I’ve just started a postdoc at the Department of Statistics, working with Yee Whye Teh. My subject of research is Bayesian Nonparametrics. Previously, I received a Bachelor degree in Economics and Business from the University of Padua, a master in Economics and a PhD in Statistics (expected, the final defense will be in January) at Bocconi University.

Publications

2017

M. Battiston,
S. Favaro,
D. M. Roy,
Y. W. Teh,
A Characterization of Product-Form Exchangeable Feature Probability Functions, Annals of Applied Probability, vol. accepted, 2017.

We characterize the class of exchangeable feature allocations assigning probability V_n,k ∏^k_l=1 W_m_lU_n−m_l to a feature allocation of n individuals, displaying k features with counts (m_1,\ldots,m_k) for these features. Each element of this class is parametrized by a countable matrix V and two sequences U and W of non-negative weights. Moreover, a consistency condition is imposed to guarantee that the distribution for feature allocations of n−1 individuals is recovered from that of n individuals, when the last individual is integrated out. In Theorem 1.1, we prove that the only members of this class satisfying the consistency condition are mixtures of the Indian Buffet Process over its mass parameter γ and mixtures of the Beta–Bernoulli model over its dimensionality parameter N. Hence, we provide a characterization of these two models as the only, up to randomization of the parameters, consistent exchangeable feature allocations having the required product form.

@article{BatFavRoy2016a,
author = {Battiston, M. and Favaro, S. and Roy, D. M. and Teh, Y. W.},
journal = {Annals of Applied Probability},
note = {ArXiv e-prints: 1607.02066},
title = {A Characterization of Product-Form Exchangeable Feature Probability Functions},
volume = {accepted},
year = {2017},
bdsk-url-1 = {https://arxiv.org/pdf/1607.02066.pdf}
}

2016

M. Battiston,
S. Favaro,
Y. W. Teh,
Multi-armed bandit for species discovery: A Bayesian nonparametric approach, Journal of the American Statistical Association, 2016.

Let (P1,...,PJ) denote J populations of animals from distinct regions. A priori, it is
unknown which species are present in each region and what are their corresponding frequencies.
Species are shared among populations and each species can be present in more than one region with
its frequency varying across populations. In this paper we consider the problem of sequentially
sampling these populations in order to observe the greatest number of different species. We adopt a
Bayesian nonparametric approach and endow (P1,...,PJ) with a Hierarchical Pitman-Yor process
prior. As a consequence of the hierarchical structure, the J unknown discrete probability measures
share the same support, that of their common random base measure. Given this prior choice,
we propose a sequential rule that, at every time step, given the information available up to that
point, selects the population from which to collect the next observation. Rather than picking the
population with the highest posterior estimate of producing a new value, the proposed rule includes
a Thompson sampling step to better balance the exploration-exploitation trade-off. We also propose
an extension of the algorithm to deal with incidence data, where multiple observations are collected
in a time period. The performance of the proposed algorithms is assessed through a simulation
study and compared to three other strategies. Finally, we compare these algorithms using a dataset
of species of trees, collected from different plots in South America.

@article{BatFavTeh2016a,
author = {Battiston, M. and Favaro, S. and Teh, Y. W.},
doi = {http://dx.doi.org/10.1080/01621459.2016.1261711},
journal = {Journal of the American Statistical Association},
title = {Multi-armed bandit for species discovery: A Bayesian nonparametric approach},
year = {2016},
bdsk-url-1 = {http://www.tandfonline.com/doi/full/10.1080/01621459.2016.1261711},
bdsk-url-2 = {http://www.tandfonline.com/doi/pdf/10.1080/01621459.2016.1261711?needAccess=true}
}