2020
DOI: 10.1111/rssb.12385
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Quasi-Bayes Properties of a Procedure for Sequential Learning in Mixture Models

Abstract: Summary Bayesian methods are often optimal, yet increasing pressure for fast computations, especially with streaming data, brings renewed interest in faster, possibly suboptimal, solutions. The extent to which these algorithms approximate Bayesian solutions is a question of interest, but often unanswered. We propose a methodology to address this question in predictive settings, when the algorithm can be reinterpreted as a probabilistic predictive rule. We specifically develop the proposed methodology for a rec… Show more

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Cited by 12 publications
(18 citation statements)
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References 39 publications
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“…The resulting measure-valued urn process provides a predictive characterization of the law of an asymptotically exchangeable sequence of random variables, which corresponds to the observation process of an implied urn sampling scheme. In fact, the model ( 6)-( 7) fits into a line of recent research, which explores efficient predictive constructions for fast online prediction or approximately-Bayesian solutions, see [11,29,32] and references therein. To that end, one direction for future work is to generalize the functional relationship in (7) and/or, as one referee suggested, to consider finitely-additive measures, along the lines discussed in [33].…”
Section: Discussionmentioning
confidence: 99%
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“…The resulting measure-valued urn process provides a predictive characterization of the law of an asymptotically exchangeable sequence of random variables, which corresponds to the observation process of an implied urn sampling scheme. In fact, the model ( 6)-( 7) fits into a line of recent research, which explores efficient predictive constructions for fast online prediction or approximately-Bayesian solutions, see [11,29,32] and references therein. To that end, one direction for future work is to generalize the functional relationship in (7) and/or, as one referee suggested, to consider finitely-additive measures, along the lines discussed in [33].…”
Section: Discussionmentioning
confidence: 99%
“…In fact, some of the predictive constructions in [11,29] can be framed in such a way. Theorem 1 extends to GMVPPs, provided that we condition all quantities on the parameter V. As a consequence, there exists a measurable function…”
Section: Generalized Measure-valued Pólya Urn Processesmentioning
confidence: 99%
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“…sequences have been introduced in [4] and [22] and then investigated in various papers; see e.g. [1], [2], [5], [6], [7], [8], [9], [11], [15], [18], [19].…”
Section: Conditional Identity In Distributionmentioning
confidence: 99%
“…sequences have been introduced in [4] and [22] and then investigated in various papers; see e.g. [1], [2], [5], [6], [7], [8], [9], [11], [14], [17], [18].…”
Section: Conditional Identity In Distributionmentioning
confidence: 99%