A Hybrid Pareto Model for Conditional Density Estimation of Asymmetric Fat-Tail Data

Julie Carreau, Yoshua Bengio
Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics, PMLR 2:51-58, 2007.

Abstract

We propose an estimator for the conditional density p(Y |X) that can adapt for asymmetric heavy tails which might depend on X. Such estimators have important applications in nance and insurance. We draw from Extreme Value Theory the tools to build a hybrid unimodal density having a parameter controlling the heaviness of the upper tail. This hybrid is a Gaussian whose upper tail has been replaced by a generalized Pareto tail. We use this hybrid in a multi-modal mixture in order to obtain a nonparametric density estimator that can easily adapt for heavy tailed data. To obtain a conditional density estimator, the parameters of the mixture estimator can be seen as functions of X and these functions learned. We show experimentally that this approach better models the conditional density in terms of likelihood than compared competing algorithms : conditional mixture models with other types of components and multivariate nonparametric models.

Cite this Paper

BibTeX
@InProceedings{pmlr-v2-carreau07a, title = {A Hybrid Pareto Model for Conditional Density Estimation of Asymmetric Fat-Tail Data}, author = {Carreau, Julie and Bengio, Yoshua}, booktitle = {Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics}, pages = {51--58}, year = {2007}, editor = {Meila, Marina and Shen, Xiaotong}, volume = {2}, series = {Proceedings of Machine Learning Research}, address = {San Juan, Puerto Rico}, month = {21--24 Mar}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v2/carreau07a/carreau07a.pdf}, url = {https://proceedings.mlr.press/v2/carreau07a.html}, abstract = {We propose an estimator for the conditional density p(Y |X) that can adapt for asymmetric heavy tails which might depend on X. Such estimators have important applications in nance and insurance. We draw from Extreme Value Theory the tools to build a hybrid unimodal density having a parameter controlling the heaviness of the upper tail. This hybrid is a Gaussian whose upper tail has been replaced by a generalized Pareto tail. We use this hybrid in a multi-modal mixture in order to obtain a nonparametric density estimator that can easily adapt for heavy tailed data. To obtain a conditional density estimator, the parameters of the mixture estimator can be seen as functions of X and these functions learned. We show experimentally that this approach better models the conditional density in terms of likelihood than compared competing algorithms : conditional mixture models with other types of components and multivariate nonparametric models.} }
Endnote
%0 Conference Paper %T A Hybrid Pareto Model for Conditional Density Estimation of Asymmetric Fat-Tail Data %A Julie Carreau %A Yoshua Bengio %B Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2007 %E Marina Meila %E Xiaotong Shen %F pmlr-v2-carreau07a %I PMLR %P 51--58 %U https://proceedings.mlr.press/v2/carreau07a.html %V 2 %X We propose an estimator for the conditional density p(Y |X) that can adapt for asymmetric heavy tails which might depend on X. Such estimators have important applications in nance and insurance. We draw from Extreme Value Theory the tools to build a hybrid unimodal density having a parameter controlling the heaviness of the upper tail. This hybrid is a Gaussian whose upper tail has been replaced by a generalized Pareto tail. We use this hybrid in a multi-modal mixture in order to obtain a nonparametric density estimator that can easily adapt for heavy tailed data. To obtain a conditional density estimator, the parameters of the mixture estimator can be seen as functions of X and these functions learned. We show experimentally that this approach better models the conditional density in terms of likelihood than compared competing algorithms : conditional mixture models with other types of components and multivariate nonparametric models.
RIS
TY - CPAPER TI - A Hybrid Pareto Model for Conditional Density Estimation of Asymmetric Fat-Tail Data AU - Julie Carreau AU - Yoshua Bengio BT - Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics DA - 2007/03/11 ED - Marina Meila ED - Xiaotong Shen ID - pmlr-v2-carreau07a PB - PMLR DP - Proceedings of Machine Learning Research VL - 2 SP - 51 EP - 58 L1 - http://proceedings.mlr.press/v2/carreau07a/carreau07a.pdf UR - https://proceedings.mlr.press/v2/carreau07a.html AB - We propose an estimator for the conditional density p(Y |X) that can adapt for asymmetric heavy tails which might depend on X. Such estimators have important applications in nance and insurance. We draw from Extreme Value Theory the tools to build a hybrid unimodal density having a parameter controlling the heaviness of the upper tail. This hybrid is a Gaussian whose upper tail has been replaced by a generalized Pareto tail. We use this hybrid in a multi-modal mixture in order to obtain a nonparametric density estimator that can easily adapt for heavy tailed data. To obtain a conditional density estimator, the parameters of the mixture estimator can be seen as functions of X and these functions learned. We show experimentally that this approach better models the conditional density in terms of likelihood than compared competing algorithms : conditional mixture models with other types of components and multivariate nonparametric models. ER -
APA
Carreau, J. & Bengio, Y.. (2007). A Hybrid Pareto Model for Conditional Density Estimation of Asymmetric Fat-Tail Data. Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 2:51-58 Available from https://proceedings.mlr.press/v2/carreau07a.html.

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