In this talk I review a couple of applications on Big Data that I personally like and I try to explain my point of view as a Mathematical Optimizer – especially concerned with discrete (integer) decisions – on the subject. I advocate a tight integration of Machine Learning and Mathematical Optimization (among others) to deal with the challenges of decision-making in Data Science. For such an integration I try to answer three questions:

1) what can optimization do for machine learning?

2) what can machine learning do for optimization?

3) which new applications can be solved by the combination of machine learning and optimization?