PDF version PDF & CDF The probability density function is $$f(x; \mu, \sigma) = {1\over\sqrt{2\pi}\sigma}e^{-{1\over2}{(x-\mu)^2\over\sigma^2}}$$ The cumulative distribution function is defined by $$F(x; \mu, \sigma) = \Phi\left({x-\mu\over\sigma}\ri…

PDF version PDF & CDF The probability density function of the uniform distribution is $$f(x; \alpha, \beta) = \begin{cases}{1\over\beta-\alpha} & \mbox{if}\ \alpha < x < \beta\\ 0 & \mbox{otherwise} \end{cases} $$ The cumulative distribu…

PDF version PDF & CDF The exponential probability density function (PDF) is $$f(x; \lambda) = \begin{cases}\lambda e^{-\lambda x} & x\geq0\\ 0 & x < 0 \end{cases}$$ The exponential cumulative distribution function (CDF) is $$F(x; \lambda) =…

PDF version PMF Suppose that a sample of size $n$ is to be chosen randomly (without replacement) from an urn containing $N$ balls, of which $m$ are white and $N-m$ are black. If we let $X$ denote the number of white balls selected, then $$f(x; N, m,…

PDF version PMF Suppose that independent trials, each having a probability $p$, $0 < p < 1$, of being a success, are performed until a success occurs. If we let $X$ equal the number of failures required, then the geometric distribution mass function…

PDF version PMF A discrete random variable $X$ is said to have a Poisson distribution with parameter $\lambda > 0$, if the probability mass function of $X$ is given by $$f(x; \lambda) = \Pr(X=x) = e^{-\lambda}{\lambda^x\over x!}$$ for $x=0, 1, 2, \cd…

PDF下载链接 PMF If the random variable $X$ follows the binomial distribution with parameters $n$ and $p$, we write $X \sim B(n, p)$. The probability of getting exactly $x$ successes in $n$ trials is given by the probability mass function: $$f(x; n, p) =…

PDF version PMF Suppose there is a sequence of independent Bernoulli trials, each trial having two potential outcomes called "success" and "failure". In each trial the probability of success is $p$ and of failure is $(1-p)$. We are obs…

PRML Chapter 2. Probability Distributions P68 conjugate priors In Bayesian probability theory, if the posterior distributions p(θ|x) are in the same family as the prior probability distributionp(θ), the prior and posterior are then called conjugate d…

Common Probability Distributions Probability Distribution A probability distribution describes the probabilities of all the possible outcomes for a random variable. A discrete random variable if one for which the number of possible outcomes can be co…

2.1. Binary Variables 1. Bernoulli distribution, p(x = 1|µ) = µ 2.Binomial distribution + 3.beta distribution(Conjugate Prior of Bernoulli distribution) The parameters a and b are often called hyperparameters because they control the distribution of…

主讲人 网络上的尼采 (新浪微博: @Nietzsche_复杂网络机器学习) 网络上的尼采(813394698) 9:11:56 开始吧,先不要发言了,先讲PRML第二章Probability Distributions.今天的内容比较多,还是边思考边打字,会比较慢,大家不要着急,上午讲不完下午会接着讲. 顾名思义,PRML第二章Probability Distributions的主要内容有:伯努利分布. 二项式 –beta共轭分布.多项式分布 -狄利克雷共轭分布 .高斯分布 .频率派和贝叶斯派…

Basics of Probability Probability density function (pdf). Let X be a continuous random variable. Then a probability distribution or probability density function (pdf) of X is a function f(x) such that any two numbers a and b with That is, the probabi…

Getting started with react.js: basic concept of React component 1 What is React.js React, or React.js is an open source javascript framework from Facebook. React.js is ideal for doing view rendering work in large scale or single page application (SPA…

摘要:Tensorflow Distributions提供了两类抽象:distributions和bijectors.distributions提供了一系列具备快速.数值稳定的采样.对数概率计算以及其他统计特征计算方法的概率分布.bijectors提供了一系列针对distribution的可组合的确定性变换. 1.Distributions 1.1 methods 一个distribution至少实现以下方法:sample.log_prob.batch_shape_tensor.event_sh…

http://msdn.microsoft.com/library/ee354180.aspx Steps: Designing a Service Contract Implementing a WCF Service What instancing mode will be used? What concurrency mode will be used? Are transactions supported for this service type? Should the service…

tomcat/mysql/hadoop http://www.linuxidc.com/Linux/2014-06/103776p2.htm http://www.aikaiyuan.com/2993.html http://xdays.me/zabbix%E7%9B%91%E6%8E%A7hadoop.html zabbix是一套基于WEB界面的提供分布式系统监视以及网络络监视功能的企业级的开源解决方案. zabbix能监视各种网络参数,保证服务器系统的安全运营:并提供灵活的通知机制以让系统管…

Flink基础概念 本文描述Flink的基础概念,翻译自https://ci.apache.org/projects/flink/flink-docs-release-1.0/concepts/concepts.html 一.程序(Progrram)和数据流(Dataflows) Flink程序的构建基础为Streams和Transformations.其中Streams为中间结果,而Transformations是将一到多个Streams作为输入,计算产生一到多个Streams作为输出的操作(…

博客内容取材于:http://www.cnblogs.com/tornadomeet/archive/2012/06/24/2560261.html 参考资料: UFLDL wiki UFLDL Stanford tornadomeet博客整理得很好,欣赏这样的学习态度. 该博客基本取材于UFLDL,在两者取舍间还是选择按照tornadomeet博客的剧本走一遍. 因为大部分概念都已熟知,在此过一遍的意义在于查缺补漏,巩固基础. 该博客年初发现,如今我也有了这样的“博客导航”,这便是正能量的传播…

Deep Learning中会接触到的关于Info Theory的一些基本概念.…

在看LDA的时候,遇到的数学公式分布有些多,因此在这里总结一下思路. 一.伯努利试验.伯努利过程与伯努利分布 先说一下什么是伯努利试验: 维基百科伯努利试验中: 伯努利试验(Bernoulli trial)是只有两种可能结果的单次随机试验. 即:对于一个随机变量而言,P(X=1)=p以及P(X=0)=1-p.一般用抛硬币来举例.另外,此处也描述了伯努利过程: 一个伯努利过程(Bernoulli process)是由重复出现独立但是相同分布的伯努利试验组成,例如抛硬币十次. 维基百科中,伯努利过程…

统计学中最常见的几种概率分布分别是正态分布(normal distribution),t分布(t distribution),F分布(F distribution)和卡方分布(χ2 distribution,chi-square distribution),其中后三种属于抽样分布. 为什么要研究概率分布呢?因为通过研究概率分布,我们可以找出数据的分布规律,并根据这些规律来解决特定条件下的问题.比如:假设随机变量X服从某个已知的分布,我们就可以利用这个分布对X的取值是否显著异于分布期望值进行检验.…

Basic Mathematics You Should Mastered 2017-08-17  21:22:40  1. Statistical distance  In statistics, probability theory, and information theory, a statistical distance quantifies the distance between two statistical objects, which can be two random va…

R编程语言已经成为统计分析中的事实标准.但在这篇文章中,我将告诉你在Python中实现统计学概念会是如此容易.我要使用Python实现一些离散和连续的概率分布.虽然我不会讨论这些分布的数学细节,但我会以链接的方式给你一些学习这些统计学概念的好资料.在讨论这些概率分布之前,我想简单说说什么是随机变量(random variable).随机变量是对一次试验结果的量化. 举个例子,一个表示抛硬币结果的随机变量可以表示成           Python   1 2 X = {1 如果正面朝上,    …

The Basics of Probability Probability measures the amount of uncertainty of an event: a fact whose occurence is uncertain. Sample space refers to the set of all possible events, denoted as . Some properties: Sum rule: Union bound: Conditional probabi…

The Central Limit Theorem (CLT), and the concept of the sampling distribution, are critical for understanding why statistical inference works. There are at least a handful of problems that require you to invoke the Central Limit Theorem on every ASQ…

概率和信息论. 概率论,表示不确定性声明数学框架.提供量化不确定性方法,提供导出新不确定性声明(statement)公理.人工智能领域,概率法则,AI系统推理,设计算法计算概率论导出表达式.概率和统计理论分析AI系统行为.概率论提出不确定声明,在不确定性存在情况下推理.信息论量化概率分布不确定性总量.Jaynes(2003).机器学习经常处理不确定量,有时处理随机(非确定性)量.20世纪80年代,研究人员对概率论量化不确定性提出信服论据.Pearl(1998). 不确定性来源.被建模系统内存的随…

正态分布变换(NDT)算法是一个配准算法,它应用于三维点的统计模型,使用标准最优化技术来确定两个点云间的最优的匹配,因为其在配准过程中不利用对应点的特征计算和匹配,所以时间比其他方法快.下面的公式推导和MATLAB程序编写都参考论文:The Normal Distributions Transform: A New Approach to Laser Scan Matching 先回顾一下算法推导和实现过程中涉及到的几个知识点: 协方差矩阵 在概率论和统计中,协方差是对两个随机变量联合分布线性相…

正态分布变换算法是一个配准算法,它应用于三维点的统计模型,使用标准优化技术来确定两个点云间的最优的匹配,因为其在配准过程中不利用对应点的特征计算和匹配,所以时间比其他方法快.下面是PCL官网上的一个例子,使用NDT配准算法将两块激光扫描数据点云匹配到一起. 先下载激光扫描数据集room_scan1.pcd 和 room_scan2.pcd. 这两块点云从不同的角度对同一个房间进行360°扫描得到.可以用CloudCompare(3D point cloud and mesh processing…

Two Types of Estimation One of the major applications of statistics is estimating population parameters from sample statistics. There are types of estimation: Point Estimate: the value of sample statistics Point estimates of average height with multi…