Initialization Transfer for Nonconvex Statistical Estimation

Nonconvex estimation can give different solutions from different starting values. With limited target data, an estimate from a related source population can provide a useful start. Population differences can make this start inaccurate and can bias a fit that pools both datasets. In this article, we study initialization transfer, which uses the source estimate only to start fitting with target data. We show how source accuracy and population differences determine entry into a region where target fitting converges. For a fixed number of parameters, reliable entry and enough updates give the same large-sample uncertainty as the target-only local solution. In noiseless sparse signal recovery, a sufficiently close source estimate permits recovery from a target sample nearly linear in the number of nonzero coefficients. For noisy recovery from squared Gaussian measurements in fixed dimension, pooling can lose target coverage even when its source fraction tends to zero. Checking the completed fit and restarting when needed preserves nominal large-sample coverage without source accuracy conditions. Simulations and a handwritten-digit analysis show improved target fitting when target data or iterations are limited, and smaller errors than pooling at larger population differences.