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In this video I am going to define what is
probably the most common type of machine

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learning problem, which is supervised
learning. I'll define supervised learning

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more formally later, but it's probably
best to explain or start with an example

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of what it is and we'll do the formal
definition later. Let's say you want to

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predict housing prices. A while back, a
student collected data sets from the

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Institute of Portland Oregon. And let's
say you plot a data set and it looks like

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this. Here on the horizontal axis, the
size of different houses in square feet,

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and on the vertical axis, the price of
different houses in thousands of dollars.

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So. Given this data, let's say you have a
friend who owns a house that is, say 750

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square feet and hoping to sell the house
and they want to know how much they can

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get for the house. So how can the learning
algorithm help you? One thing a learning

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algorithm might be able to do is put a
straight line through the data or to fit a

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straight line to the data and, based on
that, it looks like maybe the house can be

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sold for maybe about $150,000. But maybe this
isn't the only learning algorithm you can

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use. There might be a better one. For
example, instead of sending a straight

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line to the data, we might decide that
it's better to fit a quadratic

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function or a second-order polynomial to
this data. And if you do that, and make a

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prediction here, then it looks like, well,
maybe we can sell the house for closer to

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$200,000. One of the things we'll talk
about later is how to choose and how to

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decide do you want to fit a straight line
to the data or do you want to fit the

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quadratic function to the data and there's
no fair picking whichever one gives your

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friend the better house to sell. But each
of these would be a fine example of a

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learning algorithm. So this is an example
of a supervised learning algorithm. And

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the term supervised learning refers to the
fact that we gave the algorithm a data set

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in which the "right answers" were
given. That is, we gave it a data set of

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houses in which for every example in this
data set, we told it what is the right

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price so what is the actual price that,
that house sold for and the toss of the

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algorithm was to just produce more of
these right answers such as for this new

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house, you know, that your friend may be
trying to sell. To define with a bit more

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terminology this is also called a
regression problem and by regression

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problem I mean we're trying to predict a
continuous value output. Namely the price.

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So technically I guess prices can be
rounded off to the nearest cent. So maybe

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prices are actually discrete values, but
usually we think of the price of a house

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as a real number, as a scalar value, as
a continuous value number and the term

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regression refers to the fact that we're
trying to predict the sort of continuous

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values attribute. Here's another
supervised learning example, some friends

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and I were actually working on this
earlier. Let's see you want to look at

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medical records and try to predict of a
breast cancer as malignant or benign. If

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someone discovers a breast tumor, a lump
in their breast, a malignant tumor is a

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tumor that is harmful and dangerous and a
benign tumor is a tumor that is harmless.

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So obviously people care a lot about this.
Let's see a collected data set and suppose

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in your data set you have on your
horizontal axis the size of the tumor and

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on the vertical axis I'm going to plot one
or zero, yes or no, whether or not these are

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examples of tumors we've seen before are
malignant–which is one–or zero if not malignant

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or benign. So let's say our data set looks
like this where we saw a tumor of this

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size that turned out to be benign. One of
this size, one of this size. And so on.

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And sadly we also saw a few malignant
tumors, one of that size, one of that

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size, one of that size... So on. So this
example... I have five examples of benign

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tumors shown down here, and five examples
of malignant tumors shown with a vertical

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axis value of one. And let's say we have
a friend who tragically has a breast

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tumor, and let's say her breast tumor size
is maybe somewhere around this value. The

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machine learning question is, can you
estimate what is the probability, what is

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the chance that a tumor is malignant
versus benign? To introduce a bit more

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terminology this is an example of a
classification problem. The term

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classification refers to the fact that
here we're trying to predict a discrete

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value output: zero or one, malignant or
benign. And it turns out that in

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classification problems sometimes you can
have more than two values for the two

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possible values for the output. As a
concrete example maybe there are three

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types of breast cancers and so you may try
to predict the discrete value of zero,

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one, two, or three with zero being benign.
Benign tumor, so no cancer. And one may

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mean, type one cancer, like, you have
three types of cancer, whatever type one

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means. And two may mean a second type of
cancer, a three may mean a third type of

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cancer. But this would also be a
classification problem, because this other

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discrete value set of output corresponding
to, you know, no cancer, or cancer type

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one, or cancer type two, or cancer type
three. In classification problems there is

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another way to plot this data. Let me show
you what I mean. Let me use a slightly

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different set of symbols to plot this
data. So if tumor size is going to be the

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attribute that I'm going to use to predict
malignancy or benignness, I can also draw

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my data like this. I'm going to use
different symbols to denote my benign and

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malignant, or my negative and positive
examples. So instead of drawing crosses,

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I'm now going to draw O's for the benign
tumors. Like so. And I'm going to keep

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using X's to denote my malignant tumors.
Okay? I hope this is beginning to make

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sense. All I did was I took, you know,
these, my data set on top and I just

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mapped it down. To this real line like so.
And started to use different symbols,

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circles and crosses, to denote malignant
versus benign examples. Now, in this

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example we use only one feature or one
attribute, mainly, the tumor size in order

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to predict whether the tumor is malignant
or benign. In other machine learning

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problems when we have more than one
feature, more than one attribute. Here's

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an example. Let's say that instead of just
knowing the tumor size, we know both the

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age of the patients and the tumor size. In
that case maybe your data set will look

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like this where I may have a set of patients
with those ages and that tumor size and

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they look like this. And a different set
of patients, they look a little different,

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whose tumors turn out to be malignant, as
denoted by the crosses. So, let's say you

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have a friend who tragically has a
tumor. And maybe, their tumor size and age

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falls around there. So given a data set
like this, what the learning algorithm

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might do is throw the straight line
through the data to try to separate out

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the malignant tumors from the benign ones
and, so the learning algorithm may decide

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to throw the straight line like that to
separate out the two classes of tumors.

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And. You know, with this, hopefully you
can decide that your friend's tumor is

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more likely to if it's over there,
that hopefully your learning algorithm

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will say that your friend's tumor falls on
this benign side and is therefore more

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likely to be benign than malignant. In
this example we had two features, namely,

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the age of the patient and the size of the
tumor. In other machine learning problems

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we will often have more features, and my
friends that work on this problem, they

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actually use other features like these,
which is clump thickness, the clump thickness of

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the breast tumor. Uniformity of cell size
of the tumor. Uniformity of cell shape of

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the tumor, and so on, and other features
as well. And it turns out one of the interes-,

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most interesting learning algorithms that
we'll see in this class is a learning

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algorithm that can deal with, not just two
or three or five features, but an infinite

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number of features. On this slide, I've
listed a total of five different features.

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Right, two on the axes and three more up here.
But it turns out that for some learning

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problems, what you really want is not to
use, like, three or five features. But

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instead, you want to use an infinite
number of features, an infinite number of

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attributes, so that your learning
algorithm has lots of attributes or

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features or cues with which to make those
predictions. So how do you deal with an

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infinite number of features. How do you even
store an infinite number of

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things on the computer when your
computer is gonna run out of memory. It

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turns out that when we talk about an
algorithm called the Support Vector

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Machine, there will be a neat mathematical
trick that will allow a computer to deal

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with an infinite number of features. Imagine
that I didn't just write down two features

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here and three features on the right. But, imagine that
I wrote down an infinitely long list, I

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just kept writing more and more and more
features. Like an infinitely long list of

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features. Turns out, we'll be able to come
up with an algorithm that can deal with

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that. So, just to recap. In this
class we'll talk about supervised

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learning. And the idea is that, in
supervised learning, in every example in

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our data set, we are told what is the
"correct answer" that we would have

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quite liked the algorithms have predicted
on that example. Such as the price of the

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house, or whether a tumor is malignant or
benign. We also talked about the

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regression problem. And by regression,
that means that our goal is to predict a

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continuous valued output. And we talked
about the classification problem, where

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the goal is to predict a discrete value
output. Just a quick wrap up question:

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Suppose you're running a company and you
want to develop learning algorithms to

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address each of two problems. In the first
problem, you have a large inventory of

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identical items. So imagine that you have
thousands of copies of some identical

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items to sell and you want to predict how
many of these items you sell within the

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next three months. In the second problem,
problem two, you'd like--  you have lots of

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users and you want to write software to
examine each individual of your

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customer's accounts, so each one of your
customer's accounts; and for each account,

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decide whether or not the account has been
hacked or compromised. So, for each of

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these problems, should they be treated as
a classification problem, or as a

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regression problem? When the video pauses,
please use your mouse to select whichever

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of these four options on the left you
think is the correct answer. So hopefully,

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you got that this is the answer. For
problem one, I would treat this as a

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regression problem, because if I have, you
know, thousands of items, well, I would

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probably just treat this as a real value,
as a continuous value. And

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treat, therefore, the number of items I sell,
as a continuous value. And for the

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second problem, I would treat that as a
classification problem, because I might

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say, set the value I want to predict with
zero, to denote the account has not been

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hacked. And set the value one to denote an
account that has been hacked into. So just

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like, you know, breast cancer, is,
zero is benign, one is malignant. So I

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might set this be zero or one depending on
whether it's been hacked, and have an

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algorithm try to predict each one of these
two discrete values. And because there's a

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small number of discrete values, I would
therefore treat it as a classification

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problem. So, that's it for supervised
learning and in the next video I'll talk

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about unsupervised learning, which is the
other major category of learning algorithms.