One of the paramount mathematical mysteries of our times is to be able to explain the phenomenon of deep-learning i.e training neural nets.

A set function f on the subsets of a set E is called submodular if it satisfies a natural diminishing returns property: for any two subsets S \subseteq T \subseteq E and an element x outside T, we have f(T + x) - f(T) \leq f(S+x) - f(S).

This will be a tweaked version of my Qualifier talk. I will mostly focus on:
1. The notion of interventional distributions (as defined by Judea Pearl) and how they can be used to identify causal linkages.

Query algorithms are everywhere. Gradient Descent is a well-known algorithm that queries the gradient of a hidden function and moves towards the minimum of the function.