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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 27 28 29 30 31 32 33 34 35 | import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Basic.Real.Basic
namespace OAI
/-!
# Finite conditional seed kernels
The observation map can include the branch and the sacrificed mask. Its domain
is the *complete* source seed, so conditioning does not discard unused coins.
These definitions are independent of every proposed selection-rule proof.
-/
namespace MatroidProphet.Secretary
open scoped BigOperators
variable {α β : Type*} [Fintype α] [DecidableEq α] [DecidableEq β]
/-- The source mass of a fiber of the observation map. -/
noncomputable def fiberMass (p : α → ℝ) (f : α → β) (b : β) : ℝ :=
∑ a, if f a = b then p a else 0
/-- The conditional source mass, totalized by a fixed point mass on empty fibers.
The fallback only concerns observations of source probability zero. -/
noncomputable def fiberKernel (p : α → ℝ) (f : α → β) (fallback : α)
(b : β) (a : α) : ℝ :=
if fiberMass p f b = 0 then
if a = fallback then 1 else 0
else if f a = b then p a / fiberMass p f b else 0
end MatroidProphet.Secretary
end OAI
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