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arXiv · 1812.07641

Deep Variational Sufficient Dimensionality Reduction

Ershad Banijamali·Amir-Hossein Karimi·Ali Ghodsi
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Abstract

We consider the problem of sufficient dimensionality reduction (SDR), where the high-dimensional observation is transformed to a low-dimensional sub-space in which the information of the observations regarding the label variable is preserved. We propose DVSDR, a deep variational approach for sufficient dimensionality reduction. The deep structure in our model has a bottleneck that represent the low-dimensional embedding of the data. We explain the SDR problem using graphical models and use the framework of variational autoencoders to maximize the lower bound of the log-likelihood of the joint distribution of the observation and label. We show that such a maximization problem can be interpreted as solving the SDR problem. DVSDR can be easily adopted to semi-supervised learning setting. In our experiment we show that DVSDR performs competitively on classification tasks while being able to generate novel data samples.

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Ershad Banijamali, Amir-Hossein Karimi, Ali Ghodsi. 2018-12-18. Deep Variational Sufficient Dimensionality Reduction. https://arxiv.org/abs/1812.07641

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