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 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…

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…

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…

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.…

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…

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…

以下是几种常见的离散型概率分布和连续型概率分布类型: 伯努利分布(Bernoulli Distribution):常称为0-1分布,即它的随机变量只取值0或者1. 伯努利试验是单次随机试验,只有"成功"(1)或"失败"(0)这两种结果.假如某次伯努利实验成功的概率为p,失败的概率为q=1-p,那么实验成功或失败的概率可以写成:. 伯努利分布的期望: 伯努利分布的方差: 二项分布(Binomial Distribution):用以描述n次独立的伯努利实验中有x次成功的…

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,    …

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…

title: [概率论]5-8:Beta分布(The Beta Distributions) categories: - Mathematic - Probability keywords: - The Beta Distribution toc: true date: 2018-04-02 15:14:12 Abstract: 本文介绍Beta分布的相关知识内容 Keywords: The Beta Distribution 开篇废话 我们预测未来某件事情是否发生的主要依据是先验知识,于是我相…

作者:Pier Paolo Ippolito@南安普敦大学 编译:机器学习算法与Python实战(微信公众号:tjxj666) 原文:https://towardsdatascience.com/probability-distributions-in-data-science-cce6e64873a7 介绍 拥有良好的统计背景对于数据科学家的日常工作可能会大有裨益.每次我们开始探索新的数据集时,我们首先需要进行探索性数据分析(EDA),以了解某些特征的概率分布是什么.如果我们能够了解数据分布中…

常用的数据挖掘&机器学习知识(点) Basis(基础): MSE(MeanSquare Error 均方误差),LMS(Least MeanSquare 最小均方),LSM(Least Square Methods 最小二乘法),MLE(Maximum LikelihoodEstimation最大似然估计),QP(QuadraticProgramming 二次规划), CP(ConditionalProbability条件概率),JP(Joint Probability 联合概率),MP(Mar…

接上篇概率分布,这篇文章讲概率分布在python的实现. 文中的公式使用LaTex语法,即在\begin{equation}至\end{equation}的内容可以在https://www.codecogs.com/latex/eqneditor.php?lang=zh-cn页面转换出 正确的格式 二项分布(Binomial Distribution) 包含n个相同的试验 每次试验只有两个可能的结果:"成功"或"失败". 出现成功的概率p对每一次试验是相同的,失败的…