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 $(X,Y) \in \mathbb{R}^{n \times p} \times \mathbb{R}^n$ be a sample and $R \in \mathbb{R}^{n_1 \times n}, W \in \mathbb{R}^{p \times p_1}$ 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 $O\left( p_1 + C \frac{1}{p_1} \right)$, where $C
This is a theoretical paper in the field of machine learning, part of the ongoing academic research cycle.
It contributes to the mathematical understanding of random projections in OLS regression, which is foundational but not immediately disruptive.
No immediate real-world changes are indicated; it refines theoretical bounds for specific computational methods.
Further theoretical understanding of dimensionality reduction techniques in statistics.
Potential minor improvements in specific computational algorithms utilizing random projections if practically implemented.
Very long-term, could contribute to more efficient large-scale data analysis, but this is highly speculative.
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Read at arXiv cs.LG