We study strong coresets for $\ell_p$ subspace approximation. Given a matrix $A\in\mathbb{R}^{n\times d}$, the goal is to sample and rescale a small number of its rows to obtain $SA$ such that $\left\|SA(I-P_F)\right\|_{p,2}^p=(1\pm\varepsilon)\left\|A(I-P_F)\right\|_{p,2}^p$ simultaneously for every subspace $F\subset...
Hong-Hao Lin, V. Mirrokni, David P. Woodruff· 0 citations
In online inverse linear optimization, a learner recommends an action and then observes the choice of an expert who maximizes a fixed, unknown linear objective on $\mathbb{R}^{d}$; the goal is to learn to optimize this objective without observing it. Sakaue recently obtained the optimal regret $O(\sqrt d)$ with a rando...
Anupam Gupta, Guru Guruganesh, Hong-Hao Lin et al.· 0 citations
The present work builds on the differential-equation method, itself a limiting form of the auxiliary-receiver approach in network information theory using a continuum of degraded receivers, and gives a computer-assisted proof of the Courtade--Kumar conjecture.
Zi-Jie Chen, Amin Gohari, Adel Javanmard et al.· 1 citation
In [AS21], Axiotis and Sviridenko conjectured that the linear dependence on the restricted condition number in sparse convex optimization cannot be improved by a polynomial-time algorithm. We establish their conjectured lower bound for least-squares objectives, conditional on the randomized exact-volume Small-Set Expan...
Hong-Hao Lin, V. Mirrokni, David P. Woodruff· 1 citation
Stellar Colosseum is introduced, a model-agnostic harness for allocating inference across research in mathematics and theoretical computer science that demonstrates the capabilities of Colosseum through open-ended research and evaluations on theorem-proving and competitive programming benchmarks.
Hong-Hao Lin, David P. Woodruff, Yuan Deng et al.· 2 citations· ⚡1
For the $n\times n$ lower-triangular all-ones matrix $Q$, we prove a near-optimal lower bound \[ \gamma_{2,1}(Q) := \inf_{Q=AB} \|A\|_{2\to\infty}\|B\|_{1\to1} = \Omega\!\left( \frac{\log^{3/2}n}{(\log\log n)^{3/2}} \right), \] where the infimum ranges over real factorizations of arbitrary finite inner dimension. This...
Hong-Hao Lin, V. Mirrokni, David P. Woodruff· 2 citations
This work eliminates the residual-stage $O(d)$-bit payload and reduces the leading upper-bound constant by a factor of approximately $5.93$ compared with the two-stage construction of Feng et al.
Hong-Hao Lin, V. Mirrokni, David P. Woodruff· 1 citation
It is proved that for any sub-multiplicative norm, the existence of an efficient classical linear sketch is equivalent to the existence of an efficient robust turnstile algorithm, up to polynomial factors, formalizing $L_1$ embeddability as the fundamental mechanism governing both models.
Elena Gribelyuk, Honghao Lin, David P. Woodruff et al.· 0 citations
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