Deep and probabilistic learning under uncertainties cum non-spherical disturbances

Abstract

The study investigates the performances of deep and probabilistic models under uncertainties with non-spherical disturbances inherent in the data. We deemed aleatoric and epistemic uncertainties, the former inherent in the data while the later inherent in the model in  probabilistic approach. Loss, mean square error (MSE), mean absolute error (MAE) were adopted to evaluate the performance of the  models for training, testing and validating sets. Both multicollinearity and autocorrected error were inherent in the data, there exist  negative autocorrected error of magnitude 1.46 and the multicollinearity with magnitude of “inf” that implies imperfect multicollinearity were inherent in the data. Keras Dense layer and Tensor flow probability (tfp) Dense variational layer were adopted. The underlying model were constructed probabilistically to capture aleatoric, epistemic and both. The study observed that the “no uncertainty, classical and aleatoric models behaved well when data were standardised, the magnitude of loss, MAE and MSE reduced by almost 98%, this implies that the accuracy of the parameter were improved, though epistemic and both aleatoric and epistemic uncertainties models depicted poor performances of the model despite their probabilistic nature, this may be due to combination of uncertainty with non-spherical disturbances. The unstandardised data exhibited poor performances in all the models. The study therefore recommended that data should be standardised prior estimation.