Lecture

Topic Models

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Description

This lecture covers the basics of topic models, starting with clustering and density estimation, then delving into Gaussian Mixture Models (GMM) and the Latent Dirichlet Allocation (LDA) model. The instructor explains the algorithms, learning processes, and limitations of GMM and LDA, as well as the concepts of Dirichlet distribution and variational inference. The lecture concludes with extensions to the LDA model and the application of variational inference to Gaussian Mixture Models.

Official source

Ontological neighbourhood

Statistics

Statistical inference: Bayesian statistics, Mathematical statistics

Related concepts (32)

Dirichlet-multinomial distribution

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.

Dirichlet distribution

In probability and statistics, the Dirichlet distribution (after Peter Gustav Lejeune Dirichlet), often denoted , is a family of continuous multivariate probability distributions parameterized by a vector of positive reals. It is a multivariate generalization of the beta distribution, hence its alternative name of multivariate beta distribution (MBD). Dirichlet distributions are commonly used as prior distributions in Bayesian statistics, and in fact, the Dirichlet distribution is the conjugate prior of the categorical distribution and multinomial distribution.

Latent Dirichlet allocation

In natural language processing, Latent Dirichlet Allocation (LDA) is a Bayesian network (and, therefore, a generative statistical model) that explains a set of observations through unobserved groups, and each group explains why some parts of the data are similar. The LDA is an example of a Bayesian topic model. In this, observations (e.g., words) are collected into documents, and each word's presence is attributable to one of the document's topics. Each document will contain a small number of topics.

Mixture model

In statistics, a mixture model is a probabilistic model for representing the presence of subpopulations within an overall population, without requiring that an observed data set should identify the sub-population to which an individual observation belongs. Formally a mixture model corresponds to the mixture distribution that represents the probability distribution of observations in the overall population.

Topic model

In statistics and natural language processing, a topic model is a type of statistical model for discovering the abstract "topics" that occur in a collection of documents. Topic modeling is a frequently used text-mining tool for discovery of hidden semantic structures in a text body. Intuitively, given that a document is about a particular topic, one would expect particular words to appear in the document more or less frequently: "dog" and "bone" will appear more often in documents about dogs, "cat" and "meow" will appear in documents about cats, and "the" and "is" will appear approximately equally in both.

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Topic Models: Latent Dirichlet Allocation

Covers topic models, focusing on Latent Dirichlet Allocation, clustering, GMMs, Dirichlet distribution, LDA learning, and applications in digital humanities.

Topic Models: Understanding Latent Structures

Explores topic models, Gaussian mixture models, Latent Dirichlet Allocation, and variational inference in understanding latent structures within data.

Topic Models: Latent Dirichlet Allocation

Introduces Latent Dirichlet Allocation for topic modeling in documents, discussing its process, applications, and limitations.

Dirichlet-Multinomial Model

Discusses the Dirichlet distribution, Bayesian inference, posterior mean and variance, conjugate priors, and predictive distribution in the Dirichlet-Multinomial model.

Clustering & Density Estimation