Systems | Information | Learning | Optimization
 

Finding low-rank solutions via the Burer-Monteiro approach, efficiently and provably

Video: https://vimeo.com/192676538 A low rank matrix can be described as the outer product of two tall matrices, where the total number of variables is much smaller. One could exploit this observation in optimization: e.g., consider the minimization of a convex function f over low-rank matrices, where the low-rank set is …

Deep Learning in the Enhanced Cloud

Video: https://vimeo.com/192473161 Deep Learning has emerged as a singularly critical technology for enabling human-like intelligence in online services such as Azure, Office 365, Bing, Cortana, Skype, and other high-valued scenarios at Microsoft. While Deep Neural Networks (DNNs) have enabled state-of-the-art accuracy in many intelligence tasks, they are notoriously expensive and …

Stochastic Nested Composition Optimization and Beyond

Video: https://vimeo.com/191080400 Classical stochastic optimization models usually involve expected-value objective functions. However, they do not apply to the minimization of a composition of two or multiple expected-value functions, i.e., the stochastic nested composition optimization problem. Stochastic composition optimization finds wide application in estimation, risk-averse optimization, dimension reduction and reinforcement learning. …

Mixed-Integer Convex Optimization

Video: https://vimeo.com/189163584 Mixed-integer convex optimization problems are convex problems with the additional (non-convex) constraints that some variables may take only integer values. Despite the past decades’ advances in algorithms and technology for both mixed-integer *linear* and *continuous, convex* optimization, mixed-integer convex optimization problems have remained relatively more challenging and less …

The smart light sheet microscope

Video: https://vimeo.com/189185951 Fluorescence light-sheet microscopy such as Selective Plane Illumination Microscopy (SPIM) [1] is a powerful tool to image developmental processes in vivo with high-resolution over large tissue volumes [2]. The main advantages of the technology are the minimal phototoxicity due to the confined fluorescence excitation and the fast full-frame …

Geometric tools in information theory

Video: https://vimeo.com/184352560 Concepts in geometry often have parallels in information theory; for example, volume and entropy, surface area and Fisher information, sphere-packing and channel coding, and Euclidean balls and Gaussian distributions, to name a few. These similarities provide a simple way to posit theorems in one area by translating the …