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## Algebraic Machine Learning

Resource type

Authors/contributors

- Martin-Maroto, Fernando (Author)
- de Polavieja, Gonzalo G. (Author)

Title

Algebraic Machine Learning

Abstract

Machine learning algorithms use error function minimization to fit a large set of parameters in a preexisting model. However, error minimization eventually leads to a memorization of the training dataset, losing the ability to generalize to other datasets. To achieve generalization something else is needed, for example a regularization method or stopping the training when error in a validation dataset is minimal. Here we propose a different approach to learning and generalization that is parameter-free, fully discrete and that does not use function minimization. We use the training data to find an algebraic representation with minimal size and maximal freedom, explicitly expressed as a product of irreducible components. This algebraic representation is shown to directly generalize, giving high accuracy in test data, more so the smaller the representation. We prove that the number of generalizing representations can be very large and the algebra only needs to find one. We also derive and test a relationship between compression and error rate. We give results for a simple problem solved step by step, hand-written character recognition, and the Queens Completion problem as an example of unsupervised learning. As an alternative to statistical learning, algebraic learning may offer advantages in combining bottom-up and top-down information, formal concept derivation from data and large-scale parallelization.

Publication

arXiv:1803.05252 [cs, math]

Date

2018-03-14

Accessed

2019-10-10T11:42:39Z

Library Catalog

Extra

arXiv: 1803.05252

Notes

Comment: In v2 Figures 10 and 12 are images (v1 used latex commands), so all queens on board are now visible

Citation

Martin-Maroto, F., & de Polavieja, G. G. (2018). Algebraic Machine Learning.

*ArXiv:1803.05252 [Cs, Math]*. Retrieved from http://arxiv.org/abs/1803.05252
MACHINE LEARNING

Methodology

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