Finding the mean in a partition distribution.

BACKGROUND: Bayesian clustering algorithms, in particular those utilizing Dirichlet Processes (DP), return a sample of the posterior distribution of partitions of a set. However, in many applied cases a single clustering solution is desired, requiring a 'best' partition to be created from the posterior sample. It is an open research question which solution should be recommended in which situation. However, one such candidate is the sample mean, defined as the clustering with minimal squared distance to all partitions in the posterior sample, weighted by their probability. In this article, we review an algorithm that approximates this sample mean by using the Hungarian Method to compute the distance between partitions. This algorithm leaves room for further processing acceleration. RESULTS: We highlight a faster variant of the partition distance reduction that leads to a runtime complexity that is up to two orders of magnitude lower than the standard variant. We suggest two further improvements: The first is deterministic and based on an adapted dynamical version of the Hungarian Algorithm, which achieves another runtime decrease of at least one order of magnitude. The second improvement is theoretical and uses Monte Carlo techniques and the dynamic matrix inverse. Thereby we further reduce the runtime complexity by nearly the square root of one order of magnitude. CONCLUSIONS: Overall this results in a new mean partition algorithm with an acceleration factor reaching beyond that of the present algorithm by the size of the partitions. The new algorithm is implemented in Java and available on GitHub (Glassen, Mean Partition, 2018).

Hierarchical Bayesian models of cognitive development.

This article provides an introductory overview of the state of research on Hierarchical Bayesian Modeling in cognitive development. First, a brief historical summary and a definition of hierarchies in Bayesian modeling are given. Subsequently, some model structures are described based on four examples in the literature. These are models for the development of the shape bias, for learning ontological kinds and causal schemata as well as for the categorization of objects. The Bayesian modeling approach is then compared with the connectionist and nativist modeling paradigms and considered in view of Marr's (1982) three description levels of information-processing mechanisms. In this context, psychologically plausible algorithms and ideas of their neural implementation are presented. In addition to criticism and limitations of the approach, research needs are identified.

Using the Dirichlet process to form clusters of people's concerns in the context of future party identification.

Connections between interindividual differences and people's behavior has been widely researched in various contexts, often by using top-down group comparisons to explain interindividual differences. In contrast, in this study, we apply a bottom-up approach in which we identify meaningful clusters in people's concerns about various areas of life (e.g., their own health, their financial situation, the environment). We apply a novel method, Dirichlet clustering, to large-scale longitudinal data from the German Socioeconomic Panel Study (SOEP) to investigate whether concerns of people living in Germany evaluated in 2010 (t0) cluster participants into robust and separable groups, and whether these groups vary regarding their party identification in 2017 (t0 + 7). Clustering results suggest a range of different groups with specific concern patterns. Some of these notably specific patterns of concerns indicate links to party identification. In particular, some patterns show an increased identification with smaller parties as the 'Bündnis 90/Die Grünen' ('Greens'), the left wing party 'Die Linke' ('The Left') or the right-wing party 'Alternative für Deutschland' ('Alternative for Germany', AfD). Considering that we identify as many as 37 clusters in total, among them at least six with clearly different party identification, it can also be concluded that the complexity of political concerns may be larger than has been assumed before.

Correction: Using the Dirichlet process to form clusters of people's concerns in the context of future party identification.

[This corrects the article DOI: 10.1371/journal.pone.0212944.].