A randomized Halton algorithm in R

置乱 Halton 点的增益系数

Gain coefficients for scrambled Halton points

本文研究置乱 Halton 点在随机化拟蒙特卡洛中的方差增益，证明其增益系数具有 $O(\log d)$ 的显式上界，并给出 $6\leqslant d\leqslant10^6$ 时的具体界。

Quasi-Monte Carlo for an Integrand with a Singularity along a Diagonal in the Square

Quasi-Monte Carlo methods are designed for integrands of bounded variation, and this excludes singular integrands. Several methods are known for integrands that become singular on the boundary of the unit cube $[0,1]^d$ or at isolated possibly unknown points within $[0,1]^d$. Here we consider functions on the square $[0,1]^2$ that may become singular as the point approaches the diagonal line $x_1=x_2$, and we study three quadrature methods. The first method splits the square into two triangles separated by a region around the line of singularity, and applies recently developed triangle QMC rul…

稀疏随机Kaczmarz算法的扩展：多测量向量问题

Extension of Sparse Randomized Kaczmarz Algorithm for Multiple Measurement Vectors

本文提出改进的随机Kaczmarz算法解决多测量向量问题，通过共同稀疏支持实现更高效的恢复与收敛。

RPEM: Randomized Monte Carlo Parametric Expectation Maximization Algorithm

Inspired from quantum Monte Carlo, by using unbiased estimators all the time and sampling discrete and continuous variables at the same time using Metropolis algorithm, we present a novel, fast, and accurate high performance Monte Carlo Parametric Expectation Maximization (MCPEM) algorithm. We named it Randomized Parametric Expectation Maximization (RPEM). In particular, we compared RPEM with Monolix's SAEM and Certara's QRPEM for a realistic two-compartment Voriconazole model with ordinary differential equations (ODEs) and using simulated data. We show that RPEM is 3 to 4 times faster than SA…

充分利用现有资源：用于矩阵计算的高效随机算法

Make the most of what you have: Resource-efficient randomized algorithms for matrix computations

本研究提出高效随机算法，用于在有限数据预算下提升矩阵计算的精度和速度，特别关注低秩近似、隐式矩阵属性估计及超定线性最小二乘问题的稳定性。

用于主成分分析与奇异值分解分布式计算的随机算法

Randomized algorithms for distributed computation of principal component analysis and singular value decomposition

本文提出面向高长方矩阵 PCA/SVD 及任意矩阵低秩近似的分布式随机算法，并在 Spark 上证明其优于现成确定性实现且左奇异向量接近机器精度正交归一。