English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Bayesian methods are attractive and often optimal, yet nowadays pressure forfast computations, especially with streaming data and online learning, bringsrenewed interest in faster, although possibly sub-optimal, solutions. To whatextent these algorithms may approximate a Bayesian solution is a problem ofinterest, not always solved. On this background, in this paper we revisit asequential procedure proposed by Smith and Makov (1978) for unsupervisedlearning and classification in finite mixtures, and developed by M. Newton andZhang (1999), for nonparametric mixtures. Newton's algorithm is simple andfast, and theoretically intriguing. Although originally proposed as anapproximation of the Bayesian solution, its quasi-Bayes properties remainunclear. We propose a novel methodological approach. We regard the algorithm asa probabilistic learning rule, that implicitly defines an underlyingprobabilistic model; and we find this model. We can then prove that it is,asymptotically, a Bayesian, exchangeable mixture model. Moreover, while thealgorithm only offers a point estimate, our approach allows us to obtain anasymptotic posterior distribution and asymptotic credible intervals for themixing distribution. Our results also provide practical hints for tuning thealgorithm and obtaining desirable properties, as we illustrate in a simulationstudy. Beyond mixture models, our study suggests a theoretical framework thatmay be of interest for recursive quasi-Bayes methods in other settings.

Quasi-Bayes properties of a recursive procedure for mixtures