- Griffiths-Engen-McCloskey (GEM) Distribution:
- Definition.
- Function to construct samples
- Function to construct sample distribution
- GEM Figures for different
values:
- Figure 1: Distribution of weight values for each dimension
of
, shows the behavior of
for different
- Figure 2: Sample vectors
- Figure 3: Stick representation for 15
show each dimension weight with a different color. Another way of representing Figure 1.
- Polya urn.
- Definition.
- Function to model Polya urn.
- Figure 1: Distribution of independent samples of Polya urns, only high number of draws show to be distributed as a Beta distribution.
- Chinese Restaurant process.
- Definition.
- Function to model table assignations.
- Function to construct the Chinese restaurant process
- Figure 1: CRP mean
and variance
on number of tables for different
- Dirichlet Process:.
- Definitions:
- Stick-breaking representation.
- Ferguson's definition.
- Function to construct samples using the stick-breaking representation:
- Function to construct sample distribution
- DP Figures for different
- Figure 1: Draws from a DP using the stick-breaking representation.
- Figure 2: Visualization of a DP through Ferguson's definition:
,
, and the impact of the concentration parameter
- Figure 3: Visualization of a DP through Ferguson's definition: Cumulative distributions of the random probability measure
and the base measure
.
- Posterior DP:
- Posterior construction through stick-breaking.
- Function to construct the DP posterior from obseravations.
- Figure 1: DP posterior visualizations for different number of observations of an 'assumed true' DP posterior and
values in the prior.
- DP Visualizations
- Variational Inference GMM and DPMM
