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

• URL: http://arxiv.org/abs/2510.18332v1
• Date: Tue, 21 Oct 2025 06:34:22 GMT
• Title: Parametrising the Inhomogeneity Inducing Capacity of a Training Set, and its Impact on Supervised Learning
• Authors: Gargi Roy, Dalia Chakrabarty,
• Abstract summary: We refer to a parametrisation of this property of a given training set, as its inhomogeneity parameter''<n>We prove that 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.
• Score: 0.042970700836450486
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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