相关论文: Optimality of Operator-Like Wavelets for Represent…

Gaussian processes (GPs) offer appealing properties but are costly to train at scale. Sparse variational GP (SVGP) approximations reduce cost yet still rely on Cholesky decompositions of kernel matrices, ill-suited to low-precision,…

Excellent variational approximations to Gaussian process posteriors have been developed which avoid the $\mathcal{O}\left(N^3\right)$ scaling with dataset size $N$. They reduce the computational cost to $\mathcal{O}\left(NM^2\right)$, with…

We construct an algorithm for implementing the discrete wavelet transform by means of matrices in SO_2(R) for orthonormal compactly supported wavelets and matrices in SL_m(R), m > = 2, for compactly supported biorthogonal wavelets. We show…

Solving a Poisson equation is generally reduced to solving a linear system with a coefficient matrix $A$ of entries $a_{ij}$, $i,j=1,2,...,n$, from the discretized Poisson equation. Although the variational quantum algorithms are promising…

Gaussian process is one of the most popular non-parametric Bayesian methodologies for modeling the regression problem. It is completely determined by its mean and covariance functions. And its linear property makes it relatively…

This article develops a novel approach to the representation of singular integral operators of Calder\'on-Zygmund type in terms of continuous model operators, in both the classical and the bi-parametric setting. The representation is…

While the great capability of Transformers significantly boosts prediction accuracy, it could also yield overconfident predictions and require calibrated uncertainty estimation, which can be commonly tackled by Gaussian processes (GPs).…

We introduce Gaussian orthogonal latent factor processes for modeling and predicting large correlated data. To handle the computational challenge, we first decompose the likelihood function of the Gaussian random field with a…

Gaussian processes are distributions over functions that are versatile and mathematically convenient priors in Bayesian modelling. However, their use is often impeded for data with large numbers of observations, $N$, due to the cubic (in…

We introduce a scalable approach to Gaussian process inference that combines spatio-temporal filtering with natural gradient variational inference, resulting in a non-conjugate GP method for multivariate data that scales linearly with…

Gaussian processes are powerful models for probabilistic machine learning, but are limited in application by their $O(N^3)$ inference complexity. We propose a method for deriving parametric families of kernel functions with compact spatial…

Axially symmetric processes on spheres, for which the second-order dependency structure may substantially vary with shifts in latitude, are a prominent alternative to model the spatial uncertainty of natural variables located over large…

In this work we introduce a reduced-rank algorithm for Gaussian process regression. Our numerical scheme converts a Gaussian process on a user-specified interval to its Karhunen-Lo\`eve expansion, the $L^2$-optimal reduced-rank…

Zero-inflated datasets, which have an excess of zero outputs, are commonly encountered in problems such as climate or rare event modelling. Conventional machine learning approaches tend to overestimate the non-zeros leading to poor…

Wavelet decompositions of integral operators have proven their efficiency in reducing computing times for many problems, ranging from the simulation of waves or fluids to the resolution of inverse problems in imaging. Unfortunately,…

Autoencoders are a prominent model in many empirical branches of machine learning and lossy data compression. However, basic theoretical questions remain unanswered even in a shallow two-layer setting. In particular, to what degree does a…

In this work, we propose a sparse transformer architecture that incorporates prior information about the underlying data distribution directly into the transformer structure of the neural network. The design of the model is motivated by a…

Orthogonal wavelet transforms are a cornerstone of modern signal and image denoising because they combine multiscale representation, energy preservation, and perfect reconstruction. In this paper, we show that these advantages can be…

This research includes the study of some positive sampling Kantorovich operators (SK operators) and their convergence properties. A comprehensive analysis of both local and global approximation properties is presented using sampling…

This paper presents Sparse Gradient Descent as a solution for variable selection in convex piecewise linear regression, where the model is given as the maximum of $k$-affine functions $ x \mapsto \max_{j \in [k]} \langle a_j^\star, x…