Window Size Optimization for Gaussian Processes in Large Time Series Forecasting

Abstract

Many current machine learning applications rely on performance rather than on model interpretability. Robust confidence projection is underrated as well. These qualities are of key importance in experimental sciences where benefits of IA applicability is intended to precisely bound sensible results. A Gaussian Process (GP) constitutes a non-parametric soft computing method which encompasses model interpretability and transparency. Additionally GPs feature rigorous uncertainty estimations by means of convenient kernel specification fitting data stochastic properties. Extensive temporal series of data may efficiently be characterised by GPs. GPs perform selecting the most suitable distribution of solutions conditioning over observations by means of maximizing the logarithm of the marginal-likelihood of data. Selecting an appropriate time-training interval stands out as a requirement and to successfully extract unambiguous structural information from kernel hyperparameters. Nevertheless demanding computational cost in the course of the training stage, scaling as $\mathcal {O}(n^{3})$ being n the data set size, sets a trade-off on how much data to include. Our work aims at providing a general procedure to optimize input training selection to be minimum meanwhile retaining unambiguous information to the process modelled by the GP. To address this problem our ideas are evaluated performing forecasting on Madrid air-quality time series.