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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

I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
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
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
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.
Bharti
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
Daniel
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
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit 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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