From 16ef5091b40b7801726c3d504a5bfce56c264b74 Mon Sep 17 00:00:00 2001 From: lunar Date: Fri, 1 Apr 2016 13:19:25 +0200 Subject: [PATCH] Add coursera nots --- .gitignore | 1 + ...47\346\211\271\346\225\260\346\215\256.md" | 30 ++++++ ...7\346\211\271\346\225\260\346\215\256.pdf" | Bin 0 -> 62266 bytes ...50\350\215\220\347\263\273\347\273\237.md" | 88 ++++++++++++++++++ ...0\350\215\220\347\263\273\347\273\237.pdf" | Bin 0 -> 582420 bytes 5 files changed, 119 insertions(+) create mode 100644 "Notes/Coursera Machine Learning Week10 \345\244\247\346\211\271\346\225\260\346\215\256.md" create mode 100644 "Notes/Coursera Machine Learning Week10 \345\244\247\346\211\271\346\225\260\346\215\256.pdf" create mode 100644 "Notes/Coursera Machine Learning Week9 \345\274\202\345\270\270\346\243\200\346\265\213-\346\216\250\350\215\220\347\263\273\347\273\237.md" create mode 100644 "Notes/Coursera Machine Learning Week9 \345\274\202\345\270\270\346\243\200\346\265\213-\346\216\250\350\215\220\347\263\273\347\273\237.pdf" diff --git a/.gitignore b/.gitignore index b06e864..706bb54 100644 --- a/.gitignore +++ b/.gitignore @@ -210,3 +210,4 @@ FakesAssemblies/ GeneratedArtifacts/ _Pvt_Extensions/ ModelManifest.xml +*.zip diff --git "a/Notes/Coursera Machine Learning Week10 \345\244\247\346\211\271\346\225\260\346\215\256.md" "b/Notes/Coursera Machine Learning Week10 \345\244\247\346\211\271\346\225\260\346\215\256.md" new file mode 100644 index 0000000..233c491 --- /dev/null +++ "b/Notes/Coursera Machine Learning Week10 \345\244\247\346\211\271\346\225\260\346\215\256.md" @@ -0,0 +1,30 @@ +#Coursera Machine Learning Week10 大批数据 +---- +[Coursera Machine Learning](https://www.coursera.org/learn/machine-learning/home/welcome) Lunar's note +Tags: MachineLearning Coursera +##大批量数据学习 +###大训练集 +在很多情况下,大数据量带来的好处显而易见,但是在某些情况下,更多的数据不仅没有好处,还会带来计算上的问题,所以在决定使用大批量数据前要注意斟酌。(可以利用[前面提到的学习曲线](https://www.zybuluo.com/lunar/note/301822)) +###随机梯度下降 Stochastic Gradient Descent +相比于之前用的一般的批量梯度下降,随机梯度下降先将数据随机排序,然后对于每个数据单独去拟合,而不是像之前那样对所有数据一起拟合。单独拟合的话,不需要等到求完所有数据都计算一遍就能得出下降量。 +随机梯度下降的迭代次数非常多,下降路线较为曲折,但是每次迭代的速度很快,收敛后会在最优区域徘徊。 +批量梯度下降迭代次数较小,下降路线较直,但是每次迭代需要较多时间,最后收敛后就不会移动。 + ++ 小批梯度下降 + +|梯度下降方法|样本使用| +|----|----| +|批量梯度下降|每次迭代使用m个数据| +|随机梯度下降|每次迭代使用1个数据| +|小批梯度下降|每次迭代使用b个数据$b\in(1,m)$| + +随机梯度下降判断收敛的方法: +对于每k次迭代(比如1000次),计算着k次迭代的平均代价函数,画出图像判断收敛。 +###在线学习 +在线学习的要旨在于,每次获取一个样本,使用它更新算法,然后丢弃那个样本。 +适合于长期有较大数据流量的网站,因为总是有新的用户会提供样本,而且在线算法会反映出新的用户的特征。 +根本区别在于不使用固定的数据集。 +###映射约减 Map Reduce +将训练集分为几个子集,分给不同的计算机计算出各自的临时变量,然后将临时变量融合并进行迭代, + + diff --git "a/Notes/Coursera Machine Learning Week10 \345\244\247\346\211\271\346\225\260\346\215\256.pdf" "b/Notes/Coursera Machine Learning Week10 \345\244\247\346\211\271\346\225\260\346\215\256.pdf" new file mode 100644 index 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o3_i^Fr?#V`+c`iE`-`f&x>>lm{k(MmDMttdF%OTth63^b05_2Ft^fc4 literal 0 HcmV?d00001 diff --git "a/Notes/Coursera Machine Learning Week9 \345\274\202\345\270\270\346\243\200\346\265\213-\346\216\250\350\215\220\347\263\273\347\273\237.md" "b/Notes/Coursera Machine Learning Week9 \345\274\202\345\270\270\346\243\200\346\265\213-\346\216\250\350\215\220\347\263\273\347\273\237.md" new file mode 100644 index 0000000..608041b --- /dev/null +++ "b/Notes/Coursera Machine Learning Week9 \345\274\202\345\270\270\346\243\200\346\265\213-\346\216\250\350\215\220\347\263\273\347\273\237.md" @@ -0,0 +1,88 @@ +#Coursera Machine Learning Week9 异常检测/推荐系统 +---- +[Coursera Machine Learning](https://www.coursera.org/learn/machine-learning/home/welcome) Lunar's note +Tags: MachineLearning Coursera + +[TOC] + +##异常检测 Anomaly detection +###高斯分布 Gaussian Distrubution +又叫~~正太~~正态分布Normal Distrubution。 +对于$x\in \Re$,如果期望为$\mu$,方差为$\sigma^2$,那么我们就可以称,$x\sim \aleph(\mu,\sigma^2)$(读作x服从mu和sigma的高斯分布)。 +![维基百科](https://upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Normal_approximation_to_binomial.png/325px-Normal_approximation_to_binomial.png) +该分布的概率分布曲线像是山丘,以$x=\mu$对称,山丘的陡峭程度和 +相关,$\sigma$越小,曲线越陡峭。 + +#### 参数估计 +对于给定的数据集,如果认为该数据分布符合正态分布,那么可以对他们进行参数估计,即利用数据集的分布情况来估算正态分布的参数($\mu和\sigma$)。 +$\mu = \frac{1}{m}\Sigma^m_{i=1}x^i$ +$\sigma^2 = \frac{1}{m}\Sigma^m_{i=1}(x^i-\mu)^2$ +ps.概率论课上这两个公式的分母都是$m-1$但是在机器学习领域更通用m,虽然在数学理论上二者不同,但是实际应用中差别很小。 +###算法 +首先,我们要算出某个样本的估算密度,对于有n个特征值的样本x, +$p(x)=\Pi_{i=1}^n p(x_i,\mu_i,\sigma^2_i)=\Pi_{i=1}^n \frac{1}{\sqrt{2\pi}\sigma_i}exp(-\frac{(x_i-\mu_j)^2}{2\sigma_j^2})$。 +下面是具体算法步骤 +1. 选择出有利于检测出异常的特征值。 +2. 对于给出的无标签数据集,计算出正态分布的参数。 +3. 对于新的样本,计算出$p(x)$,当小于阈值时($p(x)<\varepsilon$),判定为异常。 +###算法的评估 +通过带标签的数据,我们可以用数字量化对算法的评估。 +假定CV集和测试集都是带标签的,而训练集是不带标签的数据。 +在训练结束后,我们通过CV集/测试集的数据计算出评估量: + ++ 真/假 阴/阳 值 ++ 召回率/查准率 ++ $F_1-值$ +关于这些值的含义在[Week6](https://www.zybuluo.com/lunar/note/301822)有提及。 +**选择 $\epsilon$ 值通常通过CV集中的F-score值来判断。** +###监督学习 vs. 异常检测 +|异常检测|监督学习| +|---|---| +|正负样本数量相差非常悬殊,有一项非常小|正负样本数量都很大| +|异常的类型多样(但数量不一定多),难以预料|训练集样本异常包含大多数或几乎所有的异常类型,且类型数较少| +| 欺诈检测|垃圾邮件分类| +|生产检测|天气预测| +|机器故障检测|癌症诊断| +###特征值选择 ++ 高斯化 +对于分布看起来不像正态分布的特征量,我们可以通过转换,比如log运算使其分布更加贴合高斯分布。 ++ 特征值 +选择更加能够区分正常样本和异常样本的特征值。 +###改进:多元高斯分布 +以上的异常检测不能兼顾到特征值之间的联系。比如网站用户检测,每月登陆1次可能是正常的,每月消费10笔也可能是正常的,但是如果同一用户每月只登陆一次但是消费10笔,那么可能就是异常的,然而以上的检测并不会考虑这个。当然我们可以通过增加二者的比率(每次登陆消费笔数)来解决,但是当特征值较多时,就无法如此简单的解决。所以我们引入多元高斯分布。 +对于$\mu \in \Re^n,\Sigma \in \Re^{n*n}$, +$p(x;\mu,\Sigma)=\frac{1}{(2\pi)^{n/2}|\Sigma|^{\frac{1}{2}}}exp(-\frac{1}{2}(x-\mu)^T\Sigma^{-1}(x-\mu))$ +这里$\Sigma$是个n*n的矩阵,$|\Sigma|$是该矩阵的行列式的值。 +利用如下公式进行参数拟合 +$\mu = \frac{1}{m}\Sigma^m_{i=1}x^i \quad \Sigma = \frac{1}{m}\Sigma^m_{i=1}(x^i-\mu)(x^i-\mu)^T$。 +接下来对example,计算$p(x)$并和阈值比较。 +如果数据含有重复特征值或者冗余(线性相关)特征值(如$x_1=x_2\qquad x_3=x_1+x_2$),那么协方差矩阵$\Sigma$会是不可逆的,也就不能使用多元高斯模型(m>n时也不能用)。 +##推荐系统 Recommender System +###基于内容的推荐 +设置基于内容的特征量,值越大表示包含该特征内容越多。比如($x_1(romance)$),那么一部电影的$x_1$表示该电影的爱情片成分有多少。将用户看过的电影的基于内容的特征值作为输入X,评分作为输出y,那么我们可以通过回归算法拟合每个用户的参数,并通过此对用户未评分的电影进行评级。 +###协同过滤 Collaborative Filtering +不同于上面基于内容的推荐,这里我们不事先对电影的内容提取特征值,相反,我们对用户的喜好提取特征值。 +如:用户对爱情电影的喜好为5,对动作电影的喜好为1。那么大量搜集这些信息后就可以结合用户给不同电影的评分,得到电影的内容特征值。 +我们可以看出,前面是通过电影内容特征估计用户喜好特征,后面是通过用户喜好特征来估计电影内容特征,这两种方法可以结合起来: + ++ 具体算法 +![Collaborative filtering.png-66kB][1] +我们将其统一起来,其评估函数加起来形成一个新的评估函数$J(x^1...x^m,\theta^1...\theta^u)$,最小化$J$。 ++ 步骤 +1. 初始化$x^1...x^m,\theta^1...\theta^u$ +2. 利用梯度下降最小化$J$,不断更新参数。 +3. 对于每个用户和每个电影可以估算出评分值。 + ++ 向量化实现 +将用户对各个电影的评分可以用矩阵表示。 +$$ +Y=\begin{bmatrix} +5&5&0&0\\ +5&?&?&0\\ +?&4&0&?\\ +0&0&5&4\\ +0&0&5&0\\ +\end{bmatrix} +$$ +$Y^{ij}$表示用户j对电影i的评分。那么就有$Y=X\Theta^T$,$\Theta$是各个用户的特征值;$X$是电影的特征矩阵,每行为一部电影的各个特征。 + [1]: http://static.zybuluo.com/lunar/tiir2lav8zjupf4ojldqu1lc/Collaborative%20filtering.png \ No newline at end of file diff --git "a/Notes/Coursera Machine Learning Week9 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