Related papers: A note on the Sobol' indices and interactive crite…
A committee's decisions on more than two alternatives much depend on the adopted voting method, and so does the distribution of power among the committee members. We investigate how different aggregation methods such as plurality runoff,…
Contemporary predictive models are hard to interpret as their deep nets exploit numerous complex relations between input elements. This work suggests a theoretical framework for model interpretability by measuring the contribution of…
Drawing causal inference with observational studies is the central pillar of many disciplines. One sufficient condition for identifying the causal effect is that the treatment-outcome relationship is unconfounded conditional on the observed…
Estimation mainly for two classes of popular models, single-index and partially linear single-index models, is studied in this paper. Such models feature nonstationarity. Orthogonal series expansion is used to approximate the unknown…
In the context of algebraic statistics an experimental design is described by a set of polynomials called the design ideal. This, in turn, is generated by finite sets of polynomials. Two types of generating sets are mostly used in the…
The interaction of two binary variables, assumed to be empirical observations, has three degrees of freedom when expressed as a matrix of frequencies. Usually, the size of causal influence of one variable on the other is calculated as a…
Given a bivariate random pair $(X,Y)$, a natural problem is to estimate, from a single sample $(X_i,Y_i)_{1\le i\le n}$, quantities such as $\mathbb{E}\left[ \mathbb{E}[ Y\mid X ]^2 \right]$. More broadly, sensitivity indices are designed…
By considering a least squares approximation of a given square integrable function f:[0,1]^n --> R by a shifted L-statistic function (a shifted linear combination of order statistics), we define an index which measures the global influence…
This paper focuses on the problem of modeling and estimating interaction effects between covariates and a continuous treatment variable on an outcome, using a single-index regression approach. The primary motivation is to estimate an…
Characteristic functions of several popular classes of distributions and processes admit analytic continuation into unions of strips and open coni around $\mathbb{R}\subset \mathbb{C}$. The Fourier transform techniques reduces calculation…
In a multi-index model with $k$ index vectors, the input variables are transformed by taking inner products with the index vectors. A transfer function $f: \mathbb{R}^k \to \mathbb{R}$ is applied to these inner products to generate the…
We propose a simple new index, named the $CI$-index, based on the Choquet integral to characterize the scientific output of researchers. This index is an improvement of the $A$-index and $R$-index and has a notable feature that highly cited…
Predominately in explainable artificial intelligence (XAI) research, the Shapley value (SV) is applied to determine feature attributions for any black box model. Shapley interaction indices extend the SV to define any-order feature…
Instrumental variable models allow us to identify a causal function between covariates $X$ and a response $Y$, even in the presence of unobserved confounding. Most of the existing estimators assume that the error term in the response $Y$…
In this paper we give some sufficient conditions of analyticity and univalence for functions defined by an integral operator. Next, we refine the result to a quasiconformal extension criterion with the help of the Becker's method. Further,…
In order to perform multimodal fusion of heterogeneous signals, we need to understand their interactions: how each modality individually provides information useful for a task and how this information changes in the presence of other…
Multifractals arise in various systems across nature whose scaling behavior is characterized by a continuous spectrum of multifractal exponents $\Delta_q$. In the context of Anderson transitions, the multifractality of critical wave…
In the practice of point prediction, it is desirable that forecasters receive a directive in the form of a statistical functional, such as the mean or a quantile of the predictive distribution. When evaluating and comparing competing…
Multi-head attention empowers the recent success of transformers, the state-of-the-art models that have achieved remarkable success in sequence modeling and beyond. These attention mechanisms compute the pairwise dot products between the…
Sobol' sensitivity indices allow to quantify the respective effects of random input variables and their combinations on the variance of mathematical model output. We focus on the problem of Sobol' indices estimation via a metamodeling…