Related papers: Efficient Shapley Performance Attribution for Leas…
We consider least squares estimators of the finite regression parameter $\alpha$ in the single index regression model $Y=\psi(\alpha^T X)+\epsilon$, where $X$ is a $d$-dimensional random vector, $\E(Y|X)=\psi(\alpha^T X)$, and where $\psi$…
With a rapid increase in volume and complexity of data sets, there is a need for methods that can extract useful information, for example the relationship between two data sets measured for the same persons. The Partial Least Squares (PLS)…
Shapley value is a widely used tool in explainable artificial intelligence (XAI), as it provides a principled way to attribute contributions of input features to model outputs. However, estimation of Shapley value requires capturing…
The original development of Shapley values for prediction explanation relied on the assumption that the features being described were independent. If the features in reality are dependent this may lead to incorrect explanations. Hence,…
People employ the function-on-function regression to model the relationship between two random curves. Fitting this model, widely used strategies include algorithms falling into the framework of functional partial least squares (typically…
Additive feature explanations rely primarily on game-theoretic notions such as the Shapley value by viewing features as cooperating players. The Shapley value's popularity in and outside of explainable AI stems from its axiomatic…
This paper introduces an iterative scheme for acoustic model inversion where the notion of proximity of two traces is not the usual least-squares distance, but instead involves registration as in image processing. Observed data are matched…
In partially linear single-index models, we obtain the semiparametrically efficient profile least-squares estimators of regression coefficients. We also employ the smoothly clipped absolute deviation penalty (SCAD) approach to…
We address a classical problem in statistics: adding two-way interaction terms to a regression model. As the covariate dimension increases quadratically, we develop an estimator that adapts well to this increase, while providing accurate…
We consider estimation and inference in a single index regression model with an unknown but smooth link function. In contrast to the standard approach of using kernels or regression splines, we use smoothing splines to estimate the smooth…
Model averaging techniques in the actuarial literature aim to forecast future longevity appropriately by combining forecasts derived from various models. This approach often yields more accurate predictions than those generated by a single…
Linear least squares (LLS) is perhaps the most common method of data analysis, dating back to Legendre, Gauss and Laplace. Framed as linear regression, LLS is also a backbone of mathematical statistics. Here we report on an unexpected new…
The panel data regression models have gained increasing attention in different areas of research including but not limited to econometrics, environmental sciences, epidemiology, behavioral and social sciences. However, the presence of…
The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…
The optimization problem that arises out of the least median of squared residuals method in linear regression is analyzed. To simplify the analysis, the problem is replaced by an equivalent one of minimizing the median of absolute…
We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…
Shapley values provide model agnostic feature attributions for model outcome at a particular instance by simulating feature absence under a global population distribution. The use of a global population can lead to potentially misleading…
Data valuation, or the valuation of individual datum contributions, has seen growing interest in machine learning due to its demonstrable efficacy for tasks such as noisy label detection. In particular, due to the desirable axiomatic…
We propose a penalized least-squares method to fit the linear regression model with fitted values that are invariant to invertible linear transformations of the design matrix. This invariance is important, for example, when practitioners…
Shapley values have several desirable, theoretically well-supported, properties for explaining black-box model predictions. Traditionally, Shapley values are computed post-hoc, leading to additional computational cost at inference time. To…