The Machine Learning process proceeds by generating random weights, improving the fitting starting from those random weights, then going back and generating more random weights and trying again, and so on, repeating this process a number of times until you get tired of it or until the targets do not seem to be improving for a while. It is not deterministic, and not guaranteed to find the "best" solution.
With Machine Learning it is often difficult to define what the "best" solution would even be -- a lot of the time, improving in one aspect results in some other aspect getting worse. For example, reducing the number of false negatives might come at the expense of over-classifying results as negative.
The "formulas" come up with by Machine Learning are often pretty incomprehensible. For example, it has been reported a number of times that some of the Machine Learning models can predict "race" from x-rays, and no-one understands how it is doing that.
Regression is less non-deterministic, and the models are more understandable, and faster to use for prediction. But at the same time, they tend to be much lower in "surprise" -- in making connections that humans have missed.
