Doubts on Assignment

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Vijayakumar Raju

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Jan 22, 2012, 4:25:13 PM1/22/12

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Hi,

I have few doubts in question 2 and i have just started to code in
MatLab.

In Question 2.a

The question starts with "Assuming that the class conditional density
is spherical gaussian", could you please point to any source or
references about the concepts. and it ends with finding densities, am
not sure about this either.

Then we have to compute sph_bayes(Xtest, ...), does Xtest mean x in
the dataset?

Thank you.

Jacob

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Jan 23, 2012, 8:15:44 AM1/23/12

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Hi,

Shperical gaussian should be just what is written in the first two
lines of ex. 1a, i.e.
that the distribution for the variable X is N(mu,sigma I) , where I is
the identity matrix.
This means that all the components of X are N(mu,sigma)-distributed
and independent of eachother.
In this case the levelsurfaces of the density for X are spheres, you
can plot this in matlab, or see this pic
http://personal.kenyon.edu/hartlaub/MellonProject/images/Bivariate17.gif

You are supposed to be able to plug in _any_ vector(s) into Xtest,
and the classifer should make a prediction if it has a positive
or negative label.

Does anyone know what sph is short for?

/Jacob

On Jan 22, 10:25 pm, Vijayakumar Raju <aphrovijay.s...@gmail.com>
wrote:

Vinay Jethava

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Jan 24, 2012, 4:08:05 AM1/24/12

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Dear Jacob & Vijay,

Jacob is correct about spherical Gaussian distribution. The spherical Bayes classifier is something that you have to design, assuming underlying distribution is spherical Gaussian. sph_bayes() is the spherical Bayesian classifier that has been trained using part of the dataset (this will be what gives other parameters part of the function). Note that it is different from the mean and variance estimator (sge()), though it can use sge(). For each test point (X_test), it should return either −1 or +1.