Large Scale Constrained Linear Regression Revisited: Faster Algorithms via Preconditioning

In this paper, we revisit the large-scale constrained linear regression problem and propose faster methods based on some recent developments in sketching and optimization. Our algorithms combine (accelerated) mini-batch SGD with a new method called two-step preconditioning to achieve an approximate solution with a time complexity lower than that of the state-of-the-art techniques for the low precision case. Our idea can also be extended to the high precision case, which gives an alternative implementation to the Iterative Hessian Sketch (IHS) method with significantly improved time complexity. Experiments on benchmark and synthetic datasets suggest that our methods indeed outperform existing ones considerably in both the low and high precision cases.Comment: Appear in AAAI-1

Masses and decay constants of the heavy tensor mesons with QCD sum rules

In this article, we calculate the contributions of the vacuum condensates up to dimension-6 in the operator product expansion, study the masses and decay constants of the heavy tensor mesons $D_2^*(2460)$, $D_{s2}^*(2573)$, $B_2^*(5747)$, $B_{s2}^*(5840)$ using the QCD sum rules. The predicted masses are in excellent agreement with the experimental data, while the ratios of the decay constants $\frac{f_{D_{s2}^*}}{f_{D_{2}^*}}\approx\frac{f_{B_{s2}^*}}{f_{B_{2}^*}}\approx\frac{f_{D_{s}}}{f_{D}}\mid_{\rm exp}$, where the exp denotes the experimental value.Comment: 13 pages, 13 figure