Learning-Augmented Moment Estimation on Time-Decay Models

2026-03-02

AI Summary

This work addresses the challenge of efficiently processing weighted data streams under privacy constraints in the time-decay streaming model, where traditional algorithms struggle with space complexity bottlenecks for fundamental tasks such as norm/moment estimation and frequency estimation. The paper introduces, for the first time, a systematic learning-augmented approach to this model by leveraging machine learning oracles that provide heavy-hitter information. Building on this insight, the authors design novel streaming algorithms that effectively solve norm and moment estimation, frequency estimation, and cascaded and rectangular moment estimation problems. Theoretical analysis establishes the space efficiency of the proposed methods, while experiments on both real-world and synthetic datasets demonstrate their practical efficiency and scalability, offering a new paradigm for statistical estimation over weighted data streams.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Data Mining & Knowledge Management: Data Stream Mining
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Machine learning and data science for the Web

Abstract

Motivated by the prevalence and success of machine learning, a line of recent work has studied learning-augmented algorithms in the streaming model. These results have shown that for natural and practical oracles implemented with machine learning models, we can obtain streaming algorithms with improved space efficiency that are otherwise provably impossible. On the other hand, our understanding is much more limited when items are weighted unequally, for example, in the sliding-window model, where older data must be expunged from the dataset, e.g., by privacy regulation laws. In this paper, we utilize an oracle for the heavy-hitters of datasets to give learning-augmented algorithms for a number of fundamental problems, such as norm/moment estimation, frequency estimation, cascaded norms, and rectangular moment estimation, in the time-decay setting. We complement our theoretical results with a number of empirical evaluations that demonstrate the practical efficiency of our algorithms on real and synthetic datasets.

Problem

• learning-augmented algorithms
• time-decay models
• streaming algorithms
• moment estimation
• heavy-hitters

Innovation

• learning-augmented algorithms
• time-decay models
• heavy-hitters oracle
• streaming algorithms
• moment estimation