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dd14c26 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | import OAI.Probability.MatroidProphet.Main
namespace OAI
namespace MatroidProphet
open Finset
/-- The first `K` labels of a complete order, used only to specify the experiment. -/
def orderPrefix {n : ℕ} (π : ArrivalOrder n) (K : ℕ) : Finset (Fin n) :=
Finset.univ.filter fun e => (π.symm e).val < K
/-- Labels visible in the observation prefix of the currently available history. -/
def prefixLabels {n : ℕ} {k : Fin n} (K : ℕ) (h : History n k) : Finset (Fin n) :=
(Finset.univ.filter fun j : Fin (k.val + 1) => j.val < K).image fun j => (h j).1
/-- The observed weights, extended by zero away from the observation prefix.
Repeated labels in malformed histories are summed; genuine histories have none. -/
noncomputable def prefixWeights {n : ℕ} {k : Fin n} (K : ℕ)
(h : History n k) : Weights n :=
fun e => ∑ j : Fin (k.val + 1), if j.val < K ∧ (h j).1 = e then (h j).2 else 0
end MatroidProphet
end OAI
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