Care colleghe e colleghi
il prossimo incontro del ciclo di seminari del gruppo UMI-Prisma si svolgerà come al solito il primo lunedì del mese, quindi il 5 dicembre dalle 16 alle 18 su piattaforma Teams (link alla fine del messaggio). Parleranno Antonio Lijoi e Federico Camerlenghi (cf. http://www.umi-prisma.polito.it/webinars.html); titoli ed abstract qui sotto:
------------------------------------------------------------------------------------------- Antonio Lijoi, Università Bocconi
TITLE:
Discrete random structures and Bayesian nonparametric modeling
ABSTRACT:
Discrete random structures, such as random partitions and discrete random measures, have emerged as effective tools for Bayesian modeling and have fueled exciting advances in density estimation, clustering, prediction, feature allocation and survival analysis. The Dirichlet process (DP) has undoubtedly emerged as a reference model, mostly due to its analytical tractability. Nonetheless, the DP shares also some well-known limitations that have spurred a very lively area of research aiming at the proposal and the investigation of more general and flexible discrete nonparametric priors. The talk will provide a broad overview of such classes of priors and will specifically focus on those obtained as normalization of completely random measures. Characterizations of the induced random partitions and predictive rules will be illustrated and their role in designing computational algorithms for the approximation of Bayesian inferences of interest will be highlighted, both in exchangeable and non-exchangeable settings.
Federico Camerlenghi, Milano Bicocca
TITLE:
Normalized random measures with atoms' interaction
ABSTRACT:
The seminal work of Ferguson (1973), who introduced the Dirichlet process, has spurred the definition and investigation of more general classes of Bayesian nonparametric priors, with the aim at increasing flexibility while maintaining analytical tractability. Among the numerous generalizations, a fundamental class of random probability measures has been introduced by Regazzini et al. (2003): this is the class of normalized random measures with independent increments (NRMIs). NRMIs are random probability measures with almost surely discrete realizations, defined through the specifications of two ingredients: i) a sequence of unnormalized weights, which are the jumps of a Levy process on the positive real line; ii) a sequence of i.i.d. random atoms from a common base measure. The proposed construction is appealing from a mathematical standpoint, because analytical tractability is preserved, however NRMIs do not allow interaction among atoms, which are supposed to be independent and identically distributed. In some applied frameworks, the i.i.d. assumption could be too restrictive, for instance, in model-based clustering, when they are used as mixing measures in mixture models. To overcome this limitation, we propose a new class of normalized random measures with atoms' interaction. In our construction the atoms come from a finite point process, which is marked with i.i.d. positive weights. Thus, a new class of random probability measures is obtained by normalization. The desired interaction among atoms is then induced by a suitable choice of the law of the point process, which can create a repulsive or attractive behaviour. By means of Palm calculus, we are able to characterize marginal, predictive and posterior distributions for the proposed model. We specialize all our results for several choices of the finite point process, i.e., in the Determinantal, Gibbs and Shot-Noise Cox case.
(Based on a joint work with Raffaele Argiento, Mario Beraha and Alessandra Guglielmi.) -------------------------------------------------------------------------
Grazie per l'attenzione,
Domenico Marinucci
Link per il collegamento:
https://teams.microsoft.com/l/meetup-join/19%3a667d2414be564c5d8fba30acffeb8...