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Student: Your Y is exponentially [inaudible]?

Instructor (Andrew Ng) :Yeah. Let’s see. So it turns out there are many other weighting functions you can use. It turns out that there are definitely different communities of researchers that tend to choose different choices by default. There is somewhat of a literature on debating what point – exactly what function to use. This, sort of, exponential decay function is – this happens to be a reasonably common one that seems to be a more reasonable choice on many problems, but you can actually plug in other functions as well. Did I mention what [inaudible] is it at? For those of you that are familiar with the normal distribution, or the Gaussian distribution, say this – what this formula I’ve written out here, it cosmetically looks a bit like a Gaussian distribution. Okay? But this actually has absolutely nothing to do with Gaussian distribution. So this is not that a problem with XI is Gaussian or whatever. This is no such interpretation. This is just a convenient function that happens to be a bell-shaped function, but don’t endow this of any Gaussian semantics. Okay?

So, in fact – well, if you remember the familiar bell-shaped Gaussian, again, it’s just the ways of associating with these points is that if you imagine putting this on a bell-shaped bump, centered around the position of where you want to value your hypothesis H, then there’s a saying this point here I’ll give a weight that’s proportional to the height of the Gaussian – excuse me, to the height of the bell-shaped function evaluated at this point. And the way to get to this point will be, to this training example, will be proportionate to that height and so on. Okay? And so training examples that are really far away get a very small weight.

One last small generalization to this is that normally there’s one other parameter to this algorithm, which I’ll denote as tow. Again, this looks suspiciously like the variants of a Gaussian, but this is not a Gaussian. This is a convenient form or function. This parameter tow is called the bandwidth parameter and informally it controls how fast the weights fall of with distance. Okay? So just copy my diagram from the other side, I guess. So if tow is very small, if that’s a query X, then you end up choosing a fairly narrow Gaussian – excuse me, a fairly narrow bell shape, so that the weights of the points are far away fall off rapidly. Whereas if tow is large then you’d end up choosing a weighting function that falls of relatively slowly with distance from your query. Okay?

So I hope you can, therefore, see that if you apply locally weighted linear regression to a data set that looks like this, then to ask what your hypothesis output is at a point like this you end up having a straight line making that prediction. To ask what kind of class this [inaudible] at that value you put a straight line there and you predict that value. It turns out that every time you try to vary your hypothesis, every time you ask your learning algorithm to make a prediction for how much a new house costs or whatever, you need to run a new fitting procedure and then evaluate this line that you fit just at the position of the value of X. So the position of the query where you’re trying to make a prediction. Okay? But if you do this for every point along the X-axis then you find that locally weighted regression is able to trace on this, sort of, very non-linear curve for a data set like this. Okay?

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
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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