In this video I am going to define what is probably the most common type of machine
learning problem, which is supervised learning. I'll define supervised learning
more formally later, but it's probably best to explain or start with an example
of what it is and we'll do the formal definition later. Let's say you want to
predict housing prices. A while back, a student collected data sets from the
Institute of Portland Oregon. And let's say you plot a data set and it looks like
this. Here on the horizontal axis, the size of different houses in square feet,
and on the vertical axis, the price of different houses in thousands of dollars.
So. Given this data, let's say you have a friend who owns a house that is, say 750
square feet and hoping to sell the house and they want to know how much they can
get for the house. So how can the learning algorithm help you? One thing a learning
algorithm might be able to do is put a straight line through the data or to fit a
straight line to the data and, based on that, it looks like maybe the house can be
sold for maybe about $150,000. But maybe this isn't the only learning algorithm you can
use. There might be a better one. For example, instead of sending a straight
line to the data, we might decide that it's better to fit a quadratic
function or a second-order polynomial to this data. And if you do that, and make a
prediction here, then it looks like, well, maybe we can sell the house for closer to
$200,000. One of the things we'll talk about later is how to choose and how to
decide do you want to fit a straight line to the data or do you want to fit the
quadratic function to the data and there's no fair picking whichever one gives your
friend the better house to sell. But each of these would be a fine example of a
learning algorithm. So this is an example of a supervised learning algorithm. And
the term supervised learning refers to the fact that we gave the algorithm a data set
in which the "right answers" were given. That is, we gave it a data set of
houses in which for every example in this data set, we told it what is the right
price so what is the actual price that, that house sold for and the toss of the
algorithm was to just produce more of these right answers such as for this new
house, you know, that your friend may be trying to sell. To define with a bit more
terminology this is also called a regression problem and by regression
problem I mean we're trying to predict a continuous value output. Namely the price.
So technically I guess prices can be rounded off to the nearest cent. So maybe
prices are actually discrete values, but usually we think of the price of a house
as a real number, as a scalar value, as a continuous value number and the term
regression refers to the fact that we're trying to predict the sort of continuous
values attribute. Here's another supervised learning example, some friends
and I were actually working on this earlier. Let's see you want to look at
medical records and try to predict of a breast cancer as malignant or benign. If
someone discovers a breast tumor, a lump in their breast, a malignant tumor is a
tumor that is harmful and dangerous and a benign tumor is a tumor that is harmless.
So obviously people care a lot about this. Let's see a collected data set and suppose
in your data set you have on your horizontal axis the size of the tumor and
on the vertical axis I'm going to plot one or zero, yes or no, whether or not these are
examples of tumors we've seen before are malignant–which is one–or zero if not malignant
or benign. So let's say our data set looks like this where we saw a tumor of this
size that turned out to be benign. One of this size, one of this size. And so on.
And sadly we also saw a few malignant tumors, one of that size, one of that
size, one of that size... So on. So this example... I have five examples of benign
tumors shown down here, and five examples of malignant tumors shown with a vertical
axis value of one. And let's say we have a friend who tragically has a breast
tumor, and let's say her breast tumor size is maybe somewhere around this value. The
machine learning question is, can you estimate what is the probability, what is
the chance that a tumor is malignant versus benign? To introduce a bit more
terminology this is an example of a classification problem. The term
classification refers to the fact that here we're trying to predict a discrete
value output: zero or one, malignant or benign. And it turns out that in
classification problems sometimes you can have more than two values for the two
possible values for the output. As a concrete example maybe there are three
types of breast cancers and so you may try to predict the discrete value of zero,
one, two, or three with zero being benign. Benign tumor, so no cancer. And one may
mean, type one cancer, like, you have three types of cancer, whatever type one
means. And two may mean a second type of cancer, a three may mean a third type of
cancer. But this would also be a classification problem, because this other
discrete value set of output corresponding to, you know, no cancer, or cancer type
one, or cancer type two, or cancer type three. In classification problems there is
another way to plot this data. Let me show you what I mean. Let me use a slightly
different set of symbols to plot this data. So if tumor size is going to be the
attribute that I'm going to use to predict malignancy or benignness, I can also draw
my data like this. I'm going to use different symbols to denote my benign and
malignant, or my negative and positive examples. So instead of drawing crosses,
I'm now going to draw O's for the benign tumors. Like so. And I'm going to keep
using X's to denote my malignant tumors. Okay? I hope this is beginning to make
sense. All I did was I took, you know, these, my data set on top and I just
mapped it down. To this real line like so. And started to use different symbols,
circles and crosses, to denote malignant versus benign examples. Now, in this
example we use only one feature or one attribute, mainly, the tumor size in order
to predict whether the tumor is malignant or benign. In other machine learning
problems when we have more than one feature, more than one attribute. Here's
an example. Let's say that instead of just knowing the tumor size, we know both the
age of the patients and the tumor size. In that case maybe your data set will look
like this where I may have a set of patients with those ages and that tumor size and
they look like this. And a different set of patients, they look a little different,
whose tumors turn out to be malignant, as denoted by the crosses. So, let's say you
have a friend who tragically has a tumor. And maybe, their tumor size and age
falls around there. So given a data set like this, what the learning algorithm
might do is throw the straight line through the data to try to separate out
the malignant tumors from the benign ones and, so the learning algorithm may decide
to throw the straight line like that to separate out the two classes of tumors.
And. You know, with this, hopefully you can decide that your friend's tumor is
more likely to if it's over there, that hopefully your learning algorithm
will say that your friend's tumor falls on this benign side and is therefore more
likely to be benign than malignant. In this example we had two features, namely,
the age of the patient and the size of the tumor. In other machine learning problems
we will often have more features, and my friends that work on this problem, they
actually use other features like these, which is clump thickness, the clump thickness of
the breast tumor. Uniformity of cell size of the tumor. Uniformity of cell shape of
the tumor, and so on, and other features as well. And it turns out one of the interes-,
most interesting learning algorithms that we'll see in this class is a learning
algorithm that can deal with, not just two or three or five features, but an infinite
number of features. On this slide, I've listed a total of five different features.
Right, two on the axes and three more up here. But it turns out that for some learning
problems, what you really want is not to use, like, three or five features. But
instead, you want to use an infinite number of features, an infinite number of
attributes, so that your learning algorithm has lots of attributes or
features or cues with which to make those predictions. So how do you deal with an
infinite number of features. How do you even store an infinite number of
things on the computer when your computer is gonna run out of memory. It
turns out that when we talk about an algorithm called the Support Vector
Machine, there will be a neat mathematical trick that will allow a computer to deal
with an infinite number of features. Imagine that I didn't just write down two features
here and three features on the right. But, imagine that I wrote down an infinitely long list, I
just kept writing more and more and more features. Like an infinitely long list of
features. Turns out, we'll be able to come up with an algorithm that can deal with
that. So, just to recap. In this class we'll talk about supervised
learning. And the idea is that, in supervised learning, in every example in
our data set, we are told what is the "correct answer" that we would have
quite liked the algorithms have predicted on that example. Such as the price of the
house, or whether a tumor is malignant or benign. We also talked about the
regression problem. And by regression, that means that our goal is to predict a
continuous valued output. And we talked about the classification problem, where
the goal is to predict a discrete value output. Just a quick wrap up question:
Suppose you're running a company and you want to develop learning algorithms to
address each of two problems. In the first problem, you have a large inventory of
identical items. So imagine that you have thousands of copies of some identical
items to sell and you want to predict how many of these items you sell within the
next three months. In the second problem, problem two, you'd like-- you have lots of
users and you want to write software to examine each individual of your
customer's accounts, so each one of your customer's accounts; and for each account,
decide whether or not the account has been hacked or compromised. So, for each of
these problems, should they be treated as a classification problem, or as a
regression problem? When the video pauses, please use your mouse to select whichever
of these four options on the left you think is the correct answer. So hopefully,
you got that this is the answer. For problem one, I would treat this as a
regression problem, because if I have, you know, thousands of items, well, I would
probably just treat this as a real value, as a continuous value. And
treat, therefore, the number of items I sell, as a continuous value. And for the
second problem, I would treat that as a classification problem, because I might
say, set the value I want to predict with zero, to denote the account has not been
hacked. And set the value one to denote an account that has been hacked into. So just
like, you know, breast cancer, is, zero is benign, one is malignant. So I
might set this be zero or one depending on whether it's been hacked, and have an
algorithm try to predict each one of these two discrete values. And because there's a
small number of discrete values, I would therefore treat it as a classification
problem. So, that's it for supervised learning and in the next video I'll talk
about unsupervised learning, which is the other major category of learning algorithms.