Modeling individual differences using Dirichlet processes

TLDR: A Bayesian framework for modeling individual differences, in which subjects are assumed to belong to one of a potentially infinite number of groups, is introduced, allowing us to learn flexible parameter distributions without overfitting the data, or requiring the complex computations typically required for determining the dimensionality of a model.

About: This article is published in Journal of Mathematical Psychology.The article was published on 2006-04-01 and is currently open access. It has received 147 citations till now. The article focuses on the topics: Hierarchical Dirichlet process & Latent Dirichlet allocation.

Figures

Fig. 8. Prior distributions over the number of components k for sample sizes n ranging from 1 to 25. The panel on the left shows the prior for a Dirichlet process with dispersion a ¼ 10, where the area of each rectangle is proportional to the probability associated with the corresponding value of k for a given n. The panel on the right shows the marginal prior over k for a Dirichlet process mixture in which the prior over a is an inverse Gamma( j 10 10, 10 10) distribution.

Table 1 Estimated probability with which subjects in McKinley and Nosofsky’s (1995) experiment 2 belong to the same group

Fig. 14. Last 300 trials for subjects 5, 7, 8 and 9 in McKinley and Nosofsky’s (1995) experiment 2. Black dots denote ‘‘A’’ responses, and gray dots denote ‘‘B’’ responses.

Fig. 13. Estimated posterior distributions over a and k when the infinite groups model is applied to McKinley and Nosofsky’s (1995) experiment 2.

Fig. 1. Standard modeling approaches for data from many subjects, involvin independently (panel b). The data are plotted in the lower data space, with dif parameter distributions inferred under each modeling approach.

Fig. 6. Distributions sampled from a Dirichlet process with a ¼ 100, and three different base distributions G0ð Þ. Base distributions are shown on the left, and sampled distributions are shown on the right. In the top line, the base distribution is Betað j 10; 2Þ, while in the middle row it is a uniform Betað j 1; 1Þ, while in the bottom row it is an equal mixture of a Betað j 10; 1Þ and a Betað j 1; 10Þ.