Related papers: L2 Boosting on generalized Hoeffding decomposition…
In this paper, we consider a regression model built on dependent variables. This regression modelizes an input output relationship. Under boundedness assumptions on the joint distribution function of the input variables, we show that a…
Sensitivity analysis for the unconfoundedness assumption is crucial in observational studies. For this purpose, the marginal sensitivity model (MSM) gained popularity recently due to its good interpretability and mathematical properties.…
We prove that boosting with the squared error loss, $L_2$Boosting, is consistent for very high-dimensional linear models, where the number of predictor variables is allowed to grow essentially as fast as $O$(exp(sample size)), assuming that…
High dimensional predictive regressions are useful in wide range of applications. However, the theory is mainly developed assuming that the model is stationary with time invariant parameters. This is at odds with the prevalent evidence for…
This paper presents a general iterative bias correction procedure for regression smoothers. This bias reduction schema is shown to correspond operationally to the $L_2$ Boosting algorithm and provides a new statistical interpretation for…
Exponential generalization bounds with near-tight rates have recently been established for uniformly stable learning algorithms. The notion of uniform stability, however, is stringent in the sense that it is invariant to the data-generating…
Boosting is one of the most significant developments in machine learning. This paper studies the rate of convergence of $L_2$Boosting, which is tailored for regression, in a high-dimensional setting. Moreover, we introduce so-called…
We propose a statistical inference framework for the component-wise functional gradient descent algorithm (CFGD) under normality assumption for model errors, also known as $L_2$-Boosting. The CFGD is one of the most versatile tools to…
We propose a robust inferential procedure for assessing uncertainties of parameter estimation in high-dimensional linear models, where the dimension $p$ can grow exponentially fast with the sample size $n$. Our method combines the…
Conventional compressed sensing theory assumes signals have sparse representations in a known, finite dictionary. Nevertheless, in many practical applications such as direction-of-arrival (DOA) estimation and line spectral estimation, the…
We construct a novel estimator for the diffusion coefficient of the limiting homogenized equation, when observing the slow dynamics of a multiscale model, in the case when the slow dynamics are of bounded variation. Previous research…
Performing an additive decomposition of arbitrary functions of random elements is paramount for global sensitivity analysis and, therefore, the interpretation of black-box models. The well-known seminal work of Hoeffding characterized the…
A key objective of decomposition analysis is to identify a factor (the 'mediator') contributing to disparities in an outcome between social groups. In decomposition analysis, a scholarly interest often centers on estimating how much the…
The global sensitivity analysis method, used to quantify the influence of uncertain input variables on the response variability of a numerical model, is applicable to deterministic computer code (for which the same set of input variables…
We develop a new generalized coupling approach to the study of stochastic delay equations with H\"older continuous coefficients, for which analytical PDE-based methods are not available. We prove that such equations possess unique weak…
This paper investigates quantitative estimates in the homogenization of second-order elliptic systems with periodic coefficients that oscillate on multiple separated scales. We establish large-scale interior and boundary Lipschitz estimates…
This paper conducts sensitivity analysis of random constraint and variational systems related to stochastic optimization and variational inequalities. We establish efficient conditions for well-posedness, in the sense of robust Lipschitzian…
High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a…
The functional ANOVA, or Hoeffding decomposition, provides a principled framework for interpretability by decomposing a model prediction into main effects and higher-order interactions. For independent inputs, this classical decomposition…
Consider generalized adapted stochastic integrals with respect to independently scattered random measures with second moments. We use a decoupling technique, known as the "principle of conditioning", to study their stable convergence…