<< Chapter < Page Chapter >> Page >

Actually, just quickly raise your hand if you’ve seen a Gaussian distribution before. Okay, cool. Most of you. Great. Almost everyone. So, in other words, the density for Gaussian is what you’ve seen before. The density for epsilon I would be one over root 2 pi sigma, E to the negative, epsilon I squared over 2 sigma squared, right? And the density of our epsilon I will be this bell-shaped curve with one standard deviation being a, sort of, sigma. Okay? This is form for that bell-shaped curve. So, let’s see. I can erase that. Can I erase the board? So this implies that the probability distribution of a price of a house given in si and the parameters theta, that this is going to be Gaussian with that density. Okay? In other words, saying goes as that the price of a house given the features of the house and my parameters theta, this is going to be a random variable that’s distributed Gaussian with mean theta transpose XI and variance sigma squared. Right? Because we imagine that the way the housing prices are generated is that the price of a house is equal to theta transpose XI and then plus some random Gaussian noise with variance sigma squared. So the price of a house is going to have mean theta transpose XI, again, and sigma squared, right? Does this make sense? Raise your hand if this makes sense. Yeah, okay. Lots of you.

In point of notation – oh, yes?

Student: Assuming we don’t know anything about the error, why do you assume here the error is a Gaussian?

Instructor (Andrew Ng) :Right. So, boy. Why do I see the error as Gaussian? Two reasons, right? One is that it turns out to be mathematically convenient to do so and the other is, I don’t know, I can also mumble about justifications, such as things to the central limit theorem. It turns out that if you, for the vast majority of problems, if you apply a linear regression model like this and try to measure the distribution of the errors, not all the time, but very often you find that the errors really are Gaussian. That this Gaussian model is a good assumption for the error in regression problems like these. Some of you may have heard of the central limit theorem, which says that the sum of many independent random variables will tend towards a Gaussian. So if the error is caused by many effects, like the mood of the seller, the mood of the buyer, some other features that we miss, whether the place has a garden or not, and if all of these effects are independent, then by the central limit theorem you might be inclined to believe that the sum of all these effects will be approximately Gaussian. If in practice, I guess, the two real answers are that, 1.) In practice this is actually a reasonably accurate assumption, and 2.) Is it turns out to be mathematically convenient to do so. Okay? Yeah?

Student: It seems like we’re saying if we assume that area around model has zero mean, then the area is centered around our model. Which it seems almost like we’re trying to assume what we’re trying to prove. Instructor?

Questions & Answers

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
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
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
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.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
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
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Machine learning. OpenStax CNX. Oct 14, 2013 Download for free at http://cnx.org/content/col11500/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Machine learning' conversation and receive update notifications?

Ask