An approximate KLD based experimental design for models with intractable likelihoods

Ziqiao Ao, Jinglai Li
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:3241-3251, 2020.

Abstract

Data collection is a critical step in statistical inference and data science,and the goal of statistical experimental design (ED) is to find the data collection setupthat can provide most information for the inference. In this work we consider a special type of ED problems where the likelihoods are not available in a closed form. In this case, the popular information-theoretic Kullback-Leibler divergence (KLD) based design criterioncan not be used directly, as it requires to evaluate the likelihood function. To address the issue, we derive a new utility function,which is a lower bound of the original KLD utility. This lower bound is expressed in terms of the summation of two or more entropies in the data space, and thus can be evaluated efficiently via entropy estimation methods.We provide several numerical examples to demonstrate the performance of the proposed method.

Cite this Paper

BibTeX
@InProceedings{pmlr-v108-ao20a, title = {An approximate KLD based experimental design for models with intractable likelihoods}, author = {Ao, Ziqiao and Li, Jinglai}, booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics}, pages = {3241--3251}, year = {2020}, editor = {Chiappa, Silvia and Calandra, Roberto}, volume = {108}, series = {Proceedings of Machine Learning Research}, month = {26--28 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v108/ao20a/ao20a.pdf}, url = {https://proceedings.mlr.press/v108/ao20a.html}, abstract = {Data collection is a critical step in statistical inference and data science,and the goal of statistical experimental design (ED) is to find the data collection setupthat can provide most information for the inference. In this work we consider a special type of ED problems where the likelihoods are not available in a closed form. In this case, the popular information-theoretic Kullback-Leibler divergence (KLD) based design criterioncan not be used directly, as it requires to evaluate the likelihood function. To address the issue, we derive a new utility function,which is a lower bound of the original KLD utility. This lower bound is expressed in terms of the summation of two or more entropies in the data space, and thus can be evaluated efficiently via entropy estimation methods.We provide several numerical examples to demonstrate the performance of the proposed method. } }
Endnote
%0 Conference Paper %T An approximate KLD based experimental design for models with intractable likelihoods %A Ziqiao Ao %A Jinglai Li %B Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2020 %E Silvia Chiappa %E Roberto Calandra %F pmlr-v108-ao20a %I PMLR %P 3241--3251 %U https://proceedings.mlr.press/v108/ao20a.html %V 108 %X Data collection is a critical step in statistical inference and data science,and the goal of statistical experimental design (ED) is to find the data collection setupthat can provide most information for the inference. In this work we consider a special type of ED problems where the likelihoods are not available in a closed form. In this case, the popular information-theoretic Kullback-Leibler divergence (KLD) based design criterioncan not be used directly, as it requires to evaluate the likelihood function. To address the issue, we derive a new utility function,which is a lower bound of the original KLD utility. This lower bound is expressed in terms of the summation of two or more entropies in the data space, and thus can be evaluated efficiently via entropy estimation methods.We provide several numerical examples to demonstrate the performance of the proposed method.
APA
Ao, Z. & Li, J.. (2020). An approximate KLD based experimental design for models with intractable likelihoods. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 108:3241-3251 Available from https://proceedings.mlr.press/v108/ao20a.html.

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