Latest Posts

• Sequence Model

  We illustrate basic inequality, noise complexity (e.g. Radamacher complexity, Gaussian complexity), and localization for the least square estimator in the simplest sequence model setting.

• From High-Dimensional Features to Random Approximations: The Evolution of Scalable Kernel Methods

  We describe how insight from computational mathematics shape this ​scalability journey.

• Sparse Linear Models

  This is a note on sparse linear models in high dimension.

• Dyson Series

  Some quantum mechanical calculation.

• Linear and Convex Programming

  Consider the general constrained optimization problem $\eqref{P}$ shown below, where we have not assumed anything regarding the functions $f$, $h$, $l$ (like linearity or convexity).

• Boolean Analysis

  Denote

• Point Estimation

  In this article, I breifly review the theory of point estimation.

• Classical Gradient Descent Analysis

  In this article, I recap the classical gradient descent analysis.

• Completely Positive Map

  In this article, I describe $C^*$-algebra, complete positive map, and its relationship to quantum mechanics.

• Diffusion Models

  Let us first recall how to reverse a classical diffusion process.

• Investigation in Plane Geometry

  This article records some of my proofs in plane geometry.

• New Geometry Problems

  This article records some problems in plane geometry that I, my friend Yonggang Ren, and my middle school teacher Lingfeng Chen have discovered.

• An IMO Problem Revisited

  This article records some solutions of a problem in plane geometry that I discovered.