This paper is motivated by major needs for fast and accurate on-line data analysis tools in the emerging electric energy systems, due to the recent penetration of distributed green energy, distributed intelligence, and plug-in electric vehicles. Instead of taking the traditional complex physical model based approach, this paper proposes a data-driven method, leading to an effective topology estimation approach for the smart grid. Specifically, we first introduce the data-driven topology estimation problem. Then, a novel Logistic Kernel Regression is proposed in a Bayesian framework based on Nearest Neighbors search. Notably, unlike many machine learning approaches that do not account for physical constraints, and distinctive from deterministic engineering modeling defined solely by physical laws, this paper for the first time combines the two into one single regression modeling for topology estimation. Simulation results of the proposed method show that the new method produces a topology estimate excelling the current industrial approach. Finally, the proposed method can be implemented given recent advances in machine learning, which are becoming drivers and sources of data previously unavailable in the electric power industry.