Caleb Chin

Caleb Chin, Aashish Khubchandani, Harshvardhan Maskara et al. · harvard, mit

Nearest neighbor (NN) methods have re-emerged as competitive tools for matrix completion, offering strong empirical performance and recent theoretical guarantees, including entry-wise error bounds, confidence intervals, and minimax optimality. Despite their simplicity, recent work has shown that NN approaches are robust to a range of missingness patterns and effective across diverse applications. This paper introduces N$^2$, a unified Python package and testbed that consolidates a broad class of NN-based methods through a modular, extensible interface. Built for both researchers and practitioners, N$^2$ supports rapid experimentation and benchmarking. Using this framework, we introduce a new NN variant that achieves state-of-the-art results in several settings. We also release a benchmark suite of real-world datasets, from healthcare and recommender systems to causal inference and LLM evaluation, designed to stress-test matrix completion methods beyond synthetic scenarios. Our experiments demonstrate that while classical methods excel on idealized data, NN-based techniques consistently outperform them in real-world settings.

Kyuseong Choi, Jacob Feitelberg, Caleb Chin et al. · harvard, mit

Consider a setting with multiple units (e.g., individuals, cohorts, geographic locations) and outcomes (e.g., treatments, times, items), where the goal is to learn a multivariate distribution for each unit-outcome entry, such as the distribution of a user's weekly spend and engagement under a specific mobile app version. A common challenge is the prevalence of missing not at random data, where observations are available only for certain unit-outcome combinations and the observation availability can be correlated with the properties of distributions themselves, i.e., there is unobserved confounding. An additional challenge is that for any observed unit-outcome entry, we only have a finite number of samples from the underlying distribution. We tackle these two challenges by casting the problem into a novel distributional matrix completion framework and introduce a kernel based distributional generalization of nearest neighbors to estimate the underlying distributions. By leveraging maximum mean discrepancies and a suitable factor model on the kernel mean embeddings of the underlying distributions, we establish consistent recovery of the underlying distributions even when data is missing not at random and positivity constraints are violated. Furthermore, we demonstrate that our nearest neighbors approach is robust to heteroscedastic noise, provided we have access to two or more measurements for the observed unit-outcome entries, a robustness not present in prior works on nearest neighbors with single measurements.