Skip to content

Latest commit

 

History

History
67 lines (62 loc) · 5.68 KB

README.md

File metadata and controls

67 lines (62 loc) · 5.68 KB
Raw

Dirichlet Process

Summary

Brief introduction and implementations of related concepts to Dirichlet Processes: GEM distribution, Polya Urn, Chinese restaurant process, Stick-Breaking construction, and Posterior of a DP.

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

Notebooks:

  1. DP Visualizations
  2. Variational Inference GMM and DPMM