Nonparametric Automatic Differentiation Variational Inference with Spline Approximation

Yuda Shao, Shan N Yu, Tianshu Feng
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:2656-2664, 2024.

Abstract

Automatic Differentiation Variational Inference (ADVI) is efficient in learning probabilistic models. Classic ADVI relies on the parametric approach to approximate the posterior. In this paper, we develop a spline-based nonparametric approximation approach that enables flexible posterior approximation for distributions with complicated structures, such as skewness, multimodality, and bounded support. Compared with widely-used nonparametric variational inference methods, the proposed method is easy to implement and adaptive to various data structures. By adopting the spline approximation, we derive a lower bound of the importance weighted autoencoder and establish the asymptotic consistency. Experiments demonstrate the efficiency of the proposed method in approximating complex posterior distributions and improving the performance of generative models with incomplete data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-shao24a, title = {Nonparametric Automatic Differentiation Variational Inference with Spline Approximation}, author = {Shao, Yuda and N Yu, Shan and Feng, Tianshu}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {2656--2664}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/shao24a/shao24a.pdf}, url = {https://proceedings.mlr.press/v238/shao24a.html}, abstract = {Automatic Differentiation Variational Inference (ADVI) is efficient in learning probabilistic models. Classic ADVI relies on the parametric approach to approximate the posterior. In this paper, we develop a spline-based nonparametric approximation approach that enables flexible posterior approximation for distributions with complicated structures, such as skewness, multimodality, and bounded support. Compared with widely-used nonparametric variational inference methods, the proposed method is easy to implement and adaptive to various data structures. By adopting the spline approximation, we derive a lower bound of the importance weighted autoencoder and establish the asymptotic consistency. Experiments demonstrate the efficiency of the proposed method in approximating complex posterior distributions and improving the performance of generative models with incomplete data.} }
Endnote
%0 Conference Paper %T Nonparametric Automatic Differentiation Variational Inference with Spline Approximation %A Yuda Shao %A Shan N Yu %A Tianshu Feng %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-shao24a %I PMLR %P 2656--2664 %U https://proceedings.mlr.press/v238/shao24a.html %V 238 %X Automatic Differentiation Variational Inference (ADVI) is efficient in learning probabilistic models. Classic ADVI relies on the parametric approach to approximate the posterior. In this paper, we develop a spline-based nonparametric approximation approach that enables flexible posterior approximation for distributions with complicated structures, such as skewness, multimodality, and bounded support. Compared with widely-used nonparametric variational inference methods, the proposed method is easy to implement and adaptive to various data structures. By adopting the spline approximation, we derive a lower bound of the importance weighted autoencoder and establish the asymptotic consistency. Experiments demonstrate the efficiency of the proposed method in approximating complex posterior distributions and improving the performance of generative models with incomplete data.
APA
Shao, Y., N Yu, S. & Feng, T.. (2024). Nonparametric Automatic Differentiation Variational Inference with Spline Approximation. Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:2656-2664 Available from https://proceedings.mlr.press/v238/shao24a.html.

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