Uncertainty Quantification in Learning-based Forecasting
Forecasting in financial times-series ultimately serves decision making. When forecasts are based on nonlinear models inferred with machine learning techniques it is important to estimate predictive uncertainties that can be supplied to the risk management modules of the decision maker. In spite of all the empirical successes of machine learning methods, a profound understanding of uncertainties in learning-based forecasting remains an underdeveloped and challenging area of basic research.
At OMI, we are working towards algorithms and theoretical understanding of provable consistent estimators of predictive uncertainties.
Figure 1. Convergence of our Lipschitz constant estimator to the true Lipschitz constant of a function.
Initial successes have included the development of provably consistent estimators of Lipschitz constants of general classes of functions applicable to low SNR data as well as the development of new nonparametric regression algorithms. Nascent research investigates their applicability to financial data as well as new forecasting bounds for NARX time series models driven by approximated Gaussian processes.
Figure 2. Bayesian inference over functions residing in Wavelet function spaces.