Big Data Analysis

High dimensional probability

Concentration inequality

Sub-Gaussian random variables

Chernoff bounds

Hoeffding's inequality

Maximal inequalities

High dimensional linear regression

Ordinary least square

Compressed sensing

Lasso

Variations of Lasso including group lasso, fused lasso, adaptive lasso, etc.

General high dimensional M-estimators

Variable selection consistency

High dimensional Optimization

Convex geometry

Lagrange duality

Gradient descent

Proximal gradient descent

LARS

ADMM

Mirror descent

Stochastic optimization

Large-Scale Inference

Linear model hypothesis testing

High dimensional inference

Chi-square test

Maximal test

Higher criticism

False discovery rate control