In this talk, we discuss three problems. The first is on an asynchronous multi-antenna wireless communication system and the later two are on collaborative estimation.
a) It is known that we can exploit certain type of asynchronism in a wireless communication system to our advantage. We quantify the capacity of a multi-antenna communication system with asynchronism, and observe that it can show significant improvement over a synchronous system.
b) We analyze a local popularity based recommendation algorithm that uses information about a set of similar users to recommend an item to a user. For a particular random matrix model, we would identify regimes where the local popularity based algorithm works and where it does not. We will also discuss some empirical results in light of our theoretical results and compare with an approach based on low-rank matrix completion.
c) We consider a collection of regression experiments which show clustered behavior. We study and compare several methods for this, demonstrate their applicability to the Yahoo Learning-to-rank Challenge (YLRC) dataset, and investigate an associated mathematical model. Based on empirical evaluation on the YLRC dataset as well as simulated data, we identify that a local regression (LoR) scheme is a good practical choice: it yields best or near-best prediction performance at a reasonable computational load, and it is less sensitive to the choice of the algorithm parameter. We will also discuss some analysis of the LoR method for an associated mathematical model, which sheds light on optimal parameter choice and prediction performance.