Bidirectional Random Projections

arXiv:2606.10377v1 Announce Type: cross Abstract: This paper analyzes bidirectional random projections for ordinary least squares (OLS) regression under the fixed design setting. Let (X,Y) in R^{n imes p} imes R^n be a sample and R in R^{n_1 imes n}, W in R^{p imes p_1} be two properly distributed random projections. We develop an expected excess loss bound for the OLS estimator built on (WXR, WY). Compared to an established bound for OLS estimator built on (XR, Y), the gap is approximately Oleft( p_1 + C frac{1}{p_1} right), where C scales with n_1/n and can be negative for small n_1/n. Its implications are confirmed by numerical results on real-world data.

Source: arXiv cs.LG | 2026-06-10