# Deep Variational Sufficient Dimensionality Reduction

arXiv: https://arxiv.org/abs/1812.07641 · HTML: https://mlsanity.com/paper/1812.07641/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Dec 2018.

## Built on by (most cited first, 3 of 3)

- [Nonlinear Sufficient Dimension Reduction with a Stochastic Neural Network](https://mlsanity.com/paper/2210.04349/) (2022)
- [Sufficient Dimension Reduction for High-Dimensional Regression and Low-Dimensional Embedding: Tutorial and Survey](https://mlsanity.com/paper/2110.09620/) (2021)
- [Random-projection ensemble dimension reduction](https://mlsanity.com/paper/2410.04922/) (2024)

## Abstract (arXiv)

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.