Reconciled Polynomial Machine: A Unified Representation of Shallow and Deep Learning Models

In this paper, we aim at introducing a new machine learning model, namely reconciled polynomial machine, which can provide a unified representation of existing shallow and deep machine learning models. Reconciled polynomial machine predicts the output by computing the inner product of the feature kernel function and variable reconciling function. Analysis of several concrete models, including Linear Models, FM, MVM, Perceptron, MLP and Deep Neural Networks, will be provided in this paper, which can all be reduced to the reconciled polynomial machine representations. Detailed analysis of the learning error by these models will also be illustrated in this paper based on their reduced representations from the function approximation perspective.