# Theory of Machine Learning with Limited Data

arXiv: https://arxiv.org/abs/2206.07586 · HTML: https://mlsanity.com/paper/2206.07586/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 14 references that are in the map.
- First posted on arXiv 15 Jun 2022.

## Builds on (most cited first, 2 of 2)

- [An adaptive nearest neighbor rule for classification](https://mlsanity.com/paper/1905.12717/) (2019)
- [Optimal choice: new machine learning problem and its solution](https://mlsanity.com/paper/1706.08439/) (2017)

## Abstract (arXiv)

Application of machine learning may be understood as deriving new knowledge for practical use through explaining accumulated observations, training set. Peirce used the term abduction for this kind of inference. Here I formalize the concept of abduction for real valued hypotheses, and show that 14 of the most popular textbook ML learners (every learner I tested), covering classification, regression and clustering, implement this concept of abduction inference. The approach is proposed as an alternative to statistical learning theory, which requires an impractical assumption of indefinitely increasing training set for its justification.