Finite Bernoulli coordinate sampling

Boolean masks represent coordinate sets. Product weights describe independent coordinate inclusion with a common parameter, using finite real sums.

noncomputable def Complexity.BooleanAnalysis.bernoulliWeight {ι : Type u_1} [Fintype ι] (p : ℝ) (selected : ι → Bool) : ℝ

Product Bernoulli weight of a coordinate set with inclusion parameter p.

Equations

• Complexity.BooleanAnalysis.bernoulliWeight p selected = ∏ i : ι, if selected i = true then p else 1 - p

noncomputable def Complexity.BooleanAnalysis.bernoulliAverage {ι : Type u_1} [Fintype ι] [DecidableEq ι] (p : ℝ) (f : (ι → Bool) → ℝ) : ℝ

Finite expectation over independently selected coordinates. It is a probability expectation when 0 ≤ p ≤ 1.

Equations

• Complexity.BooleanAnalysis.bernoulliAverage p f = ∑ selected : ι → Bool, Complexity.BooleanAnalysis.bernoulliWeight p selected * f selected