Featurized Density Ratio Estimation
This addresses a bottleneck in unsupervised machine learning for researchers and practitioners working with high-dimensional data, though it is an incremental improvement over existing methods.
The paper tackles the difficulty of estimating density ratios for complex, high-dimensional data by using an invertible generative model to map distributions into a common feature space, improving accuracy in tasks like mutual information estimation and targeted sampling.
Density ratio estimation serves as an important technique in the unsupervised machine learning toolbox. However, such ratios are difficult to estimate for complex, high-dimensional data, particularly when the densities of interest are sufficiently different. In our work, we propose to leverage an invertible generative model to map the two distributions into a common feature space prior to estimation. This featurization brings the densities closer together in latent space, sidestepping pathological scenarios where the learned density ratios in input space can be arbitrarily inaccurate. At the same time, the invertibility of our feature map guarantees that the ratios computed in feature space are equivalent to those in input space. Empirically, we demonstrate the efficacy of our approach in a variety of downstream tasks that require access to accurate density ratios such as mutual information estimation, targeted sampling in deep generative models, and classification with data augmentation.