相关论文: Sensitivity analysis in general metric spaces

Under the Neyman causal model, it is well-known that OLS with treatment-by-covariate interactions cannot harm asymptotic precision of estimated treatment effects in completely randomized experiments. But do such guarantees extend to…

A new notion of typicality for arbitrary probability measures on standard Borel spaces is proposed, which encompasses the classical notions of weak and strong typicality as special cases. Useful lemmas about strong typical sets, including…

A mode, or `most likely point', for a probability measure $\mu$ can be defined in various ways via the asymptotic behaviour of the $\mu$-mass of balls as their radius tends to zero. Such points are of intrinsic interest in the local theory…

Some classical uncertainty quantification problems require the estimation of multiple expectations. Estimating all of them accurately is crucial and can have a major impact on the analysis to perform, and standard existing Monte Carlo…

We consider the problem of detecting a rectangle of activation in a grid of sensors in d-dimensions with noisy measurements. This has applications to massive surveillance projects and anomaly detection in large datasets in which one detects…

Let $G$ be a sofic group, and let $\Sigma = (\sigma_n)_{n\geq 1}$ be a sofic approximation to it. For a probability-preserving $G$-system, a variant of the sofic entropy relative to $\Sigma$ has recently been defined in terms of sequences…

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.…

The hierarchically orthogonal functional decomposition of any measurable function f of a random vector X=(X_1,...,X_p) consists in decomposing f(X) into a sum of increasing dimension functions depending only on a subvector of X. Even when…

We develop an asymptotic theory of adversarial estimators ('A-estimators'). They generalize maximum-likelihood-type estimators ('M-estimators') as their average objective is maximized by some parameters and minimized by others. This class…

We introduce sparse versions of function spaces that are relevant to characterize the solutions of Euler equations without concentration. The standard Sobolev space $H^{-1}$ is given a sparse structure that allows to measure the degree of…

We introduce and investigate classes of normed or quasinormed distribution spaces of generalized smoothness that can be obtained by various interpolation methods applied to classical Sobolev, Nikolskii-Besov, and Triebel-Lizorkin spaces. An…

Variance-based global sensitivity analysis (GSA) can provide a wealth of information when applied to complex models. A well-known Achilles' heel of this approach is its computational cost which often renders it unfeasible in practice. An…

Generalized likelihoods are commonly used to obtain consistent estimators with attractive computational and robustness properties. Formally, any generalized likelihood can be used to define a generalized posterior distribution, but an…

We give a geometrical set up for the semiclassical approximation to euclidean field theories having families of minima (instantons) parametrized by suitable moduli spaces ${\cal M}$. The standard examples are of course Yang-Mills theory and…

The simplest and most widely applied method for guaranteeing differential privacy is to add instance-independent noise to a statistic of interest that is scaled to its global sensitivity. However, global sensitivity is a worst-case notion…

Sobol' sensitivity index estimators for stochastic models are functions of nested Monte Carlo estimators, which are estimators built from two nested Monte Carlo loops. The outer loop explores the input space and, for each of the…

We present a novel graph embedding space (i.e., a set of measures on graphs) for performing statistical analyses of networks. Key improvements over existing approaches include discovery of "motif-hubs" (multiple overlapping significant…

In this paper, we present perturbed law-based sensitivity indices and how to adapt them for quantile-oriented sensitivity analysis. We exhibit a simple way to compute these indices in practice using an importance sampling estimator for…

The survey covers several topics related to the asymptotic structure of various combinatorial and analytic objects such as the path spaces in graded graphs (Bratteli diagrams), invariant measures with respect to countable groups, etc. The…

ANOVA decomposition of function with random input variables provides ANOVA functionals (AFs), which contain information about the contributions of the input variables on the output variable(s). By embedding AFs into an appropriate…