Marco Battiston

• GitHub

Bayesian nonparametrics

I am a former postdoc at the Department of Statistics, working with Yee Whye Teh. My subject of research is Bayesian Nonparametrics. I received a Bachelor degree in Economics and Business from the University of Padua, a master in Economics and a PhD in Statistics at Bocconi University. Currently I am Lecturer in Statistics at Lancaster University.

Publications

2018

• M. Battiston , S. Favaro , D. M. Roy , Y. W. Teh , A Characterization of Product-Form Exchangeable Feature Probability Functions, Annals of Applied Probability, vol. 28, Jun. 2018.
  
  Project: bigbayes

  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},
    title = {A Characterization of Product-Form Exchangeable Feature Probability Functions},
    volume = {28},
    year = {2018},
    month = jun,
    bdsk-url-1 = {https://arxiv.org/pdf/1607.02066.pdf}
  }
  

• F. Ayed , M. Battiston , F. Camerlenghi , S. Favaro , Consistent estimation of the missing mass for feature models, 2018.
  
  Project: bigbayes

  @unpublished{Ayed:Battiston:Camerlenghi:Favaro2018b,
    author = {Ayed, F. and Battiston, M. and Camerlenghi, F. and Favaro, S.},
    title = {Consistent estimation of the missing mass for feature models},
    year = {2018}
  }
  

• M. Battiston , S. Favaro , Y. W. Teh , Bayesian nonparametric approaches to sample-size estimation for finding unseen species, 2018.
  
  Project: bigbayes

  @unpublished{Battiston:Favaro:Teh:2018b,
    author = {Battiston, M. and Favaro, S. and Teh, Y. W.},
    title = {Bayesian nonparametric approaches to sample-size estimation for finding unseen species},
    year = {2018}
  }
  

• F. Ayed , M. Battiston , F. Camerlenghi , S. Favaro , On the consistent estimation of the missing mass, 2018.
  
  Project: bigbayes

  @unpublished{Ayed:Battiston:Camerlenghi:Favaro2018a,
    author = {Ayed, F. and Battiston, M. and Camerlenghi, F. and Favaro, S.},
    title = {On the consistent estimation of the missing mass},
    year = {2018}
  }
  

• F. Ayed , M. Battiston , F. Camerlenghi , S. Favaro , On the Good-Turing estimator for feature allocation models, 2018.
  
  Project: bigbayes

  @unpublished{Ayed:Battiston:Camerlenghi:Favaro2018c,
    author = {Ayed, F. and Battiston, M. and Camerlenghi, F. and Favaro, S.},
    title = {On the {Good-Turing} estimator for feature allocation models},
    year = {2018}
  }
  

2017

• M. Battiston , S. Favaro , Discussion of F. Caron and E. B. Fox, "Sparse graphs using exchangeable random measures.", Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol. 79, no. 5, 2017.
  
  Project: bigbayes

  @article{Battiston:Favaro:2017a,
    author = {Battiston, M. and Favaro, S.},
    journal = {Journal of the Royal Statistical Society: Series B (Statistical Methodology)},
    number = {5},
    title = {Discussion of F. Caron and E. B. Fox, "Sparse graphs using exchangeable random measures."},
    volume = {79},
    year = {2017}
  }
  

• S. Bacallado , M. Battiston , S. Favaro , L. Trippa , Sufficientness postulates for Gibbs-type priors and hierarchial generalizations, Statistical Sciences, vol. 32, 487–500, 2017.
  
  Project: bigbayes

  @article{Battiston:Bacallado:Favaro:Trippa:2017,
    author = {Bacallado, S. and Battiston, M. and Favaro, S. and Trippa, L.},
    journal = {Statistical Sciences},
    pages = {487–-500},
    title = {Sufficientness postulates for Gibbs-type priors and hierarchial generalizations},
    volume = {32},
    year = {2017}
  }
  

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.
  
  Project: bigbayes

  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}
  }