(45 minutes to learn)
The Dirichlet distribution specifies a distribution on a n-dimensional vector and can be viewed as a probability distribution on a n-1 dimensional simplex (a simplex is an n-dimensional generalization of a triangle). Its parameters determine the distribution of mass on this simplex. The Dirichlet distribution is a conjugate prior to the categorigal and multinomial distributions, and for this reason, it is common in Bayesian statistics. Also, the Dirichlet distribution is a generalization of the beta distribution to higher dimensions (for n=2 it is the beta distribution).
This concept has the prerequisites:
Core resources (read/watch one of the following)
→ Introduction to the Dirichlet Distribution and Related Processes
Location: Ch 1 provides core information while Ch 2 focuses on sampling
→ Mathematical Monk: Machine Learning (2011)
Online videos on machine learning.
Location: Lecture 7.7.A1: Dirichlet Distribution
Supplemental resources (the following are optional, but you may find them useful)
→ Pattern Recognition and Machine Learning
A textbook for a graduate machine learning course, with a focus on Bayesian methods.
Location: Section 2.2.2 (page 76)
- We can define the Dirichlet distribution in terms of the gamma distribution .
- The Dirichlet process is a generalization of the Dirichlet distribution to possibly infinite spaces, and is useful in mixture modeling.
- The Dirichlet distribution is a conjugate prior to the categorical and multinomial distribution.
- create concept: shift + click on graph
- change concept title: shift + click on existing concept
- link together concepts: shift + click drag from one concept to another
- remove concept from graph: click on concept then press delete/backspace
- add associated content to concept: click the small circle that appears on the node when hovering over it
- other actions: use the icons in the upper right corner to optimize the graph placement, preview the graph, or download a json representation