dirichlet-matlab

MATLAB functions for working with the Dirichlet and other related distributions.

• Dirichlet distribution: dirrnd,dirpdf,dirstat
• Dirichlet-multinomial distribution: dirmnrnd,dirmnpdf,dirmnstat
• Dirichlet process: dirproc

Installation

You can add the dirichlet-matlab directory to your MATLAB search path:

addpath(genpath('dirichlet-matlab'))  

Dirichlet distribution example

A = [2, 3, 4]; % Dirichlet hyperparameters (shape vector) for a 3-dimensional distribution

X = dirrnd(A, 5); % Generate 5 random vectors
X =
   0.165180831562802   0.572367339824971   0.262451828612227
   0.107682875327566   0.410558528169850   0.481758596502584
   0.124892099736948   0.230780581503848   0.644327318759204
   0.236682038827591   0.444503367825342   0.318814593347067
   0.407190742512644   0.164892120689403   0.427917136797953
   
Y = dirpdf(X, A); % Find probability densities for X
Y =
   3.286982736584238
   6.819059741097087
   5.978502390713254
   5.091775747161138
   2.914848702465950
   
[M,MO,V,CV] = dirstat(A) % Mean, mode, variance, and covariance for each dimension
M =
   0.222222222222222   0.333333333333333   0.444444444444444
MO =
   0.166666666666667   0.333333333333333   0.500000000000000
V =
   0.017283950617284   0.022222222222222   0.024691358024691
CV =
   0.017283950617284  -0.007407407407407  -0.009876543209877
  -0.007407407407407   0.022222222222222  -0.014814814814815
  -0.009876543209877  -0.014814814814815   0.024691358024691

Random vectors from various (symmetric) Dirichlet distributions

a = [10, 10, 10]; % Symmetric Dirichlet hyperparameters
x = dirrnd(a, 500); % Generate 500 random vectors
y = dirpdf(x, a); % Find probability densities for random vectors

% Plot
plot3(x(:,1), x(:,2), x(:,3), 'ko', 'MarkerFaceColor', [166, 206, 227]./255); 
box off; grid on;
xlim([0, 1]); ylim([0, 1]); zlim([0, 1]);
set(gca, 'XTick', 0:0.2:1, 'YTick', 0:0.2:1, 'ZTick', 0:0.2:1, ...
   'YDir', 'reverse', 'XDir', 'reverse');
title('a = [10, 10, 10]');

Dirichlet-multinomial distribution example

A = [2, 3, 4]; % Dirichlet-multinomial hyperparameters (shape vector) for a 3-dimensional distribution
N = 10; % Number of trials

X = dirmnrnd(A, N, 5); % Generate 5 random vectors
X =
     3     1     6
     2     4     4
     2     4     4
     0     0    10
     0     3     7
     
Y = dirmnpmf(X, A); % Find probability mass for X
Y =
   0.023035787741670
   0.035993418346360
   0.035993418346360
   0.006535947712418
   0.027423556835322
   
[M,V,CV] = dirmnstat(A, N) % Mean, variance, and covariance for each dimension
M =
   2.222222222222222   3.333333333333333   4.444444444444445
V =
   3.283950617283951   4.222222222222222   4.691358024691358
CV =
   3.283950617283951  -1.407407407407407  -1.876543209876543
  -1.407407407407407   4.222222222222222  -2.814814814814814
  -1.876543209876543  -2.814814814814814   4.691358024691358

Dirichlet process example

A = 5; % Shape parameter
N = 10; % Number of iterations

X = dirproc(A,N); % Samples from a Dirhlet process over the sequence of natural numbers
X =
     1
     2
     1
     1
     3
     4
     5
     1
     2
     2

Sampled Dirichlet process trajectories