Related papers: Influence Function: Local Robustness and Efficienc…

We prove a version of the implicit function theorem for Lipschitz mappings $f:\mathbb{R}^{n+m}\supset A \to X$ into arbitrary metric spaces. As long as the pull-back of the Hausdorff content $\mathcal{H}_{\infty}^n$ by $f$ has positive…

This paper introduces a straightforward sieve-based approach for estimating and conducting inference on regression parameters in panel data models with interactive fixed effects. The method's key assumption is that factor loadings can be…

Influence functions approximate the "influences" of training data-points for test predictions and have a wide variety of applications. Despite the popularity, their computational cost does not scale well with model and training data size.…

Parameter estimation in empirical fields is usually undertaken using parametric models, and such models readily facilitate statistical inference. Unfortunately, they are unlikely to be sufficiently flexible to be able to adequately model…

Classical influence functions face significant challenges when applied to deep neural networks, primarily due to non-invertible Hessians and high-dimensional parameter spaces. We propose the local Bayesian influence function (BIF), an…

Many causal and policy effects of interest are defined by linear functionals of high-dimensional or non-parametric regression functions. $\sqrt{n}$-consistent and asymptotically normal estimation of the object of interest requires debiasing…

The center of interest in this work are variational problems with integral functionals depending on special nonlocal gradients. The latter correspond to truncated versions of the Riesz fractional gradient, as introduced in [Bellido, Cueto &…

We propose a new length formula that governs the iterates of the momentum method when minimizing differentiable semialgebraic functions with locally Lipschitz gradients. It enables us to establish local convergence, global convergence, and…

Whilst influence functions for linear discriminant analysis (LDA) have been found for a single discriminant when dealing with two groups, until now these have not been derived in the setting of a general number of groups. In this paper we…

We consider statistical inference for a finite-dimensional parameter in a regular semiparametric model under a distributed setting with blockwise missingness, where entire blocks of variables are unavailable at certain sites and sharing…

We consider spatially dependent functional data collected under a geostatistics setting, where locations are sampled from a spatial point process. The functional response is the sum of a spatially dependent functional effect and a spatially…

Many language tasks (e.g., Named Entity Recognition, Part-of-Speech tagging, and Semantic Role Labeling) are naturally framed as sequence tagging problems. However, there has been comparatively little work on interpretability methods for…

The increasing complexity of machine learning (ML) and artificial intelligence (AI) models has created a pressing need for tools that help scientists, engineers, and policymakers interpret and refine model decisions and predictions.…

This paper addresses the asymptotics of functionals with linear growth depending on the Riesz $s$-fractional gradient on piecewise constant functions. We consider a general class of varying energy densities and, as $s\to 1$, we characterize…

We consider nonparametric functional regression when both predictors and responses are functions. More specifically, we let $(X_1,Y_1),...,(X_n,Y_n)$ be random elements in $\mathcal{F}\times\mathcal{H}$ where $\mathcal{F}$ is a semi-metric…

Influence functions estimate effect of individual data points on predictions of the model on test data and were adapted to deep learning in Koh and Liang [2017]. They have been used for detecting data poisoning, detecting helpful and…

Influence functions efficiently estimate the effect of removing a single training data point on a model's learned parameters. While influence estimates align well with leave-one-out retraining for linear models, recent works have shown this…

There is a wide range of applications where the local extrema of a function are the key quantity of interest. However, there is surprisingly little work on methods to infer local extrema with uncertainty quantification in the presence of…

Influence functions serve as crucial tools for assessing sample influence in model interpretation, subset training set selection, noisy label detection, and more. By employing the first-order Taylor extension, influence functions can…

Ideally, any statistical inference should be robust to local influences. Although there are simple ways to check about leverage points in independent and linear problems, more complex models require more sophisticated methods.…