[R-sig-eco] mixture distributions and boosting for occupancy-detection models

[Robert Rankin]

Hello r-sig-eco'ers,

There have been two papers recently about integrating hierarchical
models (e.g., occupancy-detection models) and boosting (e.g., Boosted
regression trees), as by Hochachka et al (2012) and Hutchinson et al.
(2011, free online). In these papers they refer to creating two
different weak-learner/base function ensembles for either parameter in
the occupancy detection model (e.g., one parameter p_o for probability
that a site is truly occupied by a species, and another probability
p_d that the species is detected). I understand how to use mboost to
perform a boosted regression of X on a response whose distribution has
a single parameter; my questions are: i) is it possible to use mboost
to simultaneously boost two ensembles for two different parameters?
ii) if so, any idea how?  Another reference, Borisov et al (2009, free
online), claim's to have modified mboost to perform a Zero-inflated
Poisson, which likewise involves a mixture of two parameters, each
with their own ensemble.

I understand that the mboost allows custom Families (?mboost::Family)
to be added, by specifying a loss function and a gradient function. I
guess the loss function would be the negative log-likelihood, but can
the gradient function be different for either parameter (e.g., partial
derivative)?

Hochachka, W.M., Fink, D., Hutchinson, R.A., Sheldon, D., Wong, W.K.,
and Kelling, S. 2012. Data-intensive science applied to broad-scale
citizen science.  Trends Ecol. Evol. 27(2):130–137.
Hutchinson, R.A., Liu, L.P., and Dietterich, T.G. 2011. Incorporating
boosted regression trees into ecological latent variable models. pp.
1343–1348. In: W. Burgard and D. Roth (eds.) Proceedings of the
Twenty-Fifth AAAI Conference on Artificial Intelligence. Association
for the Advancement of Artificial Intelligence. [Available at:
http://www.aaai.org/ocs/index.php/AAAI/AAAI11/paper/viewFile/3711/4086]
Schmid, M., Potapov, S., Pfahlberg, A., and Hothorn, T. 2010.
Estimation and regularization techniques for regression models with
multidimensional prediction functions.  Statistics and Computing
20(2):139–150. [Available at:
http://epub.ub.uni-muenchen.de/7788/1/TR.pdf]

Thanks for your help,
Rob

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