Related papers: Randomized pick-freeze for sparse Sobol indices es…
The global sensitivity analysis of a complex numerical model often calls for the estimation of variance-based importance measures, named Sobol' indices. Metamodel-based techniques have been developed in order to replace the cpu…
In this paper, we develop an approach for the exact determination of the minimum sample size for estimating the parameter of an integer-valued random variable, which is parameterized by its expectation. Under some continuity and unimodal…
Global sensitivity analysis aims at quantifying respective effects of input random variables (or combinations thereof) onto variance of a physical or mathematical model response. Among the abundant literature on sensitivity measures, Sobol'…
We propose the Sobolev Independence Criterion (SIC), an interpretable dependency measure between a high dimensional random variable X and a response variable Y . SIC decomposes to the sum of feature importance scores and hence can be used…
Global sensitivity analysis (GSA) quantifies the influence of uncertain variables in a mathematical model. The Sobol' indices, a commonly used tool in GSA, seek to do this by attributing to each variable its relative contribution to the…
As its name suggests, sufficient dimension reduction (SDR) targets to estimate a subspace from data that contains all information sufficient to explain a dependent variable. Ample approaches exist to SDR, some of the most recent of which…
We introduce an index for measuring the influence of the k-th smallest variable on a pseudo-Boolean function. This index is defined from a weighted least squares approximation of the function by linear combinations of order statistic…
In high-dimensions, many variable selection methods, such as the lasso, are often limited by excessive variability and rank deficiency of the sample covariance matrix. Covariance sparsity is a natural phenomenon in high-dimensional…
We study the $\ell_p$ regression problem, which requires finding $\mathbf{x}\in\mathbb R^{d}$ that minimizes $\|\mathbf{A}\mathbf{x}-\mathbf{b}\|_p$ for a matrix $\mathbf{A}\in\mathbb R^{n \times d}$ and response vector…
The observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise…
Asymptotic lower bounds for estimation play a fundamental role in assessing the quality of statistical procedures. In this paper we propose a framework for obtaining semi-parametric efficiency bounds for sparse high-dimensional models,…
This article is about estimation and inference methods for high dimensional sparse (HDS) regression models in econometrics. High dimensional sparse models arise in situations where many regressors (or series terms) are available and the…
This paper studies nonparametric series estimation and inference for the effect of a single variable of interest x on an outcome y in the presence of potentially high-dimensional conditioning variables z. The context is an additively…
Computing the variance of a conditional expectation has often been of importance in uncertainty quantification. Sun et al. has introduced an unbiased nested Monte Carlo estimator, which they call $1\frac{1}{2}$-level simulation since the…
Many conventional statistical procedures are extremely sensitive to seemingly minor deviations from modeling assumptions. This problem is exacerbated in modern high-dimensional settings, where the problem dimension can grow with and…
For factor model, the involved covariance matrix often has no row sparse structure because the common factors may lead some variables to strongly associate with many others. Under the ultra-high dimensional paradigm, this feature causes…
In genetic studies, not only can the number of predictors obtained from microarray measurements be extremely large, there can also be multiple response variables. Motivated by such a situation, we consider semiparametric dimension reduction…
Covariance function estimation is a fundamental task in multivariate functional data analysis and arises in many applications. In this paper, we consider estimating sparse covariance functions for high-dimensional functional data, where the…
We consider the problem of variable selection in high-dimensional sparse additive models. We focus on the case that the components belong to nonparametric classes of functions. The proposed method is motivated by geometric considerations in…
In this paper a sublinear time algorithm is presented for the reconstruction of functions that can be represented by just few out of a potentially large candidate set of Fourier basis functions in high spatial dimensions, a so-called…