16 - 1 - Problem Formulation (8 min).srt

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In this next set of
在接下来的视频中，(字幕翻译：仇利克，中国海洋大学)

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videos, I would like to
我想

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tell you about recommender systems.
讲一下推荐系统。

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There are two reasons, I had
有两个原因，我想讲

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two motivations for why I wanted to talk about recommender systems.
推荐系统有两个原因

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The first is just that it
第一，仅仅因为它是

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is an important application of machine learning.
机器学习中的一个重要的应用。

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Over the last few years, occasionally I
在过去几年，我偶尔

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visit different, you know, technology
访问硅谷不同的技术公司，

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companies here in Silicon Valley

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and I often talk to people
我常和工作在这儿

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working on machine learning applications there
致力于机器学习应用的人们聊天，

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and so I've asked
我常问

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people what are the most
他们，最重要的

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important applications of machine
机器学习的应用是什么，

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learning or what are the machine
或者，你最想改进的

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learning applications that you would most like to get
机器学习应用

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an improvement in the performance of.
有哪些。

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And one of the most frequent
我最常听到的

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answers I heard was that
答案是

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there are many groups out in Silicon
现在，在硅谷有很多团体

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Valley now, trying to build better recommender systems.
试图建立很好的推荐系统。

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So, if you think about
因此，如果你考虑

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what the websites are
网站是什么

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like Amazon, or what Netflix
像亚马逊，或网飞公司

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or what eBay, or what
或易趣，或

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iTunes Genius, made by Apple
iTunes Genius，苹果开发的，

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does, there are many websites
有很多的网站

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or systems that try to
或系统试图

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recommend new products to use.
推荐新产品给用户。

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So, Amazon recommends new books
因此，亚马逊推荐新书

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to you, Netflix try to recommend
给你，网飞公司试图推荐

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new movies to you, and so on.
新电影给你，等等。

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And these sorts of recommender systems,
这些推荐系统，

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that look at what books you
浏览你过去

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may have purchased in the past,
买过什么书，

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or what movies you have rated
或过去评价过什么电影，

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in the past, but these are
但是，

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the systems that are responsible
这些系统会带来

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for today, a substantial fraction of
很大一部分收入

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Amazon's revenue and for a
为亚马逊和

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company like Netflix, the recommendations
像网飞这样的公司，

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that they make to the users
给用户推荐的电影

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is also responsible for a
也占据了

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substantial fraction of the movies
用户所看电影的一大部分。

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watched by their users. 
And so an
因此，

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improvement in performance of
对推荐系统性能的改善

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a recommender system can have

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a substantial and immediate
将对这些企业的

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impact on the bottom line of
底线有实质性和直接的影响。

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many of these

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companies. Recommender systems is kind of a funny
推荐系统是个有趣的问题，

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problem, within academic machine
在学术机器学习中

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learning so that we could
因此，我们

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go to an academic machine learning conference,
可以去参加一个学术机器学习会议，

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the problem of recommender systems,
推荐系统问题

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actually receives relatively little attention,
实际上受到很少的关注，

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or at least it's sort of a smaller
或者，至少在学术界

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fraction of what goes on within Academia.
它占了很小的份额。

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But if you look at what's happening,
但是，如果你看正在发生的事情，

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many technology companies, the ability
许多有能力构建这些系统的科技企业，

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to build these systems seems to be a high priority for many companies.
他们似乎在很多企业中占据很高的优先级。

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And that's one of the reasons why I want to talk about them in this class.
这是我为什么在这节课讨论它的原因之一。

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The second reason that I
我想讨论推荐系统地第二个原因是

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want to talk about recommender systems

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is that as we approach

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the last few sets of videos
这个班视频的最后几集

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of this class I wanted to talk about
我想讨论

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a few of the big ideas
机器学习中的一些大思想

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in machine learning and share with you,
并和大家分享，

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you know, some of the big ideas in machine learning.
你知道的，机器学习中的一些大思想。

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And we've already seen
这节课我们也看到了，

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in this class that features are
对机器学习来说，特征是

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important for machine learning, the
很重要的，

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features you choose will have
你所选择的特征

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a big effect on the performance of your learning algorithm.
将对你学习算法的性能有很大的影响。

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So there's this big idea in machine
因此，在机器学习中有一种大思想，

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learning, which is that for
它针对一些问题，

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some problems, maybe not
可能并不是

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all problems, but some problems, there
所有的问题，而是一些问题，

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are algorithms that can try
有算法可以为你

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to automatically learn a good set of features for you.
自动学习一套好的特征。

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So rather than trying to hand
因此，不要试图手动设计，

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design, or hand code the
或手写代码

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features, which is mostly what we've
这是目前为止我们常干的，

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been doing so far, there are a

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few settings where you might
有一些设置，你可以

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be able to have an
有一个算法，

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algorithm, just to learn what feature to
仅仅学习其使用的特征，

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use, and the recommender
推荐系统

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systems is just one example of that sort of setting.
就是类型设置的一个例子。

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There are many others, but engraved
还有很多其它的，但是

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through recommender systems, will be
通过推荐系统，我们将

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able to go a little
领略一小部分

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bit into this idea of learning
特征学习的思想，

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the features and you'll be
至少，你将能够

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able to see at least one example
了解到这方面的一个例子，

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of this, I think, big idea in machine learning as well.
我认为，机器学习中的大思想也是这样。

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So, without further ado, let's
因此，让我们

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get started, and talk
开始讨论

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about the recommender system problem formulation.
推荐系统问题公式化。

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As my running example, I'm
接下来的例子，我将

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going to use the
用

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modern problem of predicting movie ratings.
电影评级预测现代问题。

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So, here's a problem.
因此，这是一个问题。

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Imagine that you're a
假设你是一个

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website or a company that
网站或者公司

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sells or rents out movies, or what have you.
出售或者出租电影，或者诸如此类。

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And so, you know, Amazon, and Netflix, and
因此，你知道，亚马逊、网飞公司和

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I think iTunes are all examples
iTunes都是做这个的

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of companies that do this,
公司。

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and let's say you let
比方说，你让

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your users rate different movies,
你的用户评价不同的电影，

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using a 1 to 5 star rating.
用1到5星级评价。

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So, users may, you know,
因此，用户可能，你知道，

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something one, two, three, four or five stars.
评定一星、二星、三星、四星或五星。

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In order to make this example
为了让这个例子

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just a little bit nicer, I'm
更完善一点，我

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going to allow 0 to
将允许0到

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5 stars as well,
5星级，

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because that just makes some of the math come out just nicer.
这只是让数字呈现的更好一些。

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Although most of these websites use the 1 to 5 star scale.
虽然大多数网站使用1到5星级评价。

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So here, I have 5 movies.
这里，我有5部电影。

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You know, Love That
你们知道的，Love That

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Lasts, Romance Forever, Cute Puppies of
Lasts, Romance Forever, Cute Puppies of

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Love, Nonstop Car Chases,
Love, Nonstop Car Chases,

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and Swords vs. Karate.
and Swords vs. Karate.

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And we have 4 users, which,
我们有4个用户，

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calling, you know, Alice, Bob, Carol,
他们分别是Alice, Bob, Carol,

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and Dave, with initials A, B,
和Dave,名字首字母分别是A, B,

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C, and D, we'll call them users 1, 2, 3, and 4.
C和D,我们称呼他们用户1,2,3和用户4.

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So, let's say Alice really
比如说Alice喜欢

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likes Love That Lasts and
Love That Lasts并

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rates that 5 stars, likes Romance
给其评价5星，Romance

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Forever, rates it 5 stars.
Forever,评价5星。

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She did not watch Cute Puppies
她并没有看过Cute Puppies

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of Love, and did rate it, so we
of Love,没有进行评价，因此，我们

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don't have a rating for that,
并没有这部电影的星级评价，

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and Alice really did not
Alice 并不喜欢

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like Nonstop Car Chases or
Nonstop Car Chases或者

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Swords vs. Karate. And a different user
Swords vs. Karate. 另一个用户

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Bob, user two, maybe rated
Bob,用户2，可能评级

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a different set of movies, maybe
一些不同的电影，可能

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she likes to Love at Last,
他喜欢Love at Last,

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did not to watch Romance Forever,
并没有看过Romance Forever,

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just have a rating of 4, a 0,
仅仅评了一个4星，一个0星，

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a 0, and maybe our 3rd user,
可能第三个用户，

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rates this 0, did not watch
评价它为0星，并没有看过

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that one, 0, 5, 5, and, you know, let's just
那部电影，0, 5, 5,你知道的，让我们仅仅

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fill in some of the numbers.
用一些数字填满。

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And so just to introduce a
下面介绍一些

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bit of notation, this notation
符号，这些符号

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that we'll be using throughout, I'm going
我们将一直使用，我将

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to use NU to denote the number of users.
用NU表示用户的数量。

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So in this example, NU will be equal to 4.
因此，在这个例子中，NU=4。

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So the u-subscript stands for
u的下标表示

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users and Nm,
用户数，Nm

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going to use to denote the number
用来表示电影的数量，

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of movies, so here I have five movies
这里我有5部电影，

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so Nm equals equals 5.
因此Nm=5.

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And you know for this example, I have
这个例子你知道的，

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for this example, I have loosely
我有

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3 maybe romantic or
3部浪漫或

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romantic comedy movies and 2
浪漫喜剧和2部

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action movies and you know, if
动作片，

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you look at this small example, it
你看这个小例子，它

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looks like Alice and Bob are
看起来像是Alice和 Bob

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giving high ratings to these
评了高星级给这些

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romantic comedies or movies
浪漫喜剧或者关于爱情的电影，

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about love, and giving very
给动作片非常

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low ratings about the action
低的评价，

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movies, and for Carol and Dave, it's the opposite, right?
Carol 和 Dave，他们的评价是相反的，对吗？

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Carol and Dave, users three
Carol 和 Dave，用户3和4，

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and four, really like the
喜欢

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action movies and give them
动作片并给它们

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high ratings, but don't like
高星级，但是不喜欢

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the romance and love-
浪漫剧和

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type movies as much.
爱情剧。

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Specifically, in the recommender system
尤其在推荐系统问题中，

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problem, we are given the following data.
我们给定下面数据，

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Our data comprises the following:
我们的数据组成如下：

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we have these values r(i, j), and
我们有值r(i, j),

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r(i, j) is 1 if user
r(i, j)=1，如果用户

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J has rated movie I.
j给电影i进行了评价。

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So our users rate only
因此，用户仅仅给

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some of the movies, and so,
某些电影评价，诸如此类。

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you know, we don't have
你知道，我们没有

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ratings for those movies.
对这些电影进行评价。

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And whenever r(i, j) is equal
r(i, j)等于1，仅当

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to 1, whenever user j has
用户j

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rated movie i, we also
给电影i进行了评价。我们也

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get this number y(i, j),
得到值y(i, j)，

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which is the rating given by
它是用户j给电影i的评级。

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user j to movie i. And

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so, y(i, j) would be
因此，y(i, j)是一个

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a number from zero to
从0到5的数字，

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five, depending on the star
依赖星级评定，

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rating, zero to five
用户给

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stars that user gave that particular movie.
特定电影评价0到5，五个星级。

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So, the recommender system problem
因此，推荐系统问题

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is given this data
给出了这个数据

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that has give these r(i, j)'s
这些r(i, j)和

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and the y(i, j)'s to look
y(i, j)数据，

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through the data and
浏览数据

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look at all the movie ratings that
查找所有未被评价的电影，

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are missing and to try
并试图

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to predict what these values
预测这些电影的评价星级。

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of the question marks should be.

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In the particular example, I have
在这个特殊的例子中，我有

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a very small number of movies
非常少的电影数量

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and a very small number of users
和用户数量，

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and so most users have rated most
因此，大多数用户都对大多数电影进行了评价。

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movies but in the realistic
但在现实情况中，

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settings your users each

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00:06:56,040 --> 00:06:57,120
of your users may have rated
每个用户可能仅评价

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00:06:57,600 --> 00:06:58,940
only a minuscule fraction of your
你的一部分电影，

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movies but looking at this
但看这些数据，

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00:07:00,310 --> 00:07:01,430
data, you know, if Alice and Bob
你知道的，如果Alice和Bob

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both like the romantic movies
都喜欢浪漫剧

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00:07:03,740 --> 00:07:05,810
maybe we think that Alice would have given this a five.
我们可能认为Alice将给电影评价5星。

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Maybe we think Bob would have
Bob或许给电影评价

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00:07:07,430 --> 00:07:08,570
given this a 4.5
4.5星

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00:07:08,750 --> 00:07:10,560
or some high value, as we
或更高的星级，

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00:07:10,690 --> 00:07:11,710
think maybe Carol and Dave
Carol和Dave

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00:07:12,590 --> 00:07:15,050
were doing these very low ratings.
将给浪漫剧非常低的评价。

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And Dave, well, if Dave really likes action movies,
如果Dave真的喜欢动作片，

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maybe he would have given
他可能给

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00:07:18,490 --> 00:07:19,540
Swords and Karate a 4
Swords and Karate评价4星

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rating or maybe a 5 rating, okay?
或者5星。

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And so, our job in developing
因此，如果我们想开发

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a recommender system is to
一个推荐系统，

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come up with a learning
那我们的工作是想出一个学习算法，

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algorithm that can automatically
一个能自动

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go fill in these missing values
为我们填补这些缺失值的算法，

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for us so that we
因此，我们

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can look at, say, the
可以看看，

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movies that the user has
该用户还没有看

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not yet watched, and recommend
电影，并推荐

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new movies to that user to watch.
新电影给该用户看。

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You try to predict what else might be interesting to a user.
你试图预测一个用户感兴趣的内容。

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So that's the formalism of the recommender system problem.
因此，这是推荐系统问题的形式主义。

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In the next video we'll start
下一段视频我们将

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to develop a learning algorithm to address this problem.
开发一个学习算法解决这个问题。