Multivariate discrete distributions | Discrete distributions | Compound probability distributions
In probability theory and statistics, the Dirichlet-multinomial distribution is a family of discrete multivariate probability distributions on a finite support of non-negative integers. It is also called the Dirichlet compound multinomial distribution (DCM) or multivariate Pólya distribution (after George Pólya). It is a compound probability distribution, where a probability vector p is drawn from a Dirichlet distribution with parameter vector , and an observation drawn from a multinomial distribution with probability vector p and number of trials n. The Dirichlet parameter vector captures the prior belief about the situation and can be seen as a pseudocount: observations of each outcome that occur before the actual data is collected. The compounding corresponds to a Pólya urn scheme. It is frequently encountered in Bayesian statistics, machine learning, empirical Bayes methods and classical statistics as an overdispersed multinomial distribution. It reduces to the categorical distribution as a special case when n = 1. It also approximates the multinomial distribution arbitrarily well for large α. The Dirichlet-multinomial is a multivariate extension of the beta-binomial distribution, as the multinomial and Dirichlet distributions are multivariate versions of the binomial distribution and beta distributions, respectively. (Wikipedia).
(ML 7.7.A1) Dirichlet distribution
Definition of the Dirichlet distribution, what it looks like, intuition for what the parameters control, and some statistics: mean, mode, and variance.
From playlist Machine Learning
Value distribution of long Dirichlet polynomials and applications to the Riemann...-Maksym Radziwill
Maksym Radziwill Value distribution of long Dirichlet polynomials and applications to the Riemann zeta-function Stanford University; Member, School of Mathematics October 1, 2013 For more videos, visit http://video.ias.edu
From playlist Mathematics
(ML 7.8) Dirichlet-Categorical model (part 2)
The Dirichlet distribution is a conjugate prior for the Categorical distribution (i.e. a PMF a finite set). We derive the posterior distribution and the (posterior) predictive distribution under this model.
From playlist Machine Learning
(ML 7.7) Dirichlet-Categorical model (part 1)
The Dirichlet distribution is a conjugate prior for the Categorical distribution (i.e. a PMF a finite set). We derive the posterior distribution and the (posterior) predictive distribution under this model.
From playlist Machine Learning
Multivariate Gaussian distributions
Properties of the multivariate Gaussian probability distribution
From playlist cs273a
Multinomial and Poisson Distributions (4c)
Video Lecture from the course INST 414: Advanced Data Science at UMD's iSchool. (I stupidly wore a greenish shirt in front of a green screen.) Full course information here: http://www.umiacs.umd.edu/~jbg/teaching/INST_414/
From playlist Advanced Data Science
Topic Models: Variational Inference for Latent Dirichlet Allocation (with Xanda Schofield)
This is a single lecture from a course. If you you like the material and want more context (e.g., the lectures that came before), check out the whole course: https://sites.google.com/umd.edu/2021cl1webpage/ (Including homeworks and reading.) Xanda's Webpage: https://www.cs.hmc.edu/~xanda
From playlist Computational Linguistics I
Latent Dirichlet Allocation (Part 1 of 2)
Latent Dirichlet Allocation is a powerful machine learning technique used to sort documents by topic. Learn all about it in this video! This is part 1 of a 2 video series. Video 2: https://www.youtube.com/watch?v=BaM1uiCpj_E For information on my book "Grokking Machine Learning": https:/
From playlist Unsupervised Learning
What is a Unimodal Distribution?
Quick definition of a unimodal distribution and how it compares to a bimodal distribution and a multimodal distribution.
From playlist Probability Distributions
Henrik Hult: Power-laws and weak convergence of the Kingman coalescent
The Kingman coalescent is a fundamental process in population genetics modelling the ancestry of a sample of individuals backwards in time. In this paper, weak convergence is proved for a sequence of Markov chains consisting of two components related to the Kingman coalescent, under a pare
From playlist Probability and Statistics
(Original Paper) Latent Dirichlet Allocation (algorithm) | AISC Foundational
Toronto Deep Learning Series, 15 November 2018 Paper Review: http://www.jmlr.org/papers/volume3/blei03a/blei03a.pdf Speaker: Renyu Li (Wysdom.ai) Host: Munich Reinsurance Co-Canada Date: Nov 15th, 2018 Latent Dirichlet Allocation We describe latent Dirichlet allocation (LDA), a genera
From playlist Natural Language Processing
Continuous Distributions: Beta and Dirichlet Distributions
Video Lecture from the course INST 414: Advanced Data Science at UMD's iSchool. Full course information here: http://www.umiacs.umd.edu/~jbg/teaching/INST_414/
From playlist Advanced Data Science
undergraduate machine learning 23: Dirichlet and categorical distributions
Dirichlet and Categorical models. Application to twitter sentiment prediction with Naive Bayes. The slides are available here: http://www.cs.ubc.ca/~nando/340-2012/lectures.php This course was taught in 2012 at UBC by Nando de Freitas
From playlist undergraduate machine learning at UBC 2012
Susan Holmes: "Latent variables explain dependencies in bacterial communities"
Emerging Opportunities for Mathematics in the Microbiome 2020 "Latent variables explain dependencies in bacterial communities" Susan Holmes - Stanford University, Statistics Abstract: Data from sequencing bacterial communities are formalized as contingency tables whose columns correspond
From playlist Emerging Opportunities for Mathematics in the Microbiome 2020
Training Latent Dirichlet Allocation: Gibbs Sampling (Part 2 of 2)
This is the second of a series of two videos on Latent Dirichlet Allocation (LDA), a powerful technique to sort documents into topics. In this video, we learn to train an LDA model using Gibbs sampling. The first video is here: https://www.youtube.com/watch?v=T05t-SqKArY
From playlist Unsupervised Learning
From playlist Contributed talks One World Symposium 2020
Applied Machine Learning 2019 - Lecture 18 - Topic Models
Latent Semantic Analysis, Non-negative Matrix Factorization for Topic models, Latent Dirichlet Allocation Markov Chain Monte Carlo and Gibbs sampling Class website with slides and more materials: https://www.cs.columbia.edu/~amueller/comsw4995s19/schedule/
From playlist Applied Machine Learning - Spring 2019
What is a bimodal distribution? How to find out if data fits a bimodal.
From playlist Probability Distributions
Stanford CS234: Reinforcement Learning | Winter 2019 | Lecture 13 - Fast Reinforcement Learning III
For more information about Stanford’s Artificial Intelligence professional and graduate programs, visit: https://stanford.io/ai Professor Emma Brunskill, Stanford University http://onlinehub.stanford.edu/ Professor Emma Brunskill Assistant Professor, Computer Science Stanford AI for Hu
From playlist Stanford CS234: Reinforcement Learning | Winter 2019
Statistics: Ch 7 Sample Variability (3 of 14) The Inference of the Sample Distribution
Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn if the number of samples is greater than or equal to 25 then: 1) the distribution of the sample means is a normal distr
From playlist STATISTICS CH 7 SAMPLE VARIABILILTY