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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

are nano particles real
Missy Reply
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
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
has a lot of application modern world
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
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 .?
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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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