A cumulative distribution function (CDF) gives the probability that a random variable is less than or equal to a chosen threshold. Geometrically, it is the area under a distribution curve to the threshold’s left. section 4.2.2
In probability-of-improvement optimization, the incumbent is the cutoff. The CDF measures the area that does not improve; subtracting it from 1 gives the probability that a candidate exceeds the incumbent. section 4.2.2
Computing improvement probability
For a candidate at 0, obtain its Gaussian-process predictive mean and standard deviation, form a Normal distribution, and evaluate 1 - normal.cdf(train_y.max()). The result, such as 0.8305, is the candidate’s probability of improvement. section 4.2.2
Figure 4.11 Flowchart of how the PoI score is computed. By following this procedure, we can compute how likely any candidate point is to be able to improve from the incumbent.
Follow the flow from predictive mean and standard deviation to the CDF complement and the resulting probability-of-improvement score. section 4.2.2
