Densely Connected Neural Networks for Nonlinear Regression

Densely connected convolutional networks (DenseNet) behave well in image processing. However, for regression tasks, convolutional DenseNet may lose essential information from independent input features. To tackle this issue, we propose a novel DenseNet regression model where convolution and pooling layers are replaced by fully connected layers and the original concatenation shortcuts are maintained to reuse the feature. To investigate the effects of depth and input dimensions of the proposed model, careful validations are performed by extensive numerical simulation. The results give an optimal depth (19) and recommend a limited input dimension (under 200). Furthermore, compared with the baseline models, including support vector regression, decision tree regression, and residual regression, our proposed model with the optimal depth performs best. Ultimately, DenseNet regression is applied to predict relative humidity, and the outcome shows a high correlation with observations, which indicates that our model could advance environmental data science.