Baseline Predictor

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来自 Princeton University 的课程

Networks Illustrated: Principles without Calculus

39 个评分

Princeton University

Networks Illustrated: Principles without Calculus

39 个评分

What makes WiFi faster at home than at a coffee shop? How does Google order its search results from the trillions of webpages on the Internet? Why does Verizon charge $15 for every GB of data we use? Is it really true that we are connected in six social steps or less? These are just a few of the many intriguing questions we can ask about the social and technical networks that form integral parts of our daily lives. This course is about exploring the answers, using a language that anyone can understand. We will focus on fundamental principles like “sharing is hard”, “crowds are wise”, and “network of networks” that have guided the design and sustainability of today’s networks, and summarize the theories behind everything from the social connections we make on platforms like Facebook to the technology upon which these websites run. Unlike other networking courses, the mathematics included here are no more complicated than adding and multiplying numbers. While mathematical details are necessary to fully specify the algorithms and systems we investigate, they are not required to understand the main ideas. We use illustrations, analogies, and anecdotes about networks as pedagogical tools in lieu of detailed equations. Please note that per Princeton University policy, no certificates, credentials or reports are awarded in connection with this course.

从本节课中

Movie Recommendation on Netflix

One of the perks of having a Netflix subscription is getting recommendations of movies to watch. Behind the scenes, Netflix uses powerful algorithms to determine which will be suggested to each person specifically. In this lesson, we will take a look at the main ideas behind these algorithms.

Netflix Timeline5:21

Video Streaming5:19

Recommendation is Everywhere3:24

Netflix Recommendation System5:20

Netflix Prize: Logistics7:38

Netflix Prize: The Competition4:33

Our Example3:48

Raw Average7:13

User-movie Interactions7:00

Baseline Predictor6:57

Cosine Similarity9:18

Similarity Values10:58

Leveraging Similarity8:30

Neighborhood Predictor4:44

Performance of Different Methods3:30

Copy of Cosine Similarity9:18

与讲师见面

Christopher Brinton
Lecturer
Electrical Engineering
Mung Chiang
Professor
Electrical Engineering

Then once we have the bias values we want to actually take them and we want to come

up with the baseline predictor. And so we just basically add the bias

values in from that. And so here's a tabulation of the bias

values that we just computed just in table form.

The users are over here and the movies are over here.

And so we'll start with user D, and movie three.

And, we'll just, we'll just illustrate, just a few of these computations.

Just two of them. We'll just do, for instance, user D,

movie three. so, D and three.

Remember we start with the, the baseline or the, the raw average value of, 3.5.

Then we add in the bias of user D, which is negative 1.5, and then we add in the

bias of movie three, which is 0.75. So, remember D is a harsh critic.

And three is a, good, quote unquote, good movie.

And when we do that out, we come up with 2.75 it's value, so it's lower than the

mean, we expect it to be lower than the mean.

And, the intuition there is that movie three isn't as, quote unquote, much

better than the average than D is quote unquote more of a harsh critic than the

average. So they don't quite cancel each other out

and we do end up going below the average here for this pair, D3.

let's try User A, movie two. So we have A2 and that's a value that we

don't already know. For D3 we do have that value.

Now we want to try A2, something that we don't know.

so we do A2, we get, we start with the mean, again, of 3.5, then we add the bias

of A, which is 0.83 and then we add, the bias of movie two, which is -1.17, so

again, this is more negative than this is positive, so.

We're going to go below the average and we get 3.16.

It's here, say it's little, again, a little more below the average.

And if we continue that out, we do the baseline for all the values, this is what

we'll get in this table here. And just a note, for instance some of

values are with this, only one value actually, is 5.00.

the reason that it's not, if you did the calculation out for four you would have

bias of 8.83 and movie 3 0.75. It would go above five.

But we clip them at five because it's not possible to be greater than five.

So therefore we just clip and that's kind of an important point.

the reason we clip them at five is because we know the rating can't be

greater than five so we'd only be hurting ourselves by pushing it above five.

So if it goes above five then we just hit it at five.

And if it goes below one, then we just assume that it's one, so, we, remember we

can only be between one and five here. So, now, once you do this out, we can do

the RMSE, oh and just let me say here, also, this is a five, so that's clipped

and this is a one, so that's also clipped.

so you can do that out. you can see from D, D2 for instance, D,

that's going to go below because 2 minus 1.5 minus 1.17 is already actually a

negative number, it's below 0, even. So, we just clip that at one.

So now, the RMSE, we'll do the RMSE of the test set.

I'm just going to do it, I'm not going to do every step out this time, I'm just

going to do it all in one single step. So again, we do the square root and then

we have to find the mean of the squared errors.

So now we're right at the squared errors terms so we have 4 and 2.80, so this is 4

minus 2.80 squared plus, now the second one.

This is 2 minus 1 squared plus in the third one we have 5 minus 5 squared.

Which is just 0 because 5 minus 5 is 0. The fourth one we have 3 minus 3.5

squared. And the fifth one, it's kind of running

out of room over here, but now the fifth one.

We have 4 minus 3.85 squared, and we divide that by 5 because we're averaging

everything. So, write out, I'm going to write out

what each of these terms are when we square them in here.

We get, this is 1.44. This is 1 clearly because 2 minus 1 is 1.

1 squared is just 1. We have zero, as we said.

We have a 0.25, and, we have a, 0.0225. That's all divided by 5 to average it,

and then we take the square root of the whole thing.

And then that, when we do that out, we get 0.7365.

[SOUND] Now, it's the RMSE for the test set.

If we do the training set, we will get 0.4709, and we won't do that out again,

because there's 20 of those terms. Which would be a lot to write on paper,

but that's the idea. So now we can compare this with the RMSE

that we had before. And so now we have an improvement.

If we do an improvement over that 1.0247 which is what we had before, an RMSE, the

test set just when we did the raw averaging we're down to 0.7365 now.

So if we want to find the percent improvement over that we just do, we

start at one because everything is around, starts at 100% so we're trying to

find a percent improvement. So basically what we're going to do is

we're going to find out what fraction we are of that right now.

So 0.7365 is where we are now, and we were at 1.0247.

Right. And so we do 1 minus that because we're

trying to find the im- percent improvement.

So the lower that we are relative to this, the better.

And let's multiply that by 100%. And we get 28.13%.

So, we're, we're improved almost 30% over what we had before.

And then for this guy the improvement's actually more like 59 %.

So you can see that again we're we did much better than we did when we just did

a simple raw average. And so that somewhat explaining the

utility of using this approach, but know that the percentage improvements are

going to be way different depending upon what example, this is only one example.

And in fact the improvement could be negative, in which case we're actually

getting worse. and so it's not always guaranteed that we

are going to be getting better. Especially if there's some unknown,

patterns in the data. but on average we expect intuitively that

incorporating this is going to make our prediction better.

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