Related papers: Decompositions of functions based on arity gap

Function is defined as the ensemble of tasks that enable the product to complete the designed purpose. Functional tools, such as functional modeling, offer decision guidance in the early phase of product design, where explicit design…

Algorithmic fairness has aroused considerable interests in data mining and machine learning communities recently. So far the existing research has been mostly focusing on the development of quantitative metrics to measure algorithm…

We investigate the associativity property for functions of indefinite arities and introduce and discuss the more general property of preassociativity, a generalization of associativity which does not involve any composition of functions.

The study of essential and strongly essential variables in functions defined on finite sets is a part of $k$-valued logic. We extend the main definitions from functions to terms. This allows us to apply concepts and results of Universal…

Pair-wise loss is an approach to metric learning that learns a semantic embedding by optimizing a loss function that encourages images from the same semantic class to be mapped closer than images from different classes. The literature…

Classification is a ubiquitous and fundamental problem in artificial intelligence and machine learning, with extensive efforts dedicated to developing more powerful classifiers and larger datasets. However, the classification task is…

This letter explains an algorithm for finding a set of base functions. The method aims to capture the leading behavior of the dataset in terms of a few base functions. Implementation of the A-star search will help find these functions,…

The approximation of smooth functions with a spectral basis typically leads to rapidly decaying coefficients where the rate of decay depends on the smoothness of the function and vice-versa. The optimal number of degrees of freedom in the…

The interactions between three or more random variables are often nontrivial, poorly understood, and yet, are paramount for future advances in fields such as network information theory, neuroscience, genetics and many others. In this work,…

We introduce structured decompositions, category-theoretic structures which simultaneously generalize notions from graph theory (including treewidth, layered treewidth, co-treewidth, graph decomposition width, tree independence number,…

We prove general results about separation and weak$^\#$-convergence of boundedly finite measures on separable metric spaces and Souslin spaces. More precisely, we consider an algebra of bounded real-valued, or more generally a $*$-algebra…

A generating function of the number of homomorphisms from the fundamental group of a compact oriented or non-orientable surface without boundary into a finite group is obtained in terms of an integral over a real group algebra. We calculate…

Given a database and a target attribute of interest, how can we tell whether there exists a functional, or approximately functional dependence of the target on any set of other attributes in the data? How can we reliably, without bias to…

We identify the finite list of minimal analytic n-gaps which are not countably separated, and we prove that every analytic n-gap which is not countably separated contains a gap from our finite list.

Functional depth is the functional data analysis technique that orders a functional data set. Unlike the case of data on the real line, defining this order is non-trivial, and particularly, with functional data, there are a number of…

The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules…

We investigate the zeros of two one-parameter families of harmonic functions and describe how the number of zeros depends on the parameter. Our functions have the property that all zeros lie on certain rays in the complex plane and thus we…

computable functions are defined by abstract finite deterministic algorithms on many-sorted algebras. We show that there exist finite universal algebraic specifications that specify uniquely (up to isomorphism) (i) all abstract computable…

This paper introduces a novel decomposition framework to explain heterogeneity in causal effects observed across different studies, considering both observational and randomized settings. We present a formal decomposition of between-study…

A merit (gap) function is a map that returns zero at the solutions of problems and strictly positive values otherwise. Its minimization is equivalent to the original problem by definition, and it can estimate the distance between a given…