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…

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…

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…

PRML Chapter 1. Introduction 为了防止忘记,要把每章的重要内容都记下来,从第一章开始 2012@3@28 今天又回去稍微翻了一下第一章内容,发现第一次看的时候没有看透,每次翻都能翻出新的内容和感悟来.这主要得益于后面其他书里看到的一些内容后,再来看前面的某些话,就知道这些话不是白写的了,而是每一句都有一些深层的意义. 因此对于PRML这样的书,看一两遍是不够的,有空要多回翻 P 2 generalization的定义:The ability to categorize…

一起啃PRML - 1.2 Probability Theory @copyright 转载请注明出处 http://www.cnblogs.com/chxer/ A key concept in the field of pattern recognition is that of uncertainty. 可以看出概率论在模式识别显然是非常重要的一大块. 读其他书的时候在概率这方面就也很纠结过. 我们也还是通过一个例子来理解一下Probability Theory里面一些重要的概念. Ima…

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…

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,…