SEF: A Method for Computing Prediction Intervals by Shifting the Error Function in Neural Networks

In today's era, Neural Networks (NN) are applied in various scientific fields such as robotics, medicine, engineering, etc. However, the predictions of neural networks themselves contain a degree of uncertainty that must always be taken into account before any decision is made. This is why many researchers have focused on developing different ways to quantify the uncertainty of neural network predictions. Some of these methods are based on generating prediction intervals (PI) via neural networks for the requested target values. The SEF (Shifting the Error Function) method presented in this paper is a new method that belongs to this category of methods. The proposed approach involves training a single neural network three times, thus generating an estimate along with the corresponding upper and lower bounds for a given problem. A pivotal aspect of the method is the calculation of a parameter from the initial network's estimates, which is then integrated into the loss functions of the other two networks. This innovative process effectively produces PIs, resulting in a robust and efficient technique for uncertainty quantification. To evaluate the effectiveness of our method, a comparison in terms of successful PI generation between the SEF, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{PI}3\text{NN}$</tex> and PIVEN methods was made using two synthetic datasets.