Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.cross-validation

The Applied Higher-Order Functions cataloguesrc/rainbow/algorithms/proofs/ahof/cross_validation.clj3 definitions, 3 theorems

AHoF V4 worked cross-validation over exact rationals. A two-fold evaluation scores the folds 3/4 and 1/4; their total is exactly 1, and dividing by the fold count 2 gives the cross-validation mean 1/2. The total and the mean are proved by cross-product equivalence, composing the exact list sum with exact rational division. Scope (measured by the kernel): this module has 3 worked instances (statements about specific values). None of its theorems is a guarantee about the algorithm for all inputs; `lein verify rainbow.algorithms.proofs.ahof.cross-validation` prints this classification.

ahof-v4/fold-scores :
  → List ℚ≥0

ahof-v4/fold-count :
  → ℚ≥0

ahof-v4/mean :
  → ℚ≥0

ahof-v4/total-is-one :
  → estimation/log-likelihood-total ahof-v4/fold-scores = 1

ahof-v4/mean-is-one-half :
  → ahof-v4/mean = 1/2

ahof-v4/cross-validation :
  → proposition/conjunction (estimation/log-likelihood-total ahof-v4/fold-scores = 1) (ahof-v4/mean = 1/2)