Related papers: Reconstructing weighted voting schemes from partia…
The inverse problem of identifying the unknown spacewise dependent source F(x) in 1D wave equation is considered. Measured data are taken in the form g(t) := u(0; t). The relationship between that problem and Ground Penetrating Radar (GRR)…
Several novel imaging and non-destructive testing technologies are based on reconstructing the spatially dependent coefficient in an elliptic partial differential equation from measurements of its solution(s). In practical applications, the…
In this work, we study an inverse problem of recovering information about the weight in distributed-order time-fractional diffusion from the observation at one single point on the domain boundary. In the absence of an explicit knowledge of…
Deep Neural Networks (DNNs) have demonstrated strong capacity in supporting a wide variety of applications. Shapley value has emerged as a prominent tool to analyze feature importance to help people understand the inference process of deep…
The Shapley value (SV) and Least core (LC) are classic methods in cooperative game theory for cost/profit sharing problems. Both methods have recently been proposed as a principled solution for data valuation tasks, i.e., quantifying the…
In this paper, we propose two variable selection methods for adjusting the censoring information for survival times, such as the restricted mean survival time. To adjust for the influence of censoring, we consider an inverse survival…
In the first part of this work, we develop a novel scheme for solving nonparametric regression problems. That is the approximation of possibly low regular and noised functions from the knowledge of their approximate values given at some…
We investigate the issue of parameter estimation with nonuniform negative sampling for imbalanced data. We first prove that, with imbalanced data, the available information about unknown parameters is only tied to the relatively small…
In this research, we discuss a problem of calculating the Shapley value in bankruptcy games. We show that the decision problem of computing the Shapley value in bankruptcy games is NP-complete. We also investigate the relationship between…
This article is concerned with the derivation of numerical reconstruction schemes for the inverse moving source problem on determining source profiles in (time-fractional) evolution equations. As a continuation of the theoretical result on…
In the standard trace reconstruction problem, the goal is to \emph{exactly} reconstruct an unknown source string $\mathsf{x} \in \{0,1\}^n$ from independent "traces", which are copies of $\mathsf{x}$ that have been corrupted by a…
We give two results on PAC learning DNF formulas using membership queries in the challenging "distribution-free" learning framework, where learning algorithms must succeed for an arbitrary and unknown distribution over $\{0,1\}^n$. (1) We…
How important is the weight of a given column in determining the ranking of tuples in a table? To address such an explanation question about a ranking function, we investigate the computation of SHAP scores for column weights, adopting a…
We consider functional linear regression models where functional outcomes are associated with scalar predictors by coefficient functions with shape constraints, such as monotonicity and convexity, that apply to sub-domains of interest. To…
Shapley values have become a cornerstone of explainable AI, but they are computationally expensive to use, especially when features are dependent. Evaluating them requires approximating a large number of conditional expectations, either via…
When a controller is designed from an identified model, its performance ultimately depends on the trajectories used for identification, but pinpointing which ones help or hurt remains an open problem. We bring influence functions, a data…
The weighted entropy $H^{\rm w}_\phi (X)=H^{\rm w}_\phi (f)$ of a random variable $X$ with values $x$ and a probability-mass/density function $f$ is defined as the mean value ${\mathbb E} I^{\rm w}_\phi(X)$ of the weighted information…
We consider the problem of state estimation in dynamical systems and propose a different mechanism for handling unmodeled system uncertainties. Instead of injecting random process noise, we assign different weights to measurements so that…
Given a way to evaluate an unknown polynomial with integer coefficients, we present new algorithms to recover its nonzero coefficients and corresponding exponents. As an application, we adapt this interpolation algorithm to the problem of…
SHapley Additive exPlanations (SHAP) is a key tool for interpreting decision tree ensembles by assigning contribution values to features. It is widely used in finance, advertising, medicine, and other domains. Two main approaches to SHAP…