Session on Mathematics of..

Session on Mathematics of Machine Learning

Wednesday April 4, lecture hall 80

Organizer: Peter Grünwald

14.00-14.40 Tim van Erven, Leiden University
Online Convex Optimization: From Gambling to Minimax Theorems by Playing Repeated Games
14.40-15.20 Wouter Koolen, CWI
Bandit Algorithms for Best Arm Identification and Game Tree Search
15.20-16.00 Rui Castro, TU/e
On adaptive sensing and active learning for inference of high dimensional sparse signals


Dr. Tim van ErvenOnline Convex Optimization: From Gambling to Minimax Theorems by Playing Repeated Games
Abstract: Modeling sequential decision problems as repeated games has a long history in statistics, information theory and machine learning. Using the modern unified setting of online convex optimization, I will highlight applications that range from betting on the outcomes of football games to proving von Neumann's minimax theorem, and I will introduce open questions at the frontier of current research related to a basic model for portfolio selection in finance and to optimization of deep learning methods in machine learning.


Dr. Wouter Koolen: Bandit Algorithms for Best Arm Identification and Game Tree Search
Abstract: Sequential allocation problems with partial feedback (aka Bandit problems) have a rich tradition including applications to drug testing,  online advertisement and more recently min-max game tree search. We will start by looking at the fundamental statistical identification problem. In particular, we will see how sample complexity lower bounds can be "inverted" to derive matching optimal algorithms. We will then look at extensions of the framework suitable for finding the optimal move in min-max game trees. Throughout, the talk will focus on the main statistical and computational challenges and ideas.


Dr. Rui Castro: On adaptive sensing and active learning for inference of high dimensional sparse signals
Abstract: In many scenarios where machine learning and statistics tools are used one typically starts with a set of previously collected data, in order to learn generic relations between the various observed variables. This means such approaches rely on passive data collection methodologies. However, in many practical scenarios it is possible to adjust the data collection process based on information gleaned from previous observations, in the spirit of the "twenty-questions" game, in what is known as adaptive sensing, active learning, or sequential design of experiments. The intricate relation between data analysis and acquisition in adaptive sensing paradigms is extremely powerful, but creates complicated data dependencies making it challenging to devise simultaneously practical and theoretically sound learning methodologies. In this talk I consider estimation and detection of high-dimensional sparse signals in noise, and present (near) optimal adaptive sensing procedures that provably outperform the best possible inference methods based on non-adaptive sensing. The methods developed can also be used also for adaptive compressive sensing and for detection of (sparse) correlations, as well dealing with dynamical scenarios where the signal is changing as the data is being collected (this talk is based mainly on joint works with Ervin Tánczos).