Russell Kunes

Russell Z. Kunes, Mingzhang Yin, Max Land et al.

Gradient estimation is often necessary for fitting generative models with discrete latent variables, in contexts such as reinforcement learning and variational autoencoder (VAE) training. The DisARM estimator (Yin et al. 2020; Dong, Mnih, and Tucker 2020) achieves state of the art gradient variance for Bernoulli latent variable models in many contexts. However, DisARM and other estimators have potentially exploding variance near the boundary of the parameter space, where solutions tend to lie. To ameliorate this issue, we propose a new gradient estimator \textit{bitflip}-1 that has lower variance at the boundaries of the parameter space. As bitflip-1 has complementary properties to existing estimators, we introduce an aggregated estimator, \textit{unbiased gradient variance clipping} (UGC) that uses either a bitflip-1 or a DisARM gradient update for each coordinate. We theoretically prove that UGC has uniformly lower variance than DisARM. Empirically, we observe that UGC achieves the optimal value of the optimization objectives in toy experiments, discrete VAE training, and in a best subset selection problem.

Doron Haviv, Russell Zhang Kunes, Thomas Dougherty et al.

Optimal transport (OT) and the related Wasserstein metric (W) are powerful and ubiquitous tools for comparing distributions. However, computing pairwise Wasserstein distances rapidly becomes intractable as cohort size grows. An attractive alternative would be to find an embedding space in which pairwise Euclidean distances map to OT distances, akin to standard multidimensional scaling (MDS). We present Wasserstein Wormhole, a transformer-based autoencoder that embeds empirical distributions into a latent space wherein Euclidean distances approximate OT distances. Extending MDS theory, we show that our objective function implies a bound on the error incurred when embedding non-Euclidean distances. Empirically, distances between Wormhole embeddings closely match Wasserstein distances, enabling linear time computation of OT distances. Along with an encoder that maps distributions to embeddings, Wasserstein Wormhole includes a decoder that maps embeddings back to distributions, allowing for operations in the embedding space to generalize to OT spaces, such as Wasserstein barycenter estimation and OT interpolation. By lending scalability and interpretability to OT approaches, Wasserstein Wormhole unlocks new avenues for data analysis in the fields of computational geometry and single-cell biology.

Jason Ren, Russell Kunes, Finale Doshi-Velez

Electronic Health Record (EHR) data can be represented as discrete counts over a high dimensional set of possible procedures, diagnoses, and medications. Supervised topic models present an attractive option for incorporating EHR data as features into a prediction problem: given a patient's record, we estimate a set of latent factors that are predictive of the response variable. However, existing methods for supervised topic modeling struggle to balance prediction quality and coherence of the latent factors. We introduce a novel approach, the prediction-focused topic model, that uses the supervisory signal to retain only features that improve, or do not hinder, prediction performance. By removing features with irrelevant signal, the topic model is able to learn task-relevant, interpretable topics. We demonstrate on a EHR dataset and a movie review dataset that compared to existing approaches, prediction-focused topic models are able to learn much more coherent topics while maintaining competitive predictions.

Jason Ren, Russell Kunes, Finale Doshi-Velez

Supervised topic models are often sought to balance prediction quality and interpretability. However, when models are (inevitably) misspecified, standard approaches rarely deliver on both. We introduce a novel approach, the prediction-focused topic model, that uses the supervisory signal to retain only vocabulary terms that improve, or at least do not hinder, prediction performance. By removing terms with irrelevant signal, the topic model is able to learn task-relevant, coherent topics. We demonstrate on several data sets that compared to existing approaches, prediction-focused topic models learn much more coherent topics while maintaining competitive predictions.