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).
We consider a node-monitor pair, where updates are generated stochastically (according to a known distribution) at the node that it wishes to send to the monitor.
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.
Over the past few decades, asymptotic study of financial systems has become an integral part of practical decision making and analytics. Realistic financial systems are complex, and undesirable events in them are often rare.
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.
