Reparameterizable Subset Sampling via Continuous Relaxations
This addresses a bottleneck in machine learning for tasks requiring subset sampling, offering a novel method that enhances interpretability and model training, though it is incremental in building on existing tricks like Gumbel-softmax.
The paper tackles the problem of non-reparameterizable stochastic optimization in subset sampling by introducing a continuous relaxation that generalizes the Gumbel-max trick, enabling low-variance gradients and improving performance in tasks like feature selection, deep k-nearest neighbors, and parametric t-SNE.
Many machine learning tasks require sampling a subset of items from a collection based on a parameterized distribution. The Gumbel-softmax trick can be used to sample a single item, and allows for low-variance reparameterized gradients with respect to the parameters of the underlying distribution. However, stochastic optimization involving subset sampling is typically not reparameterizable. To overcome this limitation, we define a continuous relaxation of subset sampling that provides reparameterization gradients by generalizing the Gumbel-max trick. We use this approach to sample subsets of features in an instance-wise feature selection task for model interpretability, subsets of neighbors to implement a deep stochastic k-nearest neighbors model, and sub-sequences of neighbors to implement parametric t-SNE by directly comparing the identities of local neighbors. We improve performance in all these tasks by incorporating subset sampling in end-to-end training.