Uncertainty quantification for robust variable selection and multiple testing

Optimization-based Quantification of Simulation Input Uncertainty via Empirical Likelihood

We study an optimization-based approach to construct statistically accurate confidence intervals for simulation performance measures under nonparametric input uncertainty. This approach computes confidence bounds from simulation runs driven by probability weights defined on the data, which are obtained from solving optimization problems under suitably posited averaged divergence constraints. We illustrate how this approach offers benefits in computational efficiency and finite-sample performance compared to the bootstrap and the delta method. While resembling robust optimization, we explain th…

Contributed Discussion to Bayesian Solution Uncertainty Quantification for Differential Equations

We begin by introducing the main ideas of the paper under discussion, and we give a brief description of the method proposed. Next, we discuss an alternative approach based on B-spline expansion, and lastly we make some comments on the method's convergence rate.

Optional Pólya trees: posterior rates and uncertainty quantification

We consider statistical inference in the density estimation model using a tree-based Bayesian approach, with Optional Pólya trees as prior distribution. We derive near-optimal convergence rates for corresponding posterior distributions with respect to the supremum norm. For broad classes of Hölder-smooth densities, we show that the method automatically adapts to the unknown Hölder regularity parameter. We consider the question of uncertainty quantification by providing mathematical guarantees for credible sets from the obtained posterior distributions, leading to near-optimal uncertainty quant…

Uncertainty Quantification for nonparametric regression using Empirical Bayesian neural networks

We propose a new, two-step empirical Bayes-type of approach for neural networks. We show in context of the nonparametric regression model that the procedure (up to a logarithmic factor) provides optimal recovery of the underlying functional parameter of interest and provides Bayesian credible sets with frequentist coverage guarantees. The approach requires fitting the neural network only once, hence it is substantially faster than Bootstrapping type approaches. We demonstrate the applicability of our method over synthetic data, observing good estimation properties and reliable uncertainty quan…

Contributed Discussion to Uncertainty Quantification for the Horseshoe by Stéphanie van der Pas, Botond Szabó and Aad van der Vaart

We begin by introducing the main ideas of the paper under discussion. We discuss some interesting issues regarding adaptive component-wise credible intervals. We then briefly touch upon the concepts of self-similarity and excessive bias restriction. This is then followed by some comments on the extensive simulation study carried out in the paper.

Robust oracle estimation and uncertainty quantification for possibly sparse quantiles

A general many quantiles + noise model is studied in the robust formulation (allowing non-normal, non-independent observations), where the identifiability requirement for the noise is formulated in terms of quantiles rather than the traditional zero expectation assumption. We propose a penalization method based on the quantile loss function with appropriately chosen penalty function making inference on possibly sparse high-dimensional quantile vector. We apply a local approach to address the optimality by comparing procedures to the oracle sparsity structure. We establish that the proposed pro…

Optimal recovery and uncertainty quantification for distributed Gaussian process regression

Gaussian Processes (GP) are widely used for probabilistic modeling and inference for nonparametric regression. However, their computational complexity scales cubicly with the sample size rendering them unfeasible for large data sets. To speed up the computations various distributed methods were proposed in the literature. These methods have, however, limited theoretical underpinning. In our work we derive frequentist theoretical guarantees and limitations for a range of distributed methods for general GP priors in context of the nonparametric regression model, both for recovery and uncertainty…

Uncertainty Quantification for Bayesian CART

This work affords new insights into Bayesian CART in the context of structured wavelet shrinkage. The main thrust is to develop a formal inferential framework for Bayesian tree-based regression. We reframe Bayesian CART as a g-type prior which departs from the typical wavelet product priors by harnessing correlation induced by the tree topology. The practically used Bayesian CART priors are shown to attain adaptive near rate-minimax posterior concentration in the supremum norm in regression models. For the fundamental goal of uncertainty quantification, we construct adaptive confidence bands f…

贝叶斯优化的不确定性量化

Uncertainty Quantification for Bayesian Optimization

针对贝叶斯优化输出不确定性量化研究不足的问题，本文提出通过构建目标函数极值的置信域评估不确定性的方法，依托新推导的序贯高斯过程回归一致误差界保证置信水平，为各类采样策略和停止准则提供统一量化框架。

度量空间中的不确定性量化

Uncertainty quantification in metric spaces

本文提出一种与基础模型无关、可扩展且具一致性保证的度量空间回归不确定性量化框架，并通过 global Fréchet 模型在多类临床复杂对象上验证其有效性。

A Probabilistic Oracle Inequality and Quantification of Uncertainty of a modified Discrepancy Principle for Statistical Inverse Problems

In this note we consider spectral cut-off estimators to solve a statistical linear inverse problem under arbitrary white noise. The truncation level is determined with a recently introduced adaptive method based on the classical discrepancy principle. We provide probabilistic oracle inequalities together with quantification of uncertainty for general linear problems. Moreover, we compare the new method to existing ones, namely early stopping sequential discrepancy principle and the balancing principle, both theoretically and numerically.

基于布朗运动先验的稀疏变分高斯过程回归的逐点不确定性量化

Pointwise uncertainty quantification for sparse variational Gaussian process regression with a Brownian motion prior

本文针对采用特征向量诱导变量和重标度布朗运动先验的稀疏变分高斯过程，建立了逐点可信集频率学派覆盖率的理论保证，并精确刻画其渐近行为，揭示该方法何时保守或过度自信。

Optimal Uncertainty Quantification on moment class using canonical moments

We gain robustness on the quantification of a risk measurement by accounting for all sources of uncertainties tainting the inputs of a computer code. We evaluate the maximum quantile over a class of distributions defined only by constraints on their moments. The methodology is based on the theory of canonical moments that appears to be a well-suited framework for practical optimization.