Related papers: Axiomatic characterization of pointwise Shapley de…
We study the attribution problem, that is, the problem of attributing a change in the value of a characteristic function to its independent variables. We make three contributions. First, we propose a formalization of the problem based on a…
Over the last few years, the Shapley value, a solution concept from cooperative game theory, has found numerous applications in machine learning. In this paper, we first discuss fundamental concepts of cooperative game theory and axiomatic…
In a previous paper [1] it was discussed the viability of functional analysis using as a basis a couple of generic functions, and hence vectorial decomposition. Here we complete the paradigm exploiting one of the analysis methodologies…
Motivated by partition regularity problems of homogeneous quadratic equations, we prove multiple recurrence and convergence results for multiplicative measure preserving actions with iterates given by rational sequences involving…
We prove a theorem which provides a method for constructing points on varieties defined by certain smooth functions. We require that the functions are definable in a definably complete expansion of a real closed field and are locally…
Aspects of the theory of characteristic modes, based on their variational formulation, are presented and an explicit form of a related functional, involving only currents in a spatial domain, is derived. The new formulation leads to deeper…
By means of partial fraction method, we investigate the decomposition of rational functions. Several striking identities on harmonic numbers and generalized Apery numbers will be established, including the binomial-harmonic number identity…
A popular explainable AI (XAI) approach to quantify feature importance of a given model is via Shapley values. These Shapley values arose in cooperative games, and hence a critical ingredient to compute these in an XAI context is a…
We consider the dataset valuation problem, that is, the problem of quantifying the incremental gain, to some relevant pre-defined utility of a machine learning task, of aggregating an individual dataset to others. The Shapley value is a…
Model interpretability is one of the most intriguing problems in most of the Machine Learning models, particularly for those that are mathematically sophisticated. Computing Shapley Values are arguably the best approach so far to find the…
The complex nature of artificial neural networks raises concerns on their reliability, trustworthiness, and fairness in real-world scenarios. The Shapley value -- a solution concept from game theory -- is one of the most popular explanation…
In Machine Learning, the $\mathsf{SHAP}$-score is a version of the Shapley value that is used to explain the result of a learned model on a specific entity by assigning a score to every feature. While in general computing Shapley values is…
The numerical evaluation of an individual Bessel or Hankel function of large order and large argument is a notoriously problematic issue in physics. Recurrence relations are inefficient when an individual function of high order and argument…
We establish common fixed point theorems for two pairs of weakly compatible self-mappings using an auxiliary function of two variables. Unlike classical results, our theorems do not assume continuity of the mappings and require completeness…
Originating in game theory, Shapley values are widely used for explaining a machine learning model's prediction by quantifying the contribution of each feature's value to the prediction. This requires a scalar prediction as in binary…
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…
Variable selection or importance measurement of input variables to a machine learning model has become the focus of much research. It is no longer enough to have a good model, one also must explain its decisions. This is why there are so…
In spite of increased attention on explainable machine learning models, explaining multi-output predictions has not yet been extensively addressed. Methods that use Shapley values to attribute feature contributions to the decision making…
Multivariate functions emerge naturally in a wide variety of data-driven models. Popular choices are expressions in the form of basis expansions or neural networks. While highly effective, the resulting functions tend to be hard to…
SHAP (SHapley Additive exPlanations) has become a popular method to attribute the prediction of a machine learning model on an input to its features. One main challenge of SHAP is the computation time. An exact computation of Shapley values…