16 - 3 - Collaborative Filtering (10 min).srt

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In this video we'll talk about
在这段视频中 我们要讲
(字幕整理：中国海洋大学 黄海广,haiguang2000@qq.com )

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an approach to building a
一种构建推荐系统的方法

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recommender system that's called collaborative filtering.
叫做协同过滤(collaborative filtering)

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The algorithm that we're talking
我们所讲的算法

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about has a very interesting
有一个值得一提的

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property that it does
特点 那就是它能实现

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what is called feature learning and
对特征的学习

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by that I mean that this
我的意思是

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will be an algorithm that can
这种算法能够

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start to learn for itself what features to use.
自行学习所要使用的特征

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Here was the data set that
我们建一个数据集

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we had and we had
假定是为每一部电影准备的

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assumed that for each movie,
对每一部电影

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someone had come and told
我们找一些人来

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us how romantic that
告诉我们这部电影

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movie was and how much action there was in that movie.
浪漫指数是多少 动作指数是多少

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But as you can imagine it
但想一下就知道

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can be very difficult and time
这样做难度很大

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consuming and expensive to actually try
也很花费时间

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to get someone to, you know,
你想想 要让每个人

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watch each movie and tell
看完每一部电影

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you how romantic each movie and
告诉你你每一部电影有多浪漫 多动作

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how action packed is each
这是一件不容易的事情

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movie, and often you'll
而且通常

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want even more features than just these two.
你还会希望得到除这两个特征之外的其他指数

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So where do you get these features from?
那么你怎样才能得到这些特征呢？

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So let's change the problem
所以 让我们转移一下问题

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a bit and suppose that
假如我们

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we have a data set where
有某一个数据集

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we do not know the values of these features.
我们并不知道特征的值是多少

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So we're given the data set
所以比如我们得到一些

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of movies and of
关于电影的数据

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how the users rated them, but we
不同用户对电影的评分

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have no idea how romantic each
我们并不知道每部电影

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movie is and we have no
到底有多少浪漫的成分

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idea how action packed each
也不知道到底每部电影里面动作成分是多少

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movie is so I've replaced all of these things with question marks.
于是我把所有的问题都打上问号

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But now let's make a slightly different assumption.
现在我们稍稍改变一下这个假设

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Let's say we've gone to each of our users, and each of our users has told has told us
假设我们采访了每一位用户 而且每一位用户都告诉我们

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how much they like the
他们是否喜欢

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romantic movies and how much
爱情电影 以及

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they like action packed movies.
他们是否喜欢动作电影

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So Alice has associated a current of theta 1.
这样 Alice 就有了对应的参数 θ(1)

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Bob theta 2.
Bob 的是 θ(2)

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Carol theta 3.
Carol 的是 θ(3)

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Dave theta 4.
Dave 的是 θ(4)

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And let's say we also use this
我们还有这样的假设

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and that Alice tells us
假如 Alice 告诉我们

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that she really
她十分喜欢

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likes romantic movies and so
爱情电影

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there's a five there which
于是 Alice 的特征 x1

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is the multiplier associated with X1 and lets
对应的值就是5

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say that Alice tells us she
假设 Alice 告诉我们

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really doesn't like action movies and so there's a 0 there.
她非常不喜欢动作电影 于是这一个特征就是0

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And Bob tells us something similar
Bob 也有相似的喜好

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so we have theta 2 over here.
所以也就有了 θ(2) 的数据

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Whereas Carol tells us that
但 Carol 说

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she really likes action movies
她非常喜欢动作电影

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which is why there's a 5 there,
于是这个特征就被记录为5

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that's the multiplier associated with X2,
也就是 x2 的值

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and remember there's also
别忘了

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X0 equals 1 and let's
我们仍然有等于1的 x0

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say that Carol tells us
假设 Carol 告诉我们

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she doesn't like romantic
她不喜欢爱情电影之类的

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movies and so on, similarly for Dave.
而且戴夫也是这样

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So let's assume that somehow
于是 我们假定 某种程度上

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we can go to users and
我们就可以着眼于用户

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each user J just tells
看看任意的用户 j

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us what is the value
对应的 θ(j) 是怎样的

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of theta J for them.
这样就明确地告诉了我们

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And so basically specifies to us of how much they like different types of movies.
他们对不同题材电影的喜欢程度

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If we can get these parameters
如果我们能够从用户那里

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theta from our users then it
得到这些 θ 参考值

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turns out that it becomes possible to
那么我们理论上就能

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try to infer what are the
推测出每部电影的

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values of x1 and x2 for each movie.
x1 以及 x2 的值

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Let's look at an example.
举例来说

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Let's look at movie 1.
假如我们看电影1

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So that movie 1 has associated
于是电影1就对应于

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with it a feature vector x1.
表示特征的向量 x1 联系在一起了

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And you know this movie is called Love at last but let's ignore that.
这部电影的名字叫《爱到最后》 但这不重要

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Let's pretend we don't know what
假设我们不知道

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this movie is about, so let's ignore the title of this movie.
这部电影的主要内容 所以也不要在意电影的名字

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All we know is that Alice loved this move.
我们知道的就是 Alice 喜欢这部电影

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Bob loved this movie.
Bob 喜欢这部电影

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Carol and Dave hated this movie.
Carol 和 Dave 不喜欢它

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So what can we infer?
那么我们能推断出什么呢？

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Well, we know from the
好的 我们从

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feature vectors that Alice
特征向量知道了

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and Bob love romantic movies
Alice 和 Bob 喜欢爱情电影

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because they told us that there's a 5 here.
因为他们都在这里评了5分

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Whereas Carol and Dave,
然而 Carol 和 Dave

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we know that they hate
我们知道他们不喜欢

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romantic movies and that
爱情电影

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they love action movies. So
但喜欢动作电影

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because those are the parameter
由于你知道这些

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vectors that you know, uses 3 and 4, Carol and Dave, gave us.
是可以从 第3和第4个参数看出来的

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And so based on the fact
同时 由于我们知道

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that movie 1 is loved
Alice 和 Bob

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by Alice and Bob and
喜欢电影1

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hated by Carol and Dave, we might
而 Carol 和 Dave 不喜欢它

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reasonably conclude that this is probably a romantic movie,
我们可以推断 这可能是一部爱情片

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it is probably not much of an action movie.
而不太可能是动作片

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this example is a little
这个例子在数学上

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bit mathematically simplified but what
可能某种程度上简化了

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we're really asking is what
但我们真正需要的是

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feature vector should X1 be
特征向量 x(1) 应该是什么

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so that theta 1 transpose
才能让 θ(1) 的转置

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x1 is approximately equal to 5,
乘以x(1) 约等于5

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that's Alice's rating, and
也就是 Alice 的评分值

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theta 2 transpose x1 is
然后 θ(2) 的转置乘以 x(1)

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also approximately equal to 5,
也近似于5

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and theta 3 transpose x1 is
而 θ(3) 的转置 乘以 x(1)

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approximately equal to 0,
约等于0

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so this would be Carol's rating, and
这是 Carol 的评分

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theta 4 transpose X1
而 θ(4) 的转置乘以 x(1)

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is approximately equal to 0.
也约等于0

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And from this it looks
由此可知

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like, you know, X1 equals
x(1) 应该用

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one that's the intercept term, and
[1 1.0 0.0] 这个向量表示

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then 1.0, 0.0, that makes sense
第一个1 是截距项

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given what we know of Alice,
这样才能得出

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Bob, Carol, and Dave's preferences
Alice Bob Carol 和 Dave 四个人

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for movies and the way they rated this movie.
对电影评分的结果

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And so more generally, we can
由此及之 我们可以

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go down this list and try
继续列举 试着

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to figure out what might
弄明白

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be reasonable features for these other movies as well.
其他电影的合理特征

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Let's formalize this problem of learning the features XI.
让我们将这一学习问题标准化到任意特征 x(i)

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Let's say that our
假设我们的用户

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users have given us their preferences.
告诉了我们的偏好

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So let's say that our users have
就是说用户们

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come and, you know, told us
已经给我们提供了

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these values for theta 1
θ(1) 到 θ(nu) 的值

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through theta of NU
θ(1) 到 θ(nu) 的值

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and we want to learn the
而我们想知道

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feature vector XI for movie
电影 i 的

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number I. What we can
特征向量 x(i) 我们能做的

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do is therefore pose the following optimization problem.
是列出以下的最优化的问题

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So we want to sum over
所以 我们想要把

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all the indices J for
所有指数 j 相加

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which we have a rating
得到对电影 i 的评分

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for movie I because
因为我们

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we're trying to learn the features
想要求得电影 i 的特征

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for movie I that is this feature vector XI.
也就是向量 x(i)

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So and then what we
所以现在我们

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want to do is minimize this squared
要做的是最小化这个平方误差

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error, so we want to choose
我们要选择

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features XI, so that,
特征 x(i)

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you know, the predictive value of
使得 我们预测的用户 j

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how user J rates movie
对该电影 i 评分的预测值评分值

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I will be similar,
跟我们从用户 j 处

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will be not too far in the
实际得到的评分值

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squared error sense of the actual
不会相差太远

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value YIJ that we actually observe in
也就是这个差值

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the rating of user j
不要太大

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on movie I. So, just to
所以 总结一下

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summarize what this term does
这一阶段要做的

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is it tries to choose features
就是为所有

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XI so that for
为电影评分的

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all the users J that
用户 j

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have rated that movie, the
选择特征 x(i)

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algorithm also predicts a
这一算法同样也预测出一个值

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value for how that user would have rated that movie
表示该用户将会如何评价某部电影

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that is not too far, in
而这个预测值

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the squared error sense, from the
在平方误差的形式中

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actual value that the user had rated that movie.
与用户对该电影评分的实际值尽量接近

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So that's the squared error term.
这就是那个平方误差项了

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As usual, we can
和之前一样

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also add this sort of
我们可以加上一个正则化项

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regularization term to prevent
来防止特征的数值

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the features from becoming too big.
变得过大

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So this is how we
这就是我们

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would learn the features
如何从一部特定的电影中

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for one specific movie but
学习到特征的方法

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what we want to do is
但我们要做的是

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learn all the features for all
学习出所有电影的

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the movies and so what
所有特征

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I'm going to do is add this
所以我现在要做的是

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extra summation here so
在此加上另外的一个求和

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I'm going to sum over all Nm
我要对所有的电影 nm 求和

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movies, N subscript m movies, and minimize
n 下标 m 个电影

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this objective on top
然后最小化整个这个目标函数

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that sums of all movies.
针对所有的电影

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And if you do that, you end up with the following optimization problem.
这样你就会得到如下的最优化的问题

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And if you minimize
如果你将这个最小化

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this, you have hopefully a
就应该能得到所有电影的

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reasonable set of features for all of your movies.
一系列合理的特征

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So putting everything together, what
好的 把我们

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we, the algorithm we talked
前一个视频讨论的算法

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about in the previous video and
以及我们刚刚

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the algorithm that we just talked about in this video.
在这个视频中讲过的算法合在一起

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In the previous video, what we
上一个视频中

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showed was that you know,
我们讲的是

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if you have a set of
如果你有一系列

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movie ratings, so if you
对电影的评分 那么如果你

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have the data the rij's and
有r(i,j) 和 y(i,j)

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then you have the yij's that will be the movie ratings.
也就是对电影的评分

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Then given features for your
于是 根据不同电影的特征

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different movies we can learn these parameters theta.
我们可以得到参数 θ

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So if you knew the features,
这样 如果你知道了特征

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you can learn the parameters
你就能学习出不同用户的

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theta for your different users.
参数 θ 值

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And what we showed earlier in
我们之前

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this video is that if
这个视频中讲的是

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your users are willing to
如果用户愿意

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give you parameters, then you
为你提供参数 那么你就

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can estimate features for the different movies.
可以为不同的电影估计特征

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So this is kind of a chicken and egg problem.
这有点像鸡和蛋的问题

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Which comes first?
到底先有鸡还是先有蛋？

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You know, do we want if we can get the thetas, we can know the Xs.
就是说 如果我们能知道 θ 就能学习到 x

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If we have the Xs, we can learn the thetas.
如果我们知道 x 也会学出 θ 来

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And what you can
而这样一来 你能做的

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do is, and then
就是

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this actually works, what you
如果这真的可行的话

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can do is in fact randomly
实际上你能做的就是

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guess some value of the thetas.
随机猜de θ 的值

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Now based on your initial random
基于你一开始随机

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guess for the thetas, you can
猜测出的 θ 的值

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then go ahead and use
继你可以继续下去

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the procedure that we just talked
运用我们刚刚讲到的

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about in order to
步骤 我们可以学习出

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learn features for your different movies.
不同电影的特征

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Now given some initial set
给出已有的一些电影的

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of features for your movies you
原始特征

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can then use this first
你可以运用

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method that we talked about
我们在上一个视频中讨论过的

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in the previous video to try to get
第一种方法 可以得到

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an even better estimate for your parameters theta.
对参数 θ 的更好估计

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Now that you have a better setting of the parameters theta for your users,
这样就会为用户提供更好的参数 θ 集

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we can use that to maybe
我们就可以用这些

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even get a better set of
得到更好的

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features and so on.
特征集或者其他数据

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We can sort of keep
然后我们可以继续

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iterating, going back and forth
迭代 不停重复

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and optimizing theta, x theta,
优化θ x θ

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x theta, nd this
x θ 这非常有效

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actually works and if you
如果你

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do this, this will actually
这样做的话

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cause your album to converge
你的算法将会收敛到

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to a reasonable set of
一组合理的电影的特征

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features for you movies and a
以及一组对合理的

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reasonable set of parameters for your different users.
对不同用户参数的估计

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So this is a basic collaborative filtering algorithm.
这就是基本的协同过滤算法

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This isn't actually the final
这实际并不是最后

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algorithm that we're going to use. In the next
我们将要使用的算法

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video we are going to be able to improve
下一个视频中

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on this algorithm and make
我们将改进这个算法

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it quite a bit more computationally efficient.
让其在计算时更为高效

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But, hopefully this gives you
但是这节课希望能让你

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a sense of how you
基本了解如何

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can formulate a
构建一个问题

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problem where you can simultaneously
在这个问题中

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learn the parameters and simultaneously learn the features from the different movies.
从不同的电影处学到参数以及特征

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And for this problem, for the
对于这个问题

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recommender system problem, this is
对于推荐系统

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possible only because each user
可能就根据每个用户

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rates multiple movies and hopefully
对多部电影的评分

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each movie is rated
以及每部电影由

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by multiple users. And so
由不同用户的评分

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you can do this back and
这样你就可以反复进行这样的过程

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forth process to estimate theta
来估计出 θ 和 x

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and x.  So to
总结一下

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summarize, in this video we've
在这个视频中

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seen an initial collaborative filtering algorithm.
我们了解了最基本的协同过滤算法

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The term collaborative filtering refers
协同过滤算法指的是

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to the observation that when
当你执行这个算法时

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you run this algorithm with a
你通过一大堆用户

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large set of users, what all
得到的数据

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of these users are effectively doing are sort of
这些用户实际上在高效地

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collaboratively--or collaborating to
进行了协同合作

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get better movie ratings for
来得到每个人

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everyone because with every
对电影的评分值

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user rating some subset with the movies,
只要用户对某几部电影进行评分

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every user is helping the
每个用户就都在帮助算法

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algorithm a little bit to learn better features,
更好的学习出特征

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and then by helping--
这样 通过自己

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by rating a few movies myself, I will be helping
对几部电影评分之后

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the system learn better features and
我就能帮助系统更好的学习到特征

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then these features can be used
这些特征可以

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by the system to make better
被系统运用 为其他人

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movie predictions for everyone else.
做出更准确的电影预测

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And so there is a sense of
协同的另一层意思

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collaboration where every user is
是说每位用户

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helping the system learn better features
都在为了大家的利益

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for the common good. This
学习出更好的特征

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is this collaborative filtering.
这就是协同过滤

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And, in the next video what we
在下一个视频中

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going to do is take the ideas that
我们要把这些想法

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have worked out, and try to
付诸实施

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develop a better an even
尝试开发一种

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better algorithm, a slightly better
更完美的算法

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technique for collaborative filtering.
为协同过滤算法做出一点改进