Related papers: Influence Function: Local Robustness and Efficienc…

Influence function, a technique rooted in robust statistics, has been adapted in modern machine learning for a novel application: data attribution -- quantifying how individual training data points affect a model's predictions. However, the…

We present a framework for performing efficient regression in general metric spaces. Roughly speaking, our regressor predicts the value at a new point by computing a Lipschitz extension --- the smoothest function consistent with the…

This paper studies nonparametric local (over-)identification and the semiparametric efficiency in modern causal frameworks. We develop a unified approach that begins by translating structural models with latent variables into their induced…

Robins et al. (2008) introduced a class of influence functions (IFs) which could be used to obtain doubly robust moment functions for the corresponding parameters. However, that class does not include the IF of parameters for which the…

The influence function in peridynamic material models has a large effect on the dynamic behavior of elastic waves and in turn can greatly effect dynamic simulations of fracture propagation and material failure. Typically, the influence…

The discrete data encoded in the power moments of a positive measure, fast decaying at infinity on euclidean space, is incomplete for recovery, leading to the concept of moment indeterminateness. On the other hand, classical integral…

The goal of this paper is to extend the nonparametric estimation of Impulse Response Functions (IRF) by means of local projections in the nonlinear dynamic framework. We discuss the existence of a nonlinear autoregressive representation for…

Influence diagnostics such as influence functions and approximate maximum influence perturbations are popular in machine learning and in AI domain applications. Influence diagnostics are powerful statistical tools to identify influential…

This paper concerns the estimation of sums of functions of observable and unobservable variables. Lower bounds for the asymptotic variance and a convolution theorem are derived in general finite- and infinite-dimensional models. An explicit…

We propose and implement an approach to inference in linear instrumental variables models which is simultaneously robust and computationally tractable. Inference is based on self-normalization of sample moment conditions, and allows for…

We aim to construct a class of learning algorithms that are of practical value to applied researchers in fields such as biostatistics, epidemiology and econometrics, where the need to learn from incompletely observed information is…

This paper presents a tractable algorithm for estimating an unknown Lipschitz function from noisy observations and establishes an upper bound on its convergence rate. The approach extends max-affine methods from convex shape-restricted…

Influence functions provide a principled method to assess the contribution of individual training samples to a specific target. Yet, their high computational costs limit their applications on large-scale models and datasets. Existing…

How can we explain the predictions of a black-box model? In this paper, we use influence functions -- a classic technique from robust statistics -- to trace a model's prediction through the learning algorithm and back to its training data,…

A sharp, distribution free, non-asymptotic result is proved for the concentration of a random function around the mean function, when the randomization is generated by a finite sequence of independent data and the random functions satisfy…

We describe an iterative formalism to compute influence functionals that describe the general quantum dynamics of a subsystem beyond the assumption of linear coupling to a quadratic bath. We use a space-time tensor network representation of…

There are many nonparametric objects of interest that are a function of a conditional distribution. One important example is an average treatment effect conditional on a subset of covariates. Many of these objects have a conditional…

A number of fundamental quantities in statistical signal processing and information theory can be expressed as integral functions of two probability density functions. Such quantities are called density functionals as they map density…

In various statistical settings, the goal is to estimate a function which is restricted by the statistical model only through a conditional moment restriction. Prominent examples include the nonparametric instrumental variable framework for…

Cook's [J. Roy. Statist. Soc. Ser. B 48 (1986) 133--169] local influence approach based on normal curvature is an important diagnostic tool for assessing local influence of minor perturbations to a statistical model. However, no rigorous…