Bayesian Optimization motivation (3/4): computation of posterior and decision (acquisition) on next sample (outline)

Antonio Sala, UPV

Difficulty: **** ,       Relevance: ,      Duration: 10:49

Summary:

This video continues with the introduction and motivation to Bayesian Optimization problems which was started in video [BOmot1EN].

In video [BOmot2EN] we concluded that BO algorithms end up comprising the following steps:

• Set up a prior statistical model

• Acquire samples (this may be a costly procedure in some relevant application cases)

• Compute a posterior (conditional to the measurements)

• Carry out a statistical analysis on the posterior to decide next sample, and go to step 2, unless some termination criteria is met.

This video expands on the third step of the methodology, which is carried out in a Gaussian process with the conditional formulae from multivariate normal distributions.

The last step is also outlined... next sample may be selected in order to optimize the expected value (EV), probability of improving (PI), expected improvement (EI), we may be risky and choose a lower confidence bound (we will not likely achieve it, but we would obtain a very good sample if we did), or optimize the information gain by sampling (entropy search). A very brief description of each of these options is presented, just to get a glimpse of the main ideas, but a detailed analysis is be the topic of other materials that analyse BO in more depth, see videos [boPIEN] and [boENEN].

A quick numerical example of the methodology appears in video [boloop1EN]. Application cases and concluding remarks in video [BOmot4EN] will conclude this brief presentation of the Bayesian optimization procedures.

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