Bayesian Optimization motivation (1/4): problem statement and model classes

Antonio Sala, UPV

Difficulty: ** ,       Relevance: ,      Duration: 15:40

Summary:

This introductory video raises the need for statistical methods in optimization in some classes of applications (say, experimental optimization, data with additive random noise, etc.) where there is no model with ‘perfectly known equations’ to optimize (i.e., under the realm of deterministic optimization).

A set of algorithms that use statistical models in optimization are usually grouped under the name Bayesian optimization in literature. This video states the problem, raises the concept of ’random function’ and the need for a covariance kernel to prove, among other things, continuity of the function and, in general, introduces the idea of stochastic processes and Gaussian processes as the basic tool that most works on Bayesian optimization exploit.

Other descriptions and applications of stochastic processes are covered in the introductory video [estoc1EN]; forthcoming videos will develop the particular Bayesian optimization problem in greater depth, starting with [BOmot2EN].

*Link to my [ whole collection] of videos in English. Link to larger [ Colección completa] in Spanish.