Related papers: On one dimensional weighted Poincare inequalities …
A common goal in comparative effectiveness research is to estimate treatment effects on pre-specified subpopulations of patients. Though widely used in medical research, causal inference methods for such subgroup analysis remain…
The PAWN index is gaining traction among the modelling community as a sensitivity measure. However, the robustness to its design parameters has not yet been scrutinized: the size ($N$) and sampling ($\varepsilon$) of the model output, the…
Stochastic simulators such as Monte-Carlo estimators are widely used in science and engineering to study physical systems through their probabilistic representation. Global sensitivity analysis aims to identify the input parameters which…
This paper addresses sensitivity analysis for dynamic models, linking dependent inputs to observed outputs. The usual method to estimate Sobol indices are based on the independence of input variables. We present a method to overpass this…
We present a class of modified logarithmic Sobolev inequality, interpolating between Poincar\'e and logarithmic Sobolev inequalities, suitable for measures of the type $\exp(-|x|^\al)$ or more complex $\exp(-|x|^\al\log^\beta(2+|x|))$…
Survey weighting allows researchers to account for bias in survey samples, due to unit nonresponse or convenience sampling, using measured demographic covariates. Unfortunately, in practice, it is impossible to know whether the estimated…
We present a framework for derivative-based global sensitivity analysis (GSA) for models with high-dimensional input parameters and functional outputs. We combine ideas from derivative-based GSA, random field representation via…
Causal or unconfounded descriptive comparisons between multiple groups are common in observational studies. Motivated from a racial disparity study in health services research, we propose a unified propensity score weighting framework, the…
The problem of adaptive multivariate function estimation in the single-index regression model with random design and weak assumptions on the noise is investigated. A novel estimation procedure that adapts simultaneously to the unknown index…
We investigate properties of measures in infinite dimensional spaces in terms of Poincar\'e inequalities. A Poincar\'e inequality states that the $L^2$ variance of an admissible function is controlled by the homogeneous $H^1$ norm. In the…
Inverse problems constrained by partial differential equations (PDEs) play a critical role in model development and calibration. In many applications, there are multiple uncertain parameters in a model that must be estimated. However, high…
We propose a new statistical estimation framework for a large family of global sensitivity analysis methods. Our approach is based on rank statistics and uses an empirical correlation coefficient recently introduced by Sourav Chatterjee. We…
We propose a method to outer bound forward reachable sets on finite horizons for uncertain nonlinear systems with polynomial dynamics. This method makes use of time-dependent polynomial storage functions that satisfy appropriate dissipation…
This paper pursues a twofold goal. First, we introduce and study in detail a new notion of variational analysis called generalized metric subregularity, which is a far-going extension of the conventional metric subregularity conditions. Our…
The factor modeling for high-dimensional time series is powerful in discovering latent common components for dimension reduction and information extraction. Most available estimation methods can be divided into two categories: the…
Existing work on Multimodal Sentiment Analysis (MSA) utilizes multimodal information for prediction yet unavoidably suffers from fitting the spurious correlations between multimodal features and sentiment labels. For example, if most videos…
We extend a Gaussian functional inequality to a countable product of Gaussian measures. This inequality improves on the classical Poincare inequality for Gaussian measures. As an application, we prove that First Passage Percolation has…
This paper presents a weighted optimization framework that unifies the binary,multi-valued, continuous, as well as mixture of discrete and continuous treatment, under the unconfounded treatment assignment. With a general loss function, the…
In this study, we develop a methodology for model reduction and selection informed by global sensitivity analysis (GSA) methods. We apply these techniques to a control model that takes systolic blood pressure and thoracic tissue pressure…
We derive weighted log-Sobolev inequalities from a class of super Poincar\'e inequalities. As an application, the Talagrand inequality with larger distances are obtained. In particular, on a complete connected Riemannian manifold, we prove…