[jules]

While I would like to agree with this based on aesthetics, it didn't work that way in practice. A lot of the most successful machine learning algorithms do not have a statistical grounding or did not when they were invented. E.g. neural networks, SVM, low rank matrix approximation, k-means, decision trees/forests.

[formulaT]

Yes, the core algorithms do have this tendency (which is the exciting thing about machine learning per se), but statistics provides the context to understand them.

E.g. people used to say "neural networks are a simple, flexible functional form for y = f(X,theta)". This turned out to be wrong: SGD training of neural networks has more advantages than the flexibility of the functional form. But it was a good hypothesis and starting point.

SVMs and decision trees have no statistical justification I know of. Low rank matrix approximation and k-means are justified by latent variables and non-parametric kernel methods respectively. I agree these justifications came after the fact, but they do give a way to understand how these models work.

Most importantly, all of the small tasks surrounding training a model are purely statistical, e.g. cross validation, different measures of accuracy, handling endogenous variables, etc.