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Fix P2: registry optimization summary no longer claims global solves for τ
The generic TROP optimization summary incorrectly described the global path as solving for (μ, α, β, τ) with τ·D in the residual. The actual implementation solves for (μ, α, β, L) on control data and extracts τ_it post-hoc as residuals. Clarify the summary and point to the dedicated Global section for details. Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
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docs/methodology/REGISTRY.md

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@@ -1275,13 +1275,15 @@ Optimization (Equation 2):
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```
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(α̂, β̂, L̂) = argmin_{α,β,L} Σ_j Σ_s θ_s^{i,t} ω_j^{i,t} (1-W_js)(Y_js - α_j - β_s - L_js)² + λ_nn ||L||_*
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```
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Solved via alternating minimization. For α, β (or μ, α, β, τ in global): weighted least
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squares (closed form). For L: proximal gradient with step size η = 1/(2·max(W)):
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Solved via alternating minimization. For α, β: weighted least squares (closed form).
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The global solver adds an intercept μ and solves for (μ, α, β, L) on control data only,
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extracting τ_it post-hoc as residuals (see Global section below).
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For L: proximal gradient with step size η = 1/(2·max(W)):
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```
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Gradient step: G = L + (W/max(W)) ⊙ (R - L)
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Proximal step: L = U × soft_threshold(Σ, η·λ_nn) × V' (SVD of G = UΣV')
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```
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where R is the residual after removing fixed effects (and τ·D in global mode).
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where R is the residual after removing fixed effects.
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Both the local and global solvers use FISTA/Nesterov acceleration for the
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inner L update (O(1/k²) convergence rate, up to 20 inner iterations per
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outer alternating step).

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