  Most machine learning techniques are based upon statistical learning theory,
often simplified for the sake of computing speed. This paper is focused on the
uncertainty aspect of mathematical modeling in machine learning. Regression
analysis is chosen to further investigate the evaluation aspect of uncertainty
in model coefficients and, more importantly, in the output feature value
predictions. A survey demonstrates major stages in the conventional least
squares approach to the creation of the regression model, along with its
uncertainty estimation. On the other hand, it is shown that in machine learning
the model complexity and severe nonlinearity become serious obstacles to
uncertainty evaluation. Furthermore, the process of machine model training
demands high computing power, not available at the level of personal computers.
This is why so-called pre-trained models are widely used in such areas of
machine learning as natural language processing. The latest example of a
pre-trained model is the Generative Pre-trained Transformer 3 with hundreds of
billions of parameters and a half-terabyte training dataset. Similarly,
mathematical models built from real data are growing in complexity which is
accompanied by the growing amount of training data. However, when machine
models and their predictions are used in decision-making, one needs to estimate
uncertainty and evaluate accompanying risks. This problem could be resolved
with non-parametric techniques at the expense of greater demand for computing
power, which can be offered by modern supercomputers available, including those
utilizing graphical and tensor processing units along with the conventional
central processors.
