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数学分析笔记系列(1)-实数的完备性

九月,便开始了PhD的征途,在我面前的将是知识的星辰大海。我从事的是low-level image processing以及machine learning领域,强有力的数学工具将有助于问题的思考以及让我对繁杂数学符号少一些恐惧。九月中旬,我开始旁听香港城市大学Ciarlet教授的泛函分析课程,弱鸡的实数分析让我很难follow他的进度。因此,我才打算在科研空闲之余重新捡起数学分析相关...

Principle of Microeconomics: Introduction

1. Introduction Economics is social science that examines how people choose among the alternative availiable to them, the foundamental issue of which is scarcity. Economics is quasi-science, becau...

Logistics Regression

1. Logistic Regression Data: Inputs are continuous vectors of length $K$. Outputs are discrete. Model: Logistic function applied to dot product of parameters with input vector. Learning: Fin...

Linear Regression

1. Linear Regression Algorithm 1.1 Linear Regression and Basis Function Originally, Linear Regression is a linear combination of input variables, the goal of linear regression is find a polynomia...

Naive Bayes and Logistics Regression

1. Naive Bayes Algorithm First, we see the whole picture of Naive Bayes. Naive bayes algorithm is supervised learning algorithm, it has two formulations for different inputs, such as discrete-valu...

浅谈中国式的“孝文化”

“仁义礼智信,忠孝廉耻勇” 是中华流传几千年的传统普世价值观。其中,“孝”字,在经过千年洗礼之后,便深深植入中国广大老百姓的骨髓,扎根于生活的方方面面。现代社会价值体系中,“孝”也当仁不让地成为一种政治正确,被人说“不孝”,那便是一种极大的罪过。 在成长过程中,我印象中,有许多人,其中包括亲戚朋友,邻里街坊,都会时不时地当着父母的面夸赞我,然后转身便我说:“xx, 你爸妈辛辛苦苦赚钱供你读...

Analysis: Interger and Rational Number

1. Integers 1.1 The definition of intergers (Definition-integer): An integer is an expression of the form $a-b$, where $a$ and $b$ are natural numbers. Two integers are considered to be equal, $a...

Note(7)--Uniform Laws, empirical process theory and VC dimension

1. Uniform Convergence and Empirical Risk Minimization Empirical risk minimization is core topic in machine learning. Let’s take a binary classification as example. Given a training set ${(X_{1},...

Note(8)-- Sufficiency Statistics

1.Sufficient Statistic and Factorization Theorem 1.2 The Definition of Sufficient Statistic Sufficiency Statistics: A statistics $T(X_{1},…,X_{n})$ is said to be sufficient for the parameter $\th...

Variational Inference

1. What’s variational inference? Variational inference is an approximate technique, which is widely used in inference problem in modern statistic. As we all know, inferene problem is especially im...