Deep Variational Sufficient Dimensionality Reduction
This work addresses dimensionality reduction for machine learning applications, but it appears incremental as it builds on existing variational autoencoder frameworks.
The paper tackles the problem of sufficient dimensionality reduction (SDR) by proposing DVSDR, a deep variational approach that transforms high-dimensional data into a low-dimensional subspace while preserving label information, and it performs competitively on classification tasks and enables data generation.
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.