| import OAI.Probability.GaussianReplacement.Sampling |
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| namespace OAI |
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| open MeasureTheory ProbabilityTheory Set Filter |
| open scoped ENNReal NNReal RealInnerProductSpace Topology |
| noncomputable section |
| universe u |
| namespace CurrentProjection |
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| namespace StreamKernel |
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| 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 |
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| 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) |
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| end StreamKernel |
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| 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) |
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| end CurrentProjection |
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| end |
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| end OAI |
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