Discovering hidden structure by matrix factorization

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来自 University of Washington 的课程

机器学习基础：案例研究

7699 个评分

University of Washington

机器学习基础：案例研究

7699 个评分

课程 1（共 4 门，Specialization Machine Learning）

你是否好奇数据可以告诉你什么？你是否想在关于机器学习促进商业的核心方式上有深层次的理解？你是否想能同专家们讨论关于回归，分类，深度学习以及推荐系统的一切？在这门课上，你将会通过一系列实际案例学习来获取实践经历。在这门课结束的时候，

从本节课中

Recommending Products

Ever wonder how Amazon forms its personalized product recommendations? How Netflix suggests movies to watch? How Pandora selects the next song to stream? How Facebook or LinkedIn finds people you might connect with? Underlying all of these technologies for personalized content is something called collaborative filtering. <p>You will learn how to build such a recommender system using a variety of techniques, and explore their tradeoffs.</p> One method we examine is matrix factorization, which learns features of users and products to form recommendations. In an iPython notebook, you will use these techniques to build a real song recommender system.

The matrix completion task5:18

Recommendations from known user/item features6:00

Predictions in matrix form3:45

Discovering hidden structure by matrix factorization7:32

Bringing it all together: Featurized matrix factorization3:23

与讲师见面

Carlos Guestrin
Amazon Professor of Machine Learning
Computer Science and Engineering
Emily Fox
Amazon Professor of Machine Learning
Statistics

[MUSIC]

So to this point though,

we've assumed that we know all these Lu user topic vectors.

So we can stack them up into this L matrix.

And we know all the movie topic factors.

So we put them altogether in that R matrix.

And then, we multiply the two together to get this big prediction

of readings that every user would give to every movie.

But important thing here is the fact that we don't actually have this information.

We don't have these features about the users, or about the movies.

So instead, what we're gonna do is we're gonna flip this problem on its head.

And we're gonna try and estimate these matrices, this L and

R matrix, which is equivalent to estimating these topic vectors, or

feature vectors, for every user and every movie based on our observed ratings.

So these matrices, or these collections of topic vectors,

are the parameters of our model.

So going back to the regression

module that we had, we talked about models and their associated parameters in

thinking about estimating those parameters from data.

So this is a very similar notion.

So we have data.

What are our data?

In this case, our data are our observed ratings.

So those are the black squares.

And our parameters are these user and movie topic factors.

Okay, so what we're gonna do is we're gonna estimate each of these from

our observe reading.

So only using these black cells, we're gonna try and

estimate these L and R vectors and resulting matrices.

So how are we gonna do this?

Well, let's think of a metric for

fit just like we talked about in the regression module.

If you remember,

going back to that module we talked about something called residual sum of squares.

There we were talking about a house.

It had some set of features.

And then, [COUGH] we had weights on those features,

those weights were our parameters.

And we were predicting somehow sales price.

And then, we compared with the actual sales price, and we looked at

the square of that difference, and we summed over every house in our data set.

Well, in this case, the parameters of our model are L and R.

And our prediction, our ratings hat is gonna be <Lu,

Rv>, this notation of doing this element wise product in summing.

And that's our predicted rating.

And then, our observed rating is Rating(u,v),

and what we're gonna do is look at that difference,

the difference between our observed rating and

what we're predicting with our parameters Lu and Rv, and we're gonna square them.

And we're gonna say our residual sum

of squares of our parameters L and

R is equal to this, and then we're gonna

sum over all movies that have ratings.

So we're gonna include all u,

v pairs where [BLANK_ AUDIO] rating,

let me use u' to v' to distinguish it

from the specific u and v example I gave here.

So we're gonna add in all u' v' pairs.

Where rating u' and

rating v' are available.

And where are these available?

They are the black squares.

Just remember this picture here.

Okay, so what I'm doing is I'm taking a given L matrix and

R matrix, I'm looking at my predictions.

So I'm looking at, and I'm gonna evaluate how well I did on all these black squares.

So I'm looking at how well the L and U that I'm using fit my observed ratings.

And then, when I want to go to estimate L and R,

just like when I wanted to estimate the weights on the regression coefficients in

that housing value prediction problem, I search over, in this case, all

the user topic vectors and all the movie topic vectors, and find the combination of

this huge space of parameters that best fits my observed ratings.

And so, the reason this is called a Matrix Factorization model, so that's really key.

This is called a matrix factorization model, because I'm taking this matrix,

and approximating it with this factorization here.

But the key thing is the output of this, is a set of estimated parameters here.

And, unfortunately, I've just written over this very, very, very key point.

So I apologize for that.

Let's pause for a second, so that you get the writing.

And now, I'll just say in words this next animation is saying that there are a lot

of very efficient algorithms for doing this factorization.

And we're gonna talk about them in great extent in the recommender systems,

or matrix factorization course later on.

But then, okay, so very efficient algorithms for

computing these estimates of L and R.

How do I form my predictions?

How do I fill in all these white squares, which was my goal to start with.

Well, I just use my estimated L hat u.

And R hat v.

And I form my prediction just as we described

when we assumed that we actually knew these vectors.

Okay, well, matrix factorization is a really, really powerful tool.

And it's been proven useful on lots of different applications.

But there's one limitation, and that's a problem that we talked about a little

bit earlier of the cold-start problem where this model still can't

handle this problem of what if we get a new user or a new movie.

So that's the case where we have no ratings either for

a specific user or a specific movie.

So that might be a new movie that arrives or a new user arrives.

So this is a really important problem.

And one that, for example, Netflix faces all the time.

How do we make predictions for these users or movies?

[MUSIC]

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