GwanSiu Blog

Keep Learning, Shaping the Future

Note(7)--Uniform Laws or Uniform Tail Bounds

Previously, we discussed LLNs and tail bounds that apply to a collection of random variables taken together. In this blog, we mainly focus on uniform laws or uniform tail bounds. 1. Uniform co...

Note(6)--Extension of CLT

In this blog, we just talk about some extension of CLT. Lyapunov CLT: just requires only independent but not identically idstributed. Multivariate CLT: Original CLT is applied to one...

Note(5)--Convergence

In this blog, we will talk about Slutsky’s theorem and center limit theorem. 1. Continuous Mapping Theorem If a sequence $X_{1},…,X_{n}$ converges in probability to $X$ then for any continuou...

Note(2)--Inequality

In the early stage of statistics community, researchers paid their attention to investigate Averages of independent random variables concentrate around their expectation. Researchers try to ans...

Note(1)--Basic Review of Basic Probability

The reference materials are based on cmu 10-705,2016 and 2017. In note(1), we just review some necessary basic probability knowledge. 1. Axioms of Probability $\mathbb{P}(A)\geq 0$ ...

Analysis--Set Theory

In this article, ZFC axiom will be discussed. 1. ZFC Axiom Axiom 1(Sets are objects): If A is a set, then A is also an object. In particular, given two sets A and B, it is meaningful to ask w...

Analysis--Natural Numbers

At the begining of this year, I plan to learn mathematics analysis and it will be helpful for my future research. Thus, I decide to open a new session in my blog and write some article about tha...

Image Processing-Image Segmentation

In this article, some basic segmentation techniques are introduced: (1). Hough Transform; (2). Otsu’s Segmentation; (3).Interactive Image Segmentation; (4). Graph Cuts; (5).Mumford Shah; (6). Ac...

Image Processing-Image Restoration

In this article, image restoration and its techniques are introduced: (1). the basic concept of image restoration and its difference from image enhancement. (2).The inverse filter (3).The wiener...

Image Processing-Image Enhancement

In this article, image enhancement techology is introduced. It mainly contains: (1) Quantization and smapling; (2) Point operation: histogram equalization; (3) Spatial filter: box average(local ...