## MATLAB code for Sampling Gaussian distribution

March 18, 2009

function M = sample_gaussian(mu, Sigma, N)
mu = mu(:);
n=length(mu);
[U,D,V] = svd(Sigma);
M = randn(n,N);
M = (U*sqrt(D))*M + mu*ones(1,N);
M = M’;

## To Generate Random Numbers from a Dirichlet Distribution

March 18, 2009

The following code snippet is copied from the MATLAB Topic Modeling Toolbox by Mark Steyvers and Tom Griffiths:

function r = drchrnd(a,n)
% take a sample from a dirichlet distribution
p = length(a);
r = gamrnd(repmat(a,n,1),1,n,p);
r = r ./ repmat(sum(r,2),1,p);

The following is an example that generates three discrete distributions from a symmetric Dirichlet distribution Dir( \theta ; [ 1 1 1 1 ] ):

>> A = drchrnd([1 1 1 1], 3)

A =

0.3889 0.1738 0.0866 0.3507
0.0130 0.0874 0.6416 0.2579
0.0251 0.0105 0.2716 0.6928

>> sum(A, 2)

ans =

1
1
1

March 18, 2009

## Dirichelt Processes and Nonparametric Bayesian Modelling

March 18, 2009

r.t. An extremely good tutorial for DP. When reading it, take infinite Gaussian mixture model as ab example. After reading it, try to understand HDP.

## Questions on DP, CRP and PYP

March 5, 2009

By Section 4 of [1], it seems that both CRP and PYP produces power-law distributions, where for CRP, the power-law exponent g=1, whereas for PYP it is 1+\alpha.

From the definition of DP, a generalization of Dirichlet distribution, DP should produce multinomial distributions.

But why is the relation between DP and CRP?

References:

1. Producing power-law distributions and damping word frequencies with two-stage language models.