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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

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
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.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
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.
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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