A short note on fitting a single-index model with massive data

Abstract

This paper studies the inference problem of index coefficient in single-index models under massive dataset. Analysis of massive dataset is challenging owing to formidable computational costs or memory requirements. A natural method is the averaging divide-and-conquer approach, which splits data into several blocks, obtains the estimators for each block and then aggregates the estimators via averaging. However, there is a restriction on the number of blocks. To overcome this limitation, this paper proposed a computationally efficient method, which only requires an initial estimator and then successively refines the estimator via multiple rounds of aggregations. The proposed estimator achieves the optimal convergence rate without any restriction on the number of blocks. We present both theoretical analysis and experiments to explore the property of the proposed method.

Keywords:

• Single-index model
• massive dataset
• divide-and-conquer method

Disclosure statement

We proposed a divide-and-conquer method to deal with single-index model for massive dataset. The proposed method significantly reduces the required amount of primary memory and enjoys a very low computational cost. The proposed method achieves the same asymptotic efficiency as the estimator using all the data. Furthermore, it allows a weak condition on the sample size as a function of memory size.

Additional information

Funding

We would like to acknowledge support for this project from the Fundamental Research Funds for the Central Universities of China (No. 2232020D-43).