park-2025-lda-estimator-lower-variance
IN premise — summaries/2026/08/24/park-2024-categorical-hierarchical-concepts-sR-references-chunk-1.md
Created 2026-08-25T02:58:25+00:00
The LDA direction estimator (Eq. 5.2, using Ledoit-Wolf shrinkage for covariance) is more stable (lower variance) than the simple mean vector E(g_w) for estimating ℓ̄_w.
Summary
When estimating the average direction of separation between groups, using the shrinkage-based LDA formula gives a steadier, less noisy result than simply averaging the individual vectors. This matters because downstream steps that rely on this estimate will be less prone to wild swings from sample-to-sample, making the overall pipeline more reliable.