arXiv research

New iterative methods improve Vecchia-Laplace approximations for large data sets.

This thesis disentangles Gauss-Newton and variational approximations in Bayesian deep learning.

The paper develops new methods to approximate ruin probabilities in a perturbed risk model.

Boosting Nyström improves accuracy of matrix approximations.

We accelerate the power method for strong low-rank approximation using fast sketching.

Nyström KPCA balances computational efficiency and statistical accuracy.

Paper develops a new kernel approximation framework.

New RFs reduce kernel approximation variance and improve Transformer performance.

New method tackles convergence issues in approximating FBSDEs.

New method improves credit risk estimation and pricing.

Method approximates Riemannian barycenter on manifolds.

Deviation inequalities for stochastic approximation methods.

Abundant literature has been published on approximation methods for the forward initial margin. The most popular ones being the family of regression methods. This paper describes the mathematical foundations on which these regression approximation methods lie. We introduce mathematical rigor to show that in essence, al…

Recently, variational approximations such as the mean field approximation have received much interest. We extend the standard mean field method by using an approximating distribution that factorises into cluster potentials. This includes undirected graphs, directed acyclic graphs and junction trees. We derive generaliz…

This paper introduces a spline-based method for nonparametric ADVI that handles complex posterior distributions.

The paper approximates supply curves using a one-step basis method.

Policy gradient methods with aggregated states can achieve better performance than approximate policy iteration.

Develops consistent approximations for composite optimization problems.

Proposes a new method for optimizing large-scale models using Nyström approximation of the Hessian.

Paper approximates fractional harmonic maps with numerical methods.

Variational methods are widely used for approximate posterior inference. However, their use is typically limited to families of distributions that enjoy particular conjugacy properties. To circumvent this limitation, we propose a family of variational approximations inspired by nonparametric kernel density estimation. …

A new method for optimizing deep neural networks using TKFAC.

Resampling techniques are widely used in statistical inference and ensemble learning, in which estimators' statistical properties are essential. However, existing methods are computationally demanding, because repetitions of estimation/learning via numerical optimization/integral for each resampled data are required. I…

Proposes efficient Gaussian approximations for non-Gaussian likelihoods.

Paper improves kernel approximations for better statistical learning.

We investigate how to train kernel approximation methods that generalize well under a memory budget. Building on recent theoretical work, we define a measure of kernel approximation error which we find to be more predictive of the empirical generalization performance of kernel approximation methods than conventional me…

Collaborative filtering (CF) is a popular technique in today's recommender systems, and matrix approximation-based CF methods have achieved great success in both rating prediction and top-N recommendation tasks. However, real-world user-item rating matrices are typically sparse, incomplete and noisy, which introduce ch…

Clarifies connections between Nyström and SVGP methods for scalable GPs.

In this paper we derive an easily computed approximation to European basket call prices for a local volatility jump-diffusion model. We apply the asymptotic expansion method to find the approximate value of the lower bound of European basket call prices. If the local volatility function is time independent then there i…

We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data. In particular, we write the joint density approximately as a product of an approximate posterior dens…

We propose a general algorithm for approximating nonstandard Bayesian posterior distributions. The algorithm minimizes the Kullback-Leibler divergence of an approximating distribution to the intractable posterior distribution. Our method can be used to approximate any posterior distribution, provided that it is given i…

Bandit methods for black-box optimisation, such as Bayesian optimisation, are used in a variety of applications including hyper-parameter tuning and experiment design. Recently, \emph{multi-fidelity} methods have garnered considerable attention since function evaluations have become increasingly expensive in such appli…

Posterior refinement improves sample efficiency in Bayesian neural networks.

We are concerned with an approximation problem for a symmetric positive semidefinite matrix due to motivation from a class of nonlinear machine learning methods. We discuss an approximation approach that we call {matrix ridge approximation}. In particular, we define the matrix ridge approximation as an incomplete matri…

In this paper, we propose a low-rank approximation method based on discrete least-squares for the approximation of a multivariate function from random, noisy-free observations. Sparsity inducing regularization techniques are used within classical algorithms for low-rank approximation in order to exploit the possible sp…

Good sparse approximations are essential for practical inference in Gaussian Processes as the computational cost of exact methods is prohibitive for large datasets. The Fully Independent Training Conditional (FITC) and the Variational Free Energy (VFE) approximations are two recent popular methods. Despite superficial …

A new method improves ICA performance by approximating MDI.

Paper applies ANOVA decomposition for interpretable data approximation.

We consider variants of trust-region and cubic regularization methods for non-convex optimization, in which the Hessian matrix is approximated. Under mild conditions on the inexact Hessian, and using approximate solution of the corresponding sub-problems, we provide iteration complexity to achieve $ε$-approximate seco…

Efficiently selects predictors in sparse regression without approximations.

Efficiently reduces tensor ranks using mean-field approximation.

We propose a black-box variational inference method to approximate intractable distributions with an increasingly rich approximating class. Our method, termed variational boosting, iteratively refines an existing variational approximation by solving a sequence of optimization problems, allowing the practitioner to trad…

We propose a new analytical approximation to the $χ^2$ kernel that converges geometrically. The analytical approximation is derived with elementary methods and adapts to the input distribution for optimal convergence rate. Experiments show the new approximation leads to improved performance in image classification and …

In this paper we study recent developments in the approximation of the spread option pricing. As the Kirkś Approximation is extremely flawed in the cases when the correlation is very high, we explore a recent development that allows approximating with simplicity and accuracy the option price. To assess the goodness of …

Gaussian and bootstrap methods improve ATE estimator accuracy.

New iterative methods improve scalability of Gaussian process approximations for large data.

Natural-gradient methods enable fast and simple algorithms for variational inference, but due to computational difficulties, their use is mostly limited to \emph{minimal} exponential-family (EF) approximations. In this paper, we extend their application to estimate \emph{structured} approximations such as mixtures of E…

New method reduces variance and bias in approximating indefinite kernels.