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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

how do they get the third part x = (32)5/4
kinnecy Reply
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele 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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