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Random matrix theory plays a central role in statistical physics, computational mathematics and engineering sciences, including data assimilation, signal processing, combinatorial …
Among the data structures commonly used in machine learning, graphs are arguably one of the most general. Graphs allow the modelling of complex objects, each of which can be …
This monograph presents the main complexity theorems in convex optimization and their corresponding algorithms. It begins with the fundamental theory of black-box optimization and …
Bayesian methods for machine learning have been widely investigated, yielding principled methods for incorporating prior information into inference algorithms. This monograph …
Optimization is a ubiquitous modeling tool and is often deployed in settings which repeatedly solve similar instances of the same problem. Amortized optimization methods use …
Over the last decade, Approximate Message Passing (AMP) algorithms have become extremely popular in various structured high-dimensional statistical problems. Many of the original …
Many problems of recent interest in statistics and machine learning can be posed in the framework of convex optimization. Due to the explosion in size and complexity of modern …
Thompson sampling is an algorithm for online decision problems where actions are taken sequentially in a manner that must balance between exploiting what is known to maximize …
The authors of this monograph survey recent progress in using spectral methods including matrix and tensor decomposition techniques to learn many popular latent variable models. …