you should check this

https://www.elsevier.com/books/quantum-machine-learning/wittek/978-0-12-800953-6

Speed up and big data.

I mean they have speed up in complexity and increasing data in input.

There are a few recent experimental and theoretical examples of supervised learning protocol on quantum devices

Article Quantum Machine Learning in Feature Hilbert Spaces

https://www.nature.com/articles/s41586-019-0980-2

Up to my knowledge, one important missing element currently is a proof of a quantum supremacy over classical device, i.e., a proof of the existence of a quantum machine learning algorithm performing faster than any classical machine learning algorithm