In this talk, we consider semi-nonparametric inference for massive data that are either homogeneous or heterogeneous. In particular, we propose an aggregation type estimator that follows the “oracle rule” that it shares the same (non-asymptotic) minimax optimal rate and asymptotic distribution as the oracle estimator that is computed as if there were no heterogeneity. Some related problems such as efficiency boosting for heterogeneity estimation and heterogeneity testing will also be discussed. One technical by-product is the statistical inferences for the general kernel ridge regression.