N$^2$: A Unified Python Package and Test Bench for Nearest Neighbor-Based Matrix Completion

2025-06-04

AI Summary

This work addresses the lack of unified implementations and systematic evaluation for nearest-neighbor (NN)-based matrix completion. We introduce the first open-source Python toolkit and benchmarking platform dedicated to this paradigm. Methodologically, we design a modular architecture supporting k-NN retrieval, adaptive similarity metrics, and weighted interpolation, and propose novel NN variants. We construct a real-world benchmark suite spanning four domains—healthcare, recommendation, causal inference, and large language model evaluation—that accommodates diverse missingness mechanisms (e.g., MAR, MNAR). Experiments demonstrate that our approach significantly outperforms classical baselines—including SoftImpute and SVD—on real-world datasets, achieving state-of-the-art performance across multiple tasks. These results validate the robustness and generalization superiority of NN-based methods under non-ideal missing-data conditions.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Data Mining & Knowledge Management: Linked Open Data, Knowledge Graphs & KB Completion

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

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.

Problem

• Develops a unified Python package for nearest neighbor matrix completion
• Evaluates NN methods robustness across diverse real-world applications
• Introduces new NN variant achieving state-of-the-art performance

Innovation

• Unified Python package for NN matrix completion
• Modular interface supports rapid experimentation
• New NN variant achieves state-of-the-art results