determined by a fixed Schwartz function $w$ and a small parameter $\varepsilon>0$. We first prove that as $\varepsilon\to 0$ the ex…

Paper introduces a nonparametric functional graphical model for random functions.

Sharp comparison for sub-Gaussian random variables in convex order.

Study Gaussian approximation for deep neural networks with random weights.

We introduce a new functional measure of tail dependence for weakly dependent (asymptotically independent) random vectors, termed weak tail dependence function. The new measure is defined at the level of copulas and we compute it for several copula families such as the Gaussian copula, copulas of a class of Gaussian mi…

In this paper we model the loss function of high-dimensional optimization problems by a Gaussian random field, or equivalently a Gaussian process. Our aim is to study gradient descent in such loss functions or energy landscapes and compare it to results obtained from real high-dimensional optimization problems such as …

New method estimates Gaussian vector functions more efficiently.

Study reveals three limiting regimes for neural network functionals.

Paper presents characteristic function of Tsallis q-Gaussian and its applications.

We derive Gaussian approximations for random forest predictions using region-based stabilization.

Random neural networks with ReLU activations are non-Gaussian processes.

Gaussian processes are the leading class of distributions on random functions, but they suffer from well known issues including difficulty scaling and inflexibility with respect to certain shape constraints (such as nonnegativity). Here we propose Deep Random Splines, a flexible class of random functions obtained by tr…

The paper proposes a Gaussian mixture model for Hilbert-space-valued data.

Improved kernel ridge regression for large datasets using weighted random binning.

This paper presents a sequential randomized lowrank matrix factorization approach for incrementally predicting values of an unknown function at test points using the Gaussian Processes framework. It is well-known that in the Gaussian processes framework, the computational bottlenecks are the inversion of the (regulariz…

Standard sparse pseudo-input approximations to the Gaussian process (GP) cannot handle complex functions well. Sparse spectrum alternatives attempt to answer this but are known to over-fit. We suggest the use of variational inference for the sparse spectrum approximation to avoid both issues. We model the covariance fu…

Randomized classifiers have been shown to provide a promising approach for achieving certified robustness against adversarial attacks in deep learning. However, most existing methods only leverage Gaussian smoothing noise and only work for $\ell_2$ perturbation. We propose a general framework of adversarial certificati…

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

The study proves Gaussian universality of deep random features learning.

Study of cosmic microwave background polarization using spin random fields.

The paper connects Riemannian Gaussian distributions to random matrix theory and diffusion kernels.

Extends Gaussian process theory to Banach spaces.

We use matricial free energy to regularize autoencoders, producing Gaussian-like codes.

Deep random feature models are analyzed for their performance with exact asymptotic expressions.

The paper develops a uniform function estimator in RKHS for regression.

Develops a new method for nonlinear dimension reduction using random features.

We consider the signed density of the extremal points of (two-dimensional) scalar fields with a Gaussian distribution. We assign a positive unit charge to the maxima and minima of the function and a negative one to its saddles. At first, we compute the average density for a field in half-space with Dirichlet boundary c…

New bounds for optimal transport using Gaussian processes and rate-distortion functions.

New test detects sparse alternatives in Gaussian random fields.

A $q$-Gaussian measure is a generalization of a Gaussian measure. This generalization is obtained by replacing the exponential function with the power function of exponent $1/(1-q)$ ($q\neq 1$). The limit case $q=1$ recovers a Gaussian measure. For $1\leq q <3$, the set of all $q$-Gaussian densities over the real line …

Study on using random subspaces for ERM with various loss functions.

A new model for stock price fluctuations is proposed, based upon an analogy with the motion of tracers in Gaussian random fields, as used in turbulent dispersion models and in studies of transport in dynamically disordered media. Analytical and numerical results for this model in a special limiting case of a single-sca…

This paper improves GP-UCB by using a shifted exponential distribution for confidence parameters.

Multi-output Gaussian processes (MOGP) are probability distributions over vector-valued functions, and have been previously used for multi-output regression and for multi-class classification. A less explored facet of the multi-output Gaussian process is that it can be used as a generative model for vector-valued rando…

Enhanced Gaussian process models accelerate optimization and posterior approximation.

A new method for LDA using randomized Kaczmarz improves accuracy for large datasets.

Randomly biased data makes complex models as easy to learn as simple ones.

New method for spatiotemporal data regression using Gaussian processes.

Wide neural networks can be closely approximated by Gaussian processes, with rates depending on the activation function's properties.

We introduce a new method to explain Gaussian processes using Shapley values.

The random matrix theory method of planar Gaussian diagrammatic expansion is applied to find the mean spectral density of the Hermitian equal-time and non-Hermitian time-lagged cross-covariance estimators, firstly in the form of master equations for the most general multivariate Gaussian system, secondly for seven part…

We relate the distribution of eigenvalues of a random symmetric matrix in the Gaussian Orthogonal Ensemble to the distribution of critical values of a random linear combination of eigenfunctions of the Laplacian on a compact Riemann manifold. We then prove a central limit theorem describing what happens when the dimens…