Related papers: Towards new cross-validation-based estimators for …
Scaling analysis, in which one infers scaling exponents and a scaling function in a scaling law from given data, is a powerful tool for determining universal properties of critical phenomena in many fields of science. However, there are…
Causal inference starts with a simple idea: compare groups that differ by treatment, not much else. Traditionally, similar groups are constructed using only observed covariates; however, it remains a long-standing challenge to incorporate…
A method to reconstruct fields, source strengths and physical parameters based on Gaussian process regression is presented for the case where data are known to fulfill a given linear differential equation with localized sources. The…
Gaussian processes are powerful, yet analytically tractable models for supervised learning. A Gaussian process is characterized by a mean function and a covariance function (kernel), which are determined by a model selection criterion. The…
The increased demand for online prediction and the growing availability of large data sets drives the need for computationally efficient models. While exact Gaussian process regression shows various favorable theoretical properties…
Cross-validation is a statistical tool that can be used to improve large covariance matrix estimation. Although its efficiency is observed in practical applications and a convergence result towards the error of the non linear shrinkage is…
Gaussian processes provide probabilistic surrogates for various applications including classification, uncertainty quantification, and optimization. Using a gradient-enhanced covariance matrix can be beneficial since it provides a more…
We study online inference and asymptotic covariance estimation for the stochastic gradient descent (SGD) algorithm. While classical methods (such as plug-in and batch-means estimators) are available, they either require inaccessible…
To determine the optimal set of hyperparameters of a Gaussian process based on a large number of training data, both a linear system and a trace estimation problem must be solved. In this paper, we focus on establishing numerical methods…
Gaussian process regression is used throughout statistics and machine learning for prediction and uncertainty quantification. A Gaussian process is specified by its mean and covariance functions. Many covariance functions, including…
We propose an efficient transfer Bayesian optimization method, which finds the maximum of an expensive-to-evaluate black-box function by using data on related optimization tasks. Our method uses auxiliary information that represents the…
This paper aims at achieving a "good" estimator for the gradient of a function on a high-dimensional space. Often such functions are not sensitive in all coordinates and the gradient of the function is almost sparse. We propose a method for…
Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…
We study nonparametric Bayesian inference for the intensity function of a covariate-driven point process. We extend recent results from the literature, showing that a wide class of Gaussian priors, combined with flexible link functions,…
The order of smoothness chosen in nonparametric estimation problems is critical. This choice balances the tradeoff between model parsimony and data overfitting. The most common approach used in this context is cross-validation. However,…
In this manuscript, we study the problem of scalar-on-distribution regression; that is, instances where subject-specific distributions or densities, or in practice, repeated measures from those distributions, are the covariates related to a…
Gaussian process regression is a popular Bayesian framework for surrogate modeling of expensive data sources. As part of a broader effort in scientific machine learning, many recent works have incorporated physical constraints or other a…
In a variety of problems originating in supervised, unsupervised, and reinforcement learning, the loss function is defined by an expectation over a collection of random variables, which might be part of a probabilistic model or the external…
Recent contributions to kernel smoothing show that the performance of cross-validated bandwidth selectors improve significantly from indirectness. Indirect crossvalidation first estimates the classical cross-validated bandwidth from a more…
It is argued that all model based approaches to the selection of covariates in linear regression have failed. This applies to frequentist approaches based on P-values and to Bayesian approaches although for different reasons. In the first…