# Parametrising the Inhomogeneity Inducing Capacity of a Training Set, and its Impact on Supervised Learning

arXiv: https://arxiv.org/abs/2510.18332 · HTML: https://mlsanity.com/paper/2510.18332/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 32 references that are in the map.
- First posted on arXiv 21 Oct 2025.

## Builds on (most cited first, 3 of 3)

- [The Euclidean distance degree of an algebraic variety](https://mlsanity.com/paper/1309.0049/) (2013)
- [A Unifying Perspective on Non-Stationary Kernels for Deeper Gaussian Processes](https://mlsanity.com/paper/2309.10068/) (2023)
- [Testing for stationarity of functional time series in the frequency domain](https://mlsanity.com/paper/1701.01741/) (2017)

## Abstract (arXiv)

We introduce parametrisation of that property of the available training dataset, that necessitates an inhomogeneous correlation structure for the function that is learnt as a model of the relationship between the pair of variables, observations of which comprise the considered training data. We refer to a parametrisation of this property of a given training set, as its ``inhomogeneity parameter''. It is easy to compute this parameter for small-to-large datasets, and we demonstrate such computation on multiple publicly-available datasets, while also demonstrating that conventional ``non-stationarity'' of data does not imply a non-zero inhomogeneity parameter of the dataset. We prove that - within the probabilistic Gaussian Process-based learning approach - a training set with a non-zero inhomogeneity parameter renders it imperative, that the process that is invoked to model the sought function, be non-stationary. Following the learning of a real-world multivariate function with such a Process, quality and reliability of predictions at test inputs, are demonstrated to be affected by the inhomogeneity parameter of the training data.