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Student: Assume that we have a very huge [inaudible], for example. A very huge set of houses and want to predict the linear for each house and so should the end result for each input – I’m seeing this very constantly for –

Instructor (Andrew Ng) :Yes, you’re right. So because locally weighted regression is a non-parametric algorithm every time you make a prediction you need to fit theta to your entire training set again. So you’re actually right. If you have a very large training set then this is a somewhat expensive algorithm to use. Because every time you want to make a prediction you need to fit a straight line to a huge data set again. Turns out there are algorithms that – turns out there are ways to make this much more efficient for large data sets as well. So don’t want to talk about that. If you’re interested, look up the work of Andrew Moore on KD-trees. He, sort of, figured out ways to fit these models much more efficiently. That’s not something I want to go into today. Okay? Let me move one. Let’s take more questions later.

So, okay. So that’s locally weighted regression. Remember the outline I had, I guess, at the beginning of this lecture. What I want to do now is talk about a probabilistic interpretation of linear regression, all right? And in particular of the – it’ll be this probabilistic interpretation that let’s us move on to talk about logistic regression, which will be our first classification algorithm. So let’s put aside locally weighted regression for now. We’ll just talk about ordinary unweighted linear regression. Let’s ask the question of why least squares, right? Of all the things we could optimize how do we come up with this criteria for minimizing the square of the area between the predictions of the hypotheses and the values Y predicted. So why not minimize the absolute value of the areas or the areas to the power of four or something? What I’m going to do now is present one set of assumptions that will serve to “justify” why we’re minimizing the sum of square zero. Okay?

It turns out that there are many assumptions that are sufficient to justify why we do least squares and this is just one of them. So just because I present one set of assumptions under which least squares regression make sense, but this is not the only set of assumptions. So even if the assumptions I describe don’t hold, least squares actually still makes sense in many circumstances. But this sort of new help, you know, give one rationalization, like, one reason for doing least squares regression. And, in particular, what I’m going to do is endow the least squares model with probabilistic semantics. So let’s assume in our example of predicting housing prices, that the price of the house it’s sold four, and there’s going to be some linear function of the features, plus some term epsilon I. Okay? And epsilon I will be our error term. You can think of the error term as capturing unmodeled effects, like, that maybe there’s some other features of a house, like, maybe how many fireplaces it has or whether there’s a garden or whatever, that there are additional features that we jut fail to capture or you can think of epsilon as random noise. Epsilon is our error term that captures both these unmodeled effects. Just things we forgot to model. Maybe the function isn’t quite linear or something. As well as random noise, like maybe that day the seller was in a really bad mood and so he sold it, just refused to go for a reasonable price or something. And now I will assume that the errors have a probabilistic – have a probability distribution. I’ll assume that the errors epsilon I are distributed just till they denote epsilon I is distributive according to a probability distribution. That’s a Gaussian distribution with mean zero and variance sigma squared. Okay? So let me just scripts in here, n stands for normal, right? To denote a normal distribution, also known as the Gaussian distribution, with mean zero and covariance sigma squared.

Questions & Answers

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.
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.
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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