Related papers: SHAP values through General Fourier Representation…

Understanding why a neural network model makes certain decisions can be as important as the inference performance. Various methods have been proposed to help practitioners explain the prediction of a neural network model, of which Shapley…

This paper introduces a weighted generalized inverse framework for Fourier extensions, designed to suppress spurious oscillations in the extended region while maintaining high approximation accuracy on the original interval. By formulating…

Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…

Symbolic regression has excelled in uncovering equations from physics, chemistry, biology, and related disciplines. However, its effectiveness becomes less certain when applied to experimental data lacking inherent closed-form expressions.…

Functions that are smooth but non-periodic on a certain interval possess Fourier series that lack uniform convergence and suffer from the Gibbs phenomenon. However, they can be represented accurately by a Fourier series that is periodic on…

Shapley values are ubiquitous in interpretable Machine Learning due to their strong theoretical background and efficient implementation in the SHAP library. Computing these values previously induced an exponential cost with respect to the…

We introduce a class of algorithms for constructing Fourier representations of Gaussian processes in $1$ dimension that are valid over ranges of hyperparameter values. The scaling and frequencies of the Fourier basis functions are evaluated…

We discuss probabilistic neural networks with a fixed internal representation as models for machine understanding. Here understanding is intended as mapping data to an already existing representation which encodes an {\em a priori}…

Uncertainty estimation in machine learning has traditionally focused on the prediction stage, aiming to quantify confidence in model outputs while treating learned representations as deterministic and reliable by default. In this work, we…

Machine learning driven interatomic potentials, including Gaussian approximation potential (GAP) models, are emerging tools for atomistic simulations. Here, we address the methodological question of how one can fit GAP models that…

Existing feature attribution methods like SHAP often suffer from global dependence, failing to capture true local model behavior. This paper introduces VARSHAP, a novel model-agnostic local feature attribution method which uses the…

We propose a Bayesian framework of Gaussian process in order to extend Fisher's discriminant to classify functional data such as spectra and images. The probability structure for our extended Fisher's discriminant is explicitly formulated,…

We present a novel approach for explaining Gaussian processes (GPs) that can utilize the full analytical covariance structure present in GPs. Our method is based on the popular solution concept of Shapley values extended to stochastic…

Approximation using Fourier features is a popular technique for scaling kernel methods to large-scale problems, with myriad applications in machine learning and statistics. This method replaces the integral representation of 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…

We develop quaternionic analysis using as a guiding principle representation theory of various real forms of the conformal group. We first review the Cauchy-Fueter and Poisson formulas and explain their representation theoretic meaning. The…

Symmetric functions, which take as input an unordered, fixed-size set, are known to be universally representable by neural networks that enforce permutation invariance. These architectures only give guarantees for fixed input sizes, yet in…

We propose SHARC, a novel framework that synthesizes arbitrary, genus-agnostic shapes by means of a collection of Spherical Harmonic (SH) representations of distance fields. These distance fields are anchored at optimally placed reference…

The remarkable generalization performance of large-scale models has been challenging the conventional wisdom of the statistical learning theory. Although recent theoretical studies have shed light on this behavior in linear models and…

In this paper we consider functions in the Hardy space $\mathbf{H}_2^{p\times q}$ defined in the unit disc of matrix-valued. We show that it is possible, as in the scalar case, to decompose those functions as linear combinations of suitably…