> he criticizes all of machine learning as simply unprincipled revival of nonparametric curve estimation

He's right. 'Machine learning' is just statistics with better, cleaner names for things. The underlying theory is the same.

(The commenter below says that 'statistics explains, ML predicts', but this isn't really true. Both statistics and ML build models, whether you use these models for prediction or explanation is up to you.)

One problem is that the 'statistics' as usually taught in a college course or explained in a textbook comes from a much earlier age, before supercomputers were available to the average man; in essence, it's like a kind of machine learning as done by paper-and-pencil. In contrast, 'ML' assumes from the start that computing resources will be available.