Matthew Zhang

Matthew Zhang, Jihao Andreas Lin, Krzysztof Choromanski et al.

We study the application of graph random features (GRFs) - a recently introduced stochastic estimator of graph node kernels - to scalable Gaussian processes on discrete input spaces. We prove that (under mild assumptions) Bayesian inference with GRFs enjoys $O(N^{3/2})$ time complexity with respect to the number of nodes $N$, compared to $O(N^3)$ for exact kernels. Substantial wall-clock speedups and memory savings unlock Bayesian optimisation on graphs with over $10^6$ nodes on a single computer chip, whilst preserving competitive performance.

Krishnakumar Balasubramanian, Sinho Chewi, Murat A. Erdogdu et al.

For the task of sampling from a density $π\propto \exp(-V)$ on $\mathbb{R}^d$, where $V$ is possibly non-convex but $L$-gradient Lipschitz, we prove that averaged Langevin Monte Carlo outputs a sample with $\varepsilon$-relative Fisher information after $O( L^2 d^2/\varepsilon^2)$ iterations. This is the sampling analogue of complexity bounds for finding an $\varepsilon$-approximate first-order stationary points in non-convex optimization and therefore constitutes a first step towards the general theory of non-log-concave sampling. We discuss numerous extensions and applications of our result; in particular, it yields a new state-of-the-art guarantee for sampling from distributions which satisfy a Poincaré inequality.

Sinho Chewi, Murat A. Erdogdu, Mufan Bill Li et al.

Classically, the continuous-time Langevin diffusion converges exponentially fast to its stationary distribution $π$ under the sole assumption that $π$ satisfies a Poincaré inequality. Using this fact to provide guarantees for the discrete-time Langevin Monte Carlo (LMC) algorithm, however, is considerably more challenging due to the need for working with chi-squared or Rényi divergences, and prior works have largely focused on strongly log-concave targets. In this work, we provide the first convergence guarantees for LMC assuming that $π$ satisfies either a Latała--Oleszkiewicz or modified log-Sobolev inequality, which interpolates between the Poincaré and log-Sobolev settings. Unlike prior works, our results allow for weak smoothness and do not require convexity or dissipativity conditions.

Irene Li, Jessica Pan, Jeremy Goldwasser et al.

Electronic health records (EHRs), digital collections of patient healthcare events and observations, are ubiquitous in medicine and critical to healthcare delivery, operations, and research. Despite this central role, EHRs are notoriously difficult to process automatically. Well over half of the information stored within EHRs is in the form of unstructured text (e.g. provider notes, operation reports) and remains largely untapped for secondary use. Recently, however, newer neural network and deep learning approaches to Natural Language Processing (NLP) have made considerable advances, outperforming traditional statistical and rule-based systems on a variety of tasks. In this survey paper, we summarize current neural NLP methods for EHR applications. We focus on a broad scope of tasks, namely, classification and prediction, word embeddings, extraction, generation, and other topics such as question answering, phenotyping, knowledge graphs, medical dialogue, multilinguality, interpretability, etc.