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And then I’ll look at the negative examples, the O’s in this figure, and I’ll fit a Gaussian to that, and maybe I get a Gaussian centered over there. This is the concept of my second Gaussian, and together – we’ll say how later – together these two Gaussian densities will define a separator for these two classes, okay?

And it’ll turn out that the separator will turn out to be a little bit different from what logistic regression gives you. If you run logistic regression, you actually get the division bound to be shown in the green line, whereas Gaussian discriminant analysis gives you the blue line, okay?

Switch back to chalkboard, please. All right. Here’s the Gaussian discriminant analysis model, put into model PFY as a Bernoulli random variable as usual, but as a Bernoulli random variable and parameterized by parameter phi; you’ve seen this before. Model PFX given Y = 0 as a Gaussian – oh, you know what?

Yeah, yes, excuse me. I thought this looked strange. This should be a sigma, determined in a sigma to the one-half of the denominator there. It’s no big deal. It was – yeah, well, okay. Right. I was listing the sigma to the determining the sigma to the one-half on a previous board, excuse me.

Okay, and so I model PFX given Y = 0 as a Gaussian with mean mew0 and covariance sigma to the sigma to the minus one-half, and – okay? And so the parameters of this model are phi, mew0, mew1, and sigma, and so I can now write down the likelihood of the parameters as – oh, excuse me, actually, the log likelihood of the parameters as the log of that, right?

So, in other words, if I’m given the training set, then they can write down the log likelihood of the parameters as the log of, you know, the probative probabilities of PFXI, YI, right? And this is just equal to that where each of these terms, PFXI given YI, or PFYI is then given by one of these three equations on top, okay?

And I just want to contrast this again with discriminative learning algorithms, right? So to give this a name, I guess, this sometimes is actually called the Joint Data Likelihood – the Joint Likelihood, and let me just contrast this with what we had previously when we’re talking about logistic regression. Where I said with the log likelihood of the parameter’s theater was log of a product I = 1 to M, PFYI given XI and parameterized by a theater, right?

So back where we’re fitting logistic regression models or generalized learning models, we’re always modeling PFYI given XI and parameterized by a theater, and that was the conditional likelihood, okay, in which we’re modeling PFYI given XI, whereas, now, regenerative learning algorithms, we’re going to look at the joint likelihood which is PFXI, YI, okay?

So let’s see. So given the training sets and using the Gaussian discriminant analysis model to fit the parameters of the model, we’ll do maximize likelihood estimation as usual, and so you maximize your L with respect to the parameters phi, mew0, mew1, sigma, and so if we find the maximum likelihood estimate of parameters, you find that phi is – the maximum likelihood estimate is actually no surprise, and I’m writing this down mainly as a practice for indicating notation, all right?

Questions & Answers

can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
I'm not sure why it wrote it the other way
I got X =-6
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
Idrissa Reply
im all ears I need to learn
right! what he said ⤴⤴⤴
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?
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
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
im not good at math so would this help me
Rachael Reply
I'm not good at math so would you help me
what is the problem that i will help you to self with?
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
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
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
what is system testing
what is the application of nanotechnology?
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
anybody can imagine what will be happen after 100 years from now in nano tech world
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
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
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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