It is vital to infer signed distance functions (SDFs) from 3D point clouds. The latest methods rely on generalizing the priors learned from large scale supervision. However, the learned priors do not generalize well to various geometric variations that are unseen during training, especially for extremely sparse point clouds. To resolve this issue, we present a neural network to directly infer SDFs from single sparse point clouds without using signed distance supervision, learned priors or even normals. Our insight here is to learn surface parameterization and SDFs inference in an end-to-end manner. To make up the sparsity, we leverage parameterized surfaces as a coarse surface sampler to provide many coarse surface estimations in training iterations, according to which we mine supervision and our thin plate splines (TPS) based network infers SDFs as smooth functions in a statistical way. Our method significantly improves the generalization ability and accuracy in unseen point clouds. Our experimental results show our advantages over the state-of-the-art methods in surface reconstruction for sparse point clouds under synthetic datasets and real scans.The code is available at https://github.com/chenchao15/NeuralTPS.