A latent factor (LF) model can implement efficient analysis for a high-dimensional and sparse (HiDS) matrix from recommender systems (RSs). However, an LF model's representation learning ability to a targeted HiDS matrix is heavily proportional to its known data density. Unfortunately, an HiDS matrix's known data are limited due to users' activity limitations in RSs. Motivated by this observation, this paper proposes a Prediction-sampling-based Multilayer-structured Latent Factor (PMLF) model. Following the principle of Deep Forest [1], PMLF implements a loosely-connected multilayered LF structure, where each layer generates synthetic ratings to enrich the input for the next layer. Such an injection process is carefully monitored through a random sampling process and nonlinear activations to avoid overfitting. Thus, PMLF's representation learning ability to an HiDS matrix is significantly enhanced owing to the carefully injected estimates and its generalized multilayer-structure. Experimental results on four HiDS matrices from industrial RSs indicate that compared with six state-of-the-art LF-based and deep neural networks-based models, PMLF well balances the prediction accuracy and computational efficiency, making it satisfy demands of fast and accurate industrial applications.