Author

Junwei Lu

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Preprint Sep 2026

Optimal Linear Functional Estimation for Proportionally High-Dimensional Linear Models

We study estimation of a linear functional in random-design linear models when $\gamma=p/n \in (1, \infty)$ under the dense regime where the design covariance is unknown, and neither the regression vector nor the precision matrix is assumed sparse. Suppose the spectrum of the design covariance belongs to $[\ell,L]$, we...

Jun-Wei Lu · 0 citations

Preprint Aug 2026

On Unavoidable Faces of High-Dimensional Polytopes

Kalai's cube--simplex conjecture asserts that for all positive integers $\ell,k$, there is an integer $f(\ell,k)$ such that every polytope of dimension at least $f(\ell,k)$ has either a simplex $\ell$-face or a cube $k$-face; let $f_s(\ell,k)$ denote the threshold restricted to simple polytopes. Finiteness of $f(\ell,k...

J. De Loera, Ethan X. Fang, Sheng Guo et al. · 0 citations