Bayesian Ranking: Part I

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Networks Illustrated: Principles without Calculus

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Princeton University

Networks Illustrated: Principles without Calculus

43 ratings

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. All the features of this course are available for free. It does not offer a certificate upon completion.

From the lesson

Product Rating on Amazon

The decision of whether or not to purchase something online is often driven by the ratings that previous customers have left for it. In this lesson, we will take a look at Amazon's review system, and the see how "crowds are wise" is another important networking principle.

Amazon & eCommerce4:28

Average Ratings10:21

The Wisdom of Crowds10:03

Rating Aggregation Challenges4:11

Naive Averaging5:57

Bayesian Ranking: Part I5:32

Bayesian Ranking: Part II9:14

Bayesian Ranking in Practice5:41

What does Amazon do? Part I5:00

What does Amazon do? Part II5:29

Meet the Instructors

Christopher Brinton
Lecturer
Electrical Engineering
Mung Chiang
Professor
Electrical Engineering

So the question is, how do we deal with this issue that we brought up?

Varying sample sizes for each of the products.

So, we should somehow weight the raw rating score with the population sizes.

So, we should rate the Panasonic somehow, weight it with the total

number of 11, versus the Toshiba having a total number of 64 [UNKNOWN].

We should somehow take that into account here.

So, knowing the total number of reviews actually gives us some prior knowledge.

And what we can do is,

rather than considering each product entirely separate.

We could use some information about the entire

population over all the DVD players in doing this.

And that's going to give us the idea behind Bayesian ranking.

Right, so we want to aggregate some information across all of them.

That's going to give us an, allow us to leverage what the

total number of reviews is in each of the individual cases.

As opposed to the total number of reviews overall.

So, to do this first we can find the overall average.

And the overall average is just the average, across all the products.

So, rather than looking at each of the product categories we sum down

the total number of five stars and get the total across all DVD players.

Four stars get the totals across them.

Three stars and so forth.

So, now we have these totals here.

So, did you find the overall average?

All we need to is apply our avenging formula again as before,

but just this time using the totals rather than the individual product numbers.

And the reason that we want to do this is that that

the overall average is giving us

information about the population as a whole.

Rather than these the indi-, the products individually.

So this is going to come out to be 83 times 5.

Plus 51 times 4.

Plus 31 times 3.

Plus 17 times 2.

Plus 38 times 1.

So 83 times 5, 51 times 4, and so on.

And divide by the total number, which is 83,

plus 51, plus 31, 17, 38, which is 220.

And

when we do that out.

Comes to be 784 over 220, which is 3.564.

So that's the overall average.

3.564 across all the products.

The idea's that we want to use this overall average as a backup, right?

So this is computed based on the entire population.

Which has a higher total than any of the individual products.

So, we can illustrate what we're going to do in

Bayesian ranking, through this concept called the sliding ruler.

Right, so, suppose the, this overall average is here.

So this is the overall.

And now suppose the individual average is over here, so individual.

For instance, the overall being 3.564 as opposed to the

Panasonic average which we've shown before was well over four stars.

That could be one case where the individual is higher than the overall.

So, the idea is that we can draw, or we

can, we can connect them on just a number line here.

And, what we want to do is we want

to somehow drag the individual back towards the overall.

Depending upon how many people we used to

compute the individual as opposed to the overall.

So, the idea is that the more ratings there are for a given individual product.

The more trustworthy the individual average should be relative to the overall.

So, as we have more ratings for an individual

product, we want to trust the individual rating more.

But, as we have less ratings for an individual product, we want to use

the overall average as the backup, and slide this ruler towards the overall.

So, this could be, sup, suppose this is the adjusted.

Somewhere in between.

The idea is that as we have more ratings in

the individual case we're going to slide it towards the individual average.

And as we have less rate towards individual case and

more towards the overall we're going to slide it towards this way.

And of course, the individual could be less than the overall.

So the individual could also be back here.

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And then we would do the same thing where we could have an adjusted average here.

And in this case as we have more individual

ratings we're going to slide that back towards the individual.

As we have less individual ratings we're going to go more towards the

overall rating and leverage what we know about the population as a whole.

So, the Bayesian ranking formula in order for computing the the Bayesian rating.

Which then we use to rank the products, is we take the overall number, so

that's the overall number of products 220, times the overall average.

Which is we just computed speed 3.564, and then we add to that the individual number.

So, for each product, the individual number, which would

be 11 in this case, times the individual average.

Which, in this case, four point something for the

Panasonic, divided by the overall number plus the individual numbers.

So what we're doing is we're weighting the two averages.

By the respective numbers that we use to compute them.

Overall num, and individual num.

They're to be used to weight those averages.

Adding them together and dividing by the total number of ratings.

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