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So if – well, suppose you want to evaluate your hypothesis H at a certain point with a certain query point low K is X. Okay? And let’s say you want to know what’s the predicted value of Y at this position of X, right? So for linear regression, what we were doing was we would fit theta to minimize sum over I, YI minus theta, transpose XI squared, and return theta transpose X. Okay? So that was linear regression. In contrast, in locally weighted linear regression you’re going to do things slightly different. You’re going to look at this point X and then I’m going to look in my data set and take into account only the data points that are, sort of, in the little vicinity of X. Okay? So we’ll look at where I want to value my hypothesis. I’m going to look only in the vicinity of this point where I want to value my hypothesis, and then I’m going to take, let’s say, just these few points, and I will apply linear regression to fit a straight line just to this sub-set of the data. Okay? I’m using this sub-term sub-set – well let’s come back to that later. So we take this data set and I fit a straight line to it and maybe I get a straight line like that. And what I’ll do is then evaluate this particular value of straight line and that will be the value I return for my algorithm. I think this would be the predicted value for – this would be the value of then my hypothesis outputs in locally weighted regression. Okay?

So we’re gonna fall one up. Let me go ahead and formalize that. In locally weighted regression, we’re going to fit theta to minimize sum over I to minimize that where these terms W superscript I are called weights. There are many possible choice for ways, I’m just gonna write one down. So this E’s and minus, XI minus X squared over two. So let’s look at what these weights really are, right? So notice that – suppose you have a training example XI. So that XI is very close to X. So this is small, right? Then if XI minus X is small, so if XI minus X is close to zero, then this is E’s to the minus zero and E to the zero is one. So if XI is close to X, then WI will be close to one. In other words, the weight associated with the, I training example be close to one if XI and X are close to each other. Conversely if XI minus X is large then – I don’t know, what would WI be?

Student: Zero.

Instructor (Andrew Ng) :Zero, right. Close to zero. Right. So if XI is very far from X then this is E to the minus of some large number and E to the minus some large number will be close to zero. Okay? So the picture is, if I’m quarrying at a certain point X, shown on the X axis, and if my data set, say, look like that, then I’m going to give the points close to this a large weight and give the points far away a small weight. So for the points that are far away, WI will be close to zero. And so as if for the points that are far away, they will not contribute much at all to this summation, right? So I think this is sum over I of one times this quadratic term for points by points plus zero times this quadratic term for faraway points. And so the effect of using this weighting is that locally weighted linear regression fits a set of parameters theta, paying much more attention to fitting the points close by accurately. Whereas ignoring the contribution from faraway points. Okay? Yeah?

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
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Source:  OpenStax, Machine learning. OpenStax CNX. Oct 14, 2013 Download for free at http://cnx.org/content/col11500/1.4
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