Communication-Efficient Accurate Statistical Estimation

Area of Science:

• Distributed Systems
• Statistical Inference
• Optimization Algorithms

Background:

• Traditional statistical inference faces challenges in distributed data settings due to communication costs and privacy concerns.
• Existing methods may not be suitable for large-scale distributed datasets requiring efficient processing.

Purpose of the Study:

• To develop and investigate novel Communication-Efficient Accurate Statistical Estimators (CEASE) for distributed data analysis.
• To address the limitations of traditional methods in distributed environments by proposing iterative algorithms for optimization.

Main Methods:

• Implementation of CEASE through iterative algorithms for distributed optimization.
• Node machines perform parallel computations and communicate with a central processor for aggregated updates.
• Algorithms adapt to loss function similarity and benefit from large local sample sizes.

Main Results:

• CEASE algorithms demonstrate rapid convergence and linear convergence guarantees under general conditions.
• The contraction rate of optimization errors is explicitly presented, showing dependence on local sample size.
• Improved statistical accuracy per iteration is achieved, with statistical efficiency attainable in finite steps.

Conclusions:

• CEASE algorithms provide a communication-efficient and statistically accurate approach for distributed data inference.
• The proposed methods overcome traditional limitations and offer superior performance validated by numerical experiments.
• Conditions for the statistical efficiency of one-step CEASE estimators are identified.