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b317718 | 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 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 | import OAI.Probability.GaussianReplacement.Sampling
namespace OAI
open MeasureTheory ProbabilityTheory Set Filter
open scoped ENNReal NNReal RealInnerProductSpace Topology
noncomputable section
universe u
namespace CurrentProjection
namespace StreamKernel
def sharedSuccess {d M T : ℕ} {Ξ : Type*} [MeasurableSpace Ξ]
(π : Measure Ξ) (K : Ξ → CompletedLearner d M T) (ε : ℝ) : ℝ≥0∞ :=
∫⁻ ξ, (K ξ).uniformSuccess ε ∂π
def StreamingMain (p₀ : ℝ≥0∞) : Prop :=
∃ c : ℝ, 0 < c ∧ ∀ M : ℕ → ℕ,
Asymptotics.IsLittleO atTop (fun d => (M d : ℝ)) (fun d => (d : ℝ)^2) →
∃ d₀ : ℕ, ∀ d : ℕ, d₀ ≤ d → ∀ T : ℕ, ∀ ε : ℝ,
0 < ε → ε ≤ 1/10 →
∀ (Ξ : Type) [MeasurableSpace Ξ] [StandardBorelSpace Ξ]
(π : Measure Ξ) [IsProbabilityMeasure π]
(K : Ξ → CompletedLearner d (M d) T),
AEMeasurable (fun ξ => (K ξ).uniformSuccess ε) π →
p₀ ≤ sharedSuccess π K ε → c * (d : ℝ) * Real.log (1/ε) ≤ (T : ℝ)
end StreamKernel
def CriticalStreamingMain : Prop := StreamKernel.StreamingMain (3/5)
def LevelsStreamingMain : Prop := StreamKernel.StreamingMain (2/3)
def HybridStreamingMain : Prop := StreamKernel.StreamingMain (2/3)
def FiberStreamingMain : Prop := StreamKernel.StreamingMain (2/3)
end CurrentProjection
end
end OAI
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