How can you prove that one improvement you've brought to an algorithm is really an improvement over not doing anything? Are you familiar with A/B testing?

How can you prove that one improvement you've brought to an algorithm is really an improvement over not doing anything? Are you familiar with A/B testing?



Example with linear regression:
- F-statistic (ANOVA)

F=RSS1−RSS2p2−p1RSS2n−p2F=RSS1−RSS2p2−p1RSS2n−p2

p1p1: number of parameters of model 1
p2p2: number of parameters of model 2
nn: number of observations

Under the null hypothesis that model 2 doesn't provide a significantly better fit than model 1, FF will have an FF distribution with (p2−p1,n−p2)(p2−p1,n−p2) degrees of freedom. The null hypothesis is rejected if the FF calculated from the data is greater than the critical value of the FF distribution for some desired significance level.

Others: AIC/BIC (regression), cross-validation: assessing test error on a test/validation set

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