Grace Tompkins, Tatiana Krikella, Swaleh Hussain
One of the fundamental challenges in machine learning in data science is dealing with missing and incomplete data. This paper proposes theoretically justified methodology for using incomplete data in neural networks, eliminating the need for direct completion of the data by imputation or other commonly used methods in existing literature. The authors propose identifying missing data points with a parametric density and then training it together with the rest of the network's parameters. The neuron's response at the first hidden layer is generalized by taking its expected value to process this probabilistic representation. This process is essentially calculating the average activation of the neuron over imputations drawn from the missing data's density. The proposed approach is advantageous as it has the ability to train neural networks using incomplete observations from datasets, which are ubiquitous in practice. This approach also requires minimal adjustments and modifications to existing architectures. Theoretical results of this study show that this process does not lead to a loss of information, while experimental results showed the practical uses of this methodology on several different types of networks.