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That’s the [inaudible] but, yes. You are assuming that the error has zero mean. Which is, yeah, right. I think later this quarter we get to some of the other things, but for now just think of this as a mathematically – it’s actually not an unreasonable assumption. I guess, in machine learning all the assumptions we make are almost never true in the absence sense,right? Because, for instance, housing prices are priced to dollars and cents, so the error will be – errors in prices are not continued as value random variables, because houses can only be priced at a certain number of dollars and a certain number of cents and you never have fractions of cents in housing prices. Whereas a Gaussian random variable would. So in that sense, assumptions we make are never “absolutely true,” but for practical purposes this is a accurate enough assumption that it’ll be useful to make. Okay? I think in a week or two, we’ll actually come back to selected more about the assumptions we make and when they help our learning algorithms and when they hurt our learning algorithms. We’ll say a bit more about it when we talk about generative and discriminative learning algorithms, like, in a week or two. Okay?

So let’s point out one bit of notation, which is that when I wrote this down I actually wrote P of YI given XI and then semicolon theta and I’m going to use this notation when we are not thinking of theta as a random variable. So in statistics, though, sometimes it’s called the frequentist’s point of view, where you think of there as being some, sort of, true value of theta that’s out there that’s generating the data say, but we don’t know what theta is, but theta is not a random vehicle, right? So it’s not like there’s some random value of theta out there. It’s that theta is – there’s some true value of theta out there. It’s just that we don’t know what the true value of theta is. So if theta is not a random variable, then I’m going to avoid writing P of YI given XI comma theta, because this would mean that probably of YI conditioned on X and theta and you can only condition on random variables. So at this part of the class where we’re taking sort of frequentist’s viewpoint rather than the Dasian viewpoint, in this part of class we’re thinking of theta not as a random variable, but just as something we’re trying to estimate and use the semicolon notation. So the way to read this is this is the probability of YI given XI and parameterized by theta. Okay? So you read the semicolon as parameterized by. And in the same way here, I’ll say YI given XI parameterized by theta is distributed Gaussian with that.

All right. So we’re gonna make one more assumption. Let’s assume that the error terms are IID, okay? Which stands for Independently and Identically Distributed. So it’s going to assume that the error terms are independent of each other, right? The identically distributed part just means that I’m assuming the outcome for the same Gaussian distribution or the same variance, but the more important part of is this is that I’m assuming that the epsilon I’s are independent of each other. Now, let’s talk about how to fit a model. The probability of Y given X parameterized by theta – I’m actually going to give this another name. I’m going to write this down and we’ll call this the likelihood of theta as the probability of Y given X parameterized by theta. And so this is going to be the product over my training set like that. Which is, in turn, going to be a product of those Gaussian densities that I wrote down just now, right? Okay?

Questions & Answers

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
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
How can I make nanorobot?
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
how can I make nanorobot?
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.
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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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