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Bidirectional random projections
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DOI：10.1016/j.spl.2026.110806.png)
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Abstract
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This paper analyzes bi-directional random projection for ordinary least square (OLS) regression under the fixed design setting. Let (X, Y) is an element of Rn & times;p & times; Rnbe a sample and R is an element of Rn1 & times;n, W is an element of Rp & times;p1 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 O p1+C 1, where C scales with n1/nand can be p 1 negative for small n1/n. Its implications are confirmed by numerical results on real-world data.
Keywords:
Random projection
Bidirectional random projection
Ordinary least square
Expected excess loss
High dimensional data
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