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And then when you need to classify a new example, when you have a new patient, and you want to decide is this cancer malignant or benign, you then take your new cancer, and you match it to your model of malignant cancers, and you match it to your model of benign cancers, and you see which model it matches better, and depending on which model it matches better to, you then predict whether the new cancer is malignant or benign, okay?

So what I just described, just this cross of methods where you build a second model for malignant cancers and a separate model for benign cancers is called a generative learning algorithm, and let me just, kind of, formalize this. So in the models that we’ve been talking about previously, those were actually all discriminative learning algorithms, and studied more formally, a discriminative learning algorithm is one that either learns PFY given X directly, or even learns a hypothesis that outputs value 0, 1 directly, okay? So logistic regression is an example of a discriminative learning algorithm.

In contrast, a generative learning algorithm of models PFX given Y. The probability of the features given the class label, and as a technical detail, it also models PFY, but that’s a less important thing, and the interpretation of this is that a generative model builds a probabilistic model for what the features looks like, conditioned on the class label, okay? In other words, conditioned on whether a cancer is malignant or benign, it models probability distribution over what the features of the cancer looks like.

Then having built this model – having built a model for PFX given Y and PFY, then by Bayes rule, obviously, you can compute PFY given 1, conditioned on X. This is just PFX given Y = 1 × PFX ÷ PFX, and, if necessary, you can calculate the denominator using this, right? And so by modeling PFX given Y and modeling PFY, you can actually use Bayes rule to get back to PFY given X, but a generative model – generative learning algorithm starts in modeling PFX given Y, rather than PFY given X, okay?

We’ll talk about some of the tradeoffs, and why this may be a better or worse idea than a discriminative model a bit later. Let’s go for a specific example of a generative learning algorithm, and for this specific motivating example, I’m going to assume that your input feature is X and RN and are continuous values, okay?

And under this assumption, let me describe to you a specific algorithm called Gaussian Discriminant Analysis, and the, I guess, core assumption is that we’re going to assume in the Gaussian discriminant analysis model of that PFX given Y is Gaussian, okay?

So actually just raise your hand, how many of you have seen a multivariate Gaussian before – not a 1D Gaussian, but the higher range though? Okay, cool, like maybe half of you, two-thirds of you. So let me just say a few words about Gaussians, and for those of you that have seen it before, it’ll be a refresher.

So we say that a random variable Z is distributed Gaussian, multivariate Gaussian as – and the script N for normal with parameters mean U and covariance sigma squared. If Z has a density 1 over 2 Pi, sigma 2, okay? That’s the formula for the density as a generalization of the one dimension of Gaussians and no more the familiar bell-shape curve. It’s a high dimension vector value random variable Z.

Questions & Answers

so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
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.
what is biological synthesis of nanoparticles
Sanket 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?
I'm interested in nanotube
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
I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
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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