Generalized Linear Models for Aggregated Data

Avradeep Bhowmik, Joydeep Ghosh, Oluwasanmi Koyejo
Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, PMLR 38:93-101, 2015.

Abstract

Databases in domains such as healthcare are routinely released to the public in aggregated form. Unfortunately, naive modeling with aggregated data may significantly diminish the accuracy of inferences at the individual level. This paper addresses the scenario where features are provided at the individual level, but the target variables are only available as histogram aggregates or order statistics. We consider a limiting case of generalized linear modeling when the target variables are only known up to permutation, and explore how this relates to permutation testing; a standard technique for assessing statistical dependency. Based on this relationship, we propose a simple algorithm to estimate the model parameters and individual level inferences via alternating imputation and standard generalized linear model fitting. Our results suggest the effectiveness of the proposed approach when, in the original data, permutation testing accurately ascertains the veracity of the linear relationship. The framework is extended to general histogram data with larger bins - with order statistics such as the median as a limiting case. Our experimental results on simulated data and aggregated healthcare data suggest a diminishing returns property with respect to the granularity of the histogram - when a linear relationship holds in the original data, the targets can be predicted accurately given relatively coarse histograms.

Cite this Paper

BibTeX
@InProceedings{pmlr-v38-bhowmik15, title = {{Generalized Linear Models for Aggregated Data}}, author = {Bhowmik, Avradeep and Ghosh, Joydeep and Koyejo, Oluwasanmi}, booktitle = {Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics}, pages = {93--101}, year = {2015}, editor = {Lebanon, Guy and Vishwanathan, S. V. N.}, volume = {38}, series = {Proceedings of Machine Learning Research}, address = {San Diego, California, USA}, month = {09--12 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v38/bhowmik15.pdf}, url = {https://proceedings.mlr.press/v38/bhowmik15.html}, abstract = {Databases in domains such as healthcare are routinely released to the public in aggregated form. Unfortunately, naive modeling with aggregated data may significantly diminish the accuracy of inferences at the individual level. This paper addresses the scenario where features are provided at the individual level, but the target variables are only available as histogram aggregates or order statistics. We consider a limiting case of generalized linear modeling when the target variables are only known up to permutation, and explore how this relates to permutation testing; a standard technique for assessing statistical dependency. Based on this relationship, we propose a simple algorithm to estimate the model parameters and individual level inferences via alternating imputation and standard generalized linear model fitting. Our results suggest the effectiveness of the proposed approach when, in the original data, permutation testing accurately ascertains the veracity of the linear relationship. The framework is extended to general histogram data with larger bins - with order statistics such as the median as a limiting case. Our experimental results on simulated data and aggregated healthcare data suggest a diminishing returns property with respect to the granularity of the histogram - when a linear relationship holds in the original data, the targets can be predicted accurately given relatively coarse histograms.} }
Endnote
%0 Conference Paper %T Generalized Linear Models for Aggregated Data %A Avradeep Bhowmik %A Joydeep Ghosh %A Oluwasanmi Koyejo %B Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2015 %E Guy Lebanon %E S. V. N. Vishwanathan %F pmlr-v38-bhowmik15 %I PMLR %P 93--101 %U https://proceedings.mlr.press/v38/bhowmik15.html %V 38 %X Databases in domains such as healthcare are routinely released to the public in aggregated form. Unfortunately, naive modeling with aggregated data may significantly diminish the accuracy of inferences at the individual level. This paper addresses the scenario where features are provided at the individual level, but the target variables are only available as histogram aggregates or order statistics. We consider a limiting case of generalized linear modeling when the target variables are only known up to permutation, and explore how this relates to permutation testing; a standard technique for assessing statistical dependency. Based on this relationship, we propose a simple algorithm to estimate the model parameters and individual level inferences via alternating imputation and standard generalized linear model fitting. Our results suggest the effectiveness of the proposed approach when, in the original data, permutation testing accurately ascertains the veracity of the linear relationship. The framework is extended to general histogram data with larger bins - with order statistics such as the median as a limiting case. Our experimental results on simulated data and aggregated healthcare data suggest a diminishing returns property with respect to the granularity of the histogram - when a linear relationship holds in the original data, the targets can be predicted accurately given relatively coarse histograms.
RIS
TY - CPAPER TI - Generalized Linear Models for Aggregated Data AU - Avradeep Bhowmik AU - Joydeep Ghosh AU - Oluwasanmi Koyejo BT - Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics DA - 2015/02/21 ED - Guy Lebanon ED - S. V. N. Vishwanathan ID - pmlr-v38-bhowmik15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 38 SP - 93 EP - 101 L1 - http://proceedings.mlr.press/v38/bhowmik15.pdf UR - https://proceedings.mlr.press/v38/bhowmik15.html AB - Databases in domains such as healthcare are routinely released to the public in aggregated form. Unfortunately, naive modeling with aggregated data may significantly diminish the accuracy of inferences at the individual level. This paper addresses the scenario where features are provided at the individual level, but the target variables are only available as histogram aggregates or order statistics. We consider a limiting case of generalized linear modeling when the target variables are only known up to permutation, and explore how this relates to permutation testing; a standard technique for assessing statistical dependency. Based on this relationship, we propose a simple algorithm to estimate the model parameters and individual level inferences via alternating imputation and standard generalized linear model fitting. Our results suggest the effectiveness of the proposed approach when, in the original data, permutation testing accurately ascertains the veracity of the linear relationship. The framework is extended to general histogram data with larger bins - with order statistics such as the median as a limiting case. Our experimental results on simulated data and aggregated healthcare data suggest a diminishing returns property with respect to the granularity of the histogram - when a linear relationship holds in the original data, the targets can be predicted accurately given relatively coarse histograms. ER -
APA
Bhowmik, A., Ghosh, J. & Koyejo, O.. (2015). Generalized Linear Models for Aggregated Data. Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 38:93-101 Available from https://proceedings.mlr.press/v38/bhowmik15.html.

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