Scale-invariant Optimal Sampling for Rare-events Data and Sparse Models.

Area of Science:

• Statistics
• Machine Learning
• Data Science

Background:

• Subsampling addresses computational challenges in massive datasets, especially those with rare events.
• Optimal subsampling is crucial to prevent information loss from overly aggressive sampling.
• Existing methods are sensitive to data scaling and can be negatively impacted by inactive features.

Purpose of the Study:

• To develop a scale-invariant optimal subsampling method for sparse models with rare events.
• To minimize prediction error rather than model parameters.
• To address the challenge of inactive features inflating subsampling probabilities.

Main Methods:

• Introduced an adaptive lasso estimator for rare-events data, establishing its oracle properties.
• Derived a scale-invariant optimal subsampling function to minimize prediction error for inverse probability weighted (IPW) adaptive lasso.
• Proposed a maximum sampled conditional likelihood (MSCL) estimator to enhance efficiency.

Main Results:

• The proposed scale-invariant subsampling method effectively mitigates information loss and improves estimation efficiency.
• The adaptive lasso estimator demonstrates oracle properties for rare-events data.
• Numerical experiments confirm the performance of the developed methods on simulated and real-world data.

Conclusions:

• The novel scale-invariant subsampling approach provides a robust solution for analyzing massive datasets with rare events and inactive features.
• The methods enhance prediction accuracy and estimation efficiency in sparse modeling contexts.
• This work offers theoretical guarantees and practical validation for improved subsampling techniques.