Big data and probably approximately correct learning in the presence of noise: Implications For financial risk management

High accuracy forecasts are essential to financial risk management, where machine learning algorithms are frequently employed. We derive a new theoretical bound on the sample complexity for Probably Approximately Correct (PAC) learning in the presence of noise, and does not require specification of the hypothesis set |H|. We demonstrate that for realistic financial applications where |H| is typically infinite. This is contrary to prior theoretical conclusions. We further show that noise, which is a non-trivial component of big data, has a dominating impact on the data size required for PAC learning. Consequently, contrary to current big data trends, we argue that high quality data is more important than large volumes of data. This paper additionally demonstrates that the level of algorithmic sophistication, specifically the Vapnik-Chervonenkis (VC) dimension, needs to be traded-off against data requirements to ensure optimal algorithmic performance. Finally, our new Theorem can be applied to a wider range of machine learning algorithms, as it does not impose finite |H| requirements. This paper contributes to theoretical and applied research in the domain of machine learning for financial applications