Composite Neural Network Theory and Application to PM2 5 Prediction

This work investigates the framework and statistical performance guarantee of the composite neural network, which is composed of a collection of pre-trained and non-instantiated neural network models connected as a rooted directed acyclic graph, for solving complicated applications. A pre-trained neural network model is generally well trained, targeted to approximate a specific function. The advantages of adopting a pre-trained model as a component in composing a complicated neural network are two-fold. One is benefiting from the intelligence and diligence of domain experts, and the other is saving effort in data acquisition as well as computing resources and time for model training. Despite a general belief that a composite neural network may perform better than any a single component, the overall performance characteristics are not clear. In this work, we propose the framework of a composite network, and prove that a composite neural network performs better than any of its pre-trained components with a high probability. In the study, we explore a complicated application—PM2.5 prediction—to support the correctness of the proposed composite network theory. In the empirical evaluations of PM2.5 prediction, the constructed composite neural network models perform better than other machine learning models.