Kichang Choi

Albert Gong, Kyuseong Choi, Raaz Dwivedi · harvard, mit

The kernel thinning algorithm of Dwivedi & Mackey (2024) provides a better-than-i.i.d. compression of a generic set of points. By generating high-fidelity coresets of size significantly smaller than the input points, KT is known to speed up unsupervised tasks like Monte Carlo integration, uncertainty quantification, and non-parametric hypothesis testing, with minimal loss in statistical accuracy. In this work, we generalize the KT algorithm to speed up supervised learning problems involving kernel methods. Specifically, we combine two classical algorithms--Nadaraya-Watson (NW) regression or kernel smoothing, and kernel ridge regression (KRR)--with KT to provide a quadratic speed-up in both training and inference times. We show how distribution compression with KT in each setting reduces to constructing an appropriate kernel, and introduce the Kernel-Thinned NW and Kernel-Thinned KRR estimators. We prove that KT-based regression estimators enjoy significantly superior computational efficiency over the full-data estimators and improved statistical efficiency over i.i.d. subsampling of the training data. En route, we also provide a novel multiplicative error guarantee for compressing with KT. We validate our design choices with both simulations and real data experiments.

Jacob Feitelberg, Dwaipayan Saha, Kyuseong Choi et al. · harvard, mit

Missing data is a pervasive problem in tabular settings. Existing solutions range from simple averaging to complex generative adversarial networks. However, due to huge variance in performance across real-world domains and time-consuming hyperparameter tuning, no default imputation method exists. Building on TabPFN, a recent tabular foundation model for supervised learning, we propose TabImpute, a pre-trained transformer that delivers accurate and fast zero-shot imputations requiring no fitting or hyperparameter tuning at inference-time. To train and evaluate TabImpute, we introduce (i) an entry-wise featurization for tabular settings, which enables a $100\times$ speedup over the previous TabPFN imputation method, (ii) a synthetic training data generation pipeline incorporating realistic missingness patterns, which boosts test-time performance, and (iii) MissBench, a comprehensive benchmark for evaluation of imputation methods with $42$ OpenML datasets and $13$ missingness patterns. MissBench spans domains such as medicine, finance, and engineering, showcasing TabImpute's robust performance compared to $11$ established imputation methods.