Encoding of data sets and algorithms

In many high-impact applications, it is important to ensure the quality of the output of a machine learning algorithm as well as its reliability in comparison to the complexity of the algorithm used. In this paper, we have initiated a mathematically rigorous theory to decide which models (algorithms applied on data sets) are close to each other in terms of certain metrics, such as performance and the complexity level of the algorithm. This involves creating a grid on the hypothetical spaces of data sets and algorithms so as to identify a finite set of probability distributions from which the data sets are sampled and a finite set of algorithms. A given threshold metric acting on this grid will express the nearness (or statistical distance) of each algorithm and data set of interest to any given application. A technically difficult part of this project is to estimate the so-called metric entropy of a compact subset of functions of infinitely many variables that arise in the definition of these spaces. (c) 2023 The Authors. Published by Elsevier B.V. on behalf of IMACS. This is an open access article under the CC BY-NC-ND license (http:// creativecommons .org /licenses /by-nc -nd /4 .0/).