Abstract
This paper introduces an approach to missing data imputation based on deep auto-encoder models, adequate to high-dimensional data exhibiting complex dependencies, such as images. The method exploits the properties of the vector field associated to an auto-encoder, which allows to approximate the gradient of the log-density from its reconstruction error, based on which we propose a projected gradient ascent algorithm to obtain the conditionally most probable estimate of the missing values. Our approach does not require any specialized training procedure and can be used together with any auto-encoder model trained on complete data in a classical way. Experiments performed on benchmark datasets show that imputations produced by our model are sharp and realistic.
The is the extended version of an extended abstract [25] presented at the ICLR Workshop on the Integration of Deep Neural Models and Differential Equations.
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Notes
- 1.
A GMM can also be learned from incomplete data, but the imputation process does not change.
- 2.
For a comparison between different auto-encoder models in the proposed procedure the reader is referred to our workshop paper [25].
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Acknowledgements
The work of M. Śmieja was supported by the National Science Centre (Poland) grant no. 2018/31/B/ST6/00993. The work of Ł. Struski was supported by the National Science Centre (Poland) grant no. 2017/25/B/ST6/01271 as well as the Foundation for Polish Science Grant No. POIR.04.04.00-00-14DE/18-00 co-financed by the European Union under the European Regional Development Fund. The work of M. Juda was supported by the National Science Centre (Poland) grant no. 2014/14/A/ST1/00453 and 2015/19/D/ST6/01215.
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Śmieja, M., Kołomycki, M., Struski, Ł., Juda, M., Figueiredo, M.A.T. (2020). Iterative Imputation of Missing Data Using Auto-Encoder Dynamics. In: Yang, H., Pasupa, K., Leung, A.CS., Kwok, J.T., Chan, J.H., King, I. (eds) Neural Information Processing. ICONIP 2020. Lecture Notes in Computer Science(), vol 12534. Springer, Cham. https://doi.org/10.1007/978-3-030-63836-8_22
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