Unstructured point clouds of varying sizes are increasingly acquired in a variety of environments through laser triangulation or Light Detection and Ranging (LiDAR). Predicting a vector response based on unstructured point clouds is a common problem that arises in a wide variety of applications. The current literature relies on several pre-processing steps such as structured subsampling and feature extraction to analyze the point cloud data. Those techniques lead to quantization artifacts and do not consider the relationship between the regression response and the point cloud during pre-processing. Therefore, we propose a general and holistic ``Bayesian Nonlinear Tensor Learning and Modeler’’ (ANTLER) to model the relationship of unstructured, varying-size point cloud data with a vector response. The proposed ANTLER simultaneously optimizes a nonlinear tensor dimensionality reduction and a nonlinear regression model with a 3D point cloud input and a regression response. ANTLER can consider the complex data representation, high-dimensionality, and inconsistent size of the 3D point cloud data. Note to Practitioners— This paper is motivated by a real-world case study concerning the prediction of the transmission error and eccentricity based on unstructured point clouds of varying sizes in gear manufacturing. In the current state-of-the-art method, those characteristics can only be obtained via expensive and time-consuming Finite Element Analysis (FEA) or test benches. The proposed ANTLER framework can directly link the measurement point clouds with a vector response and serves as a guiding example for the immense potential of the ANTLER.