In the task of distribution-to-distribution regression, a recently proposed model, distribution regression network (DRN) (Kou et al., 2018) has shown superior performance compared to conventional neural networks while using much fewer parameters. The key novelty of DRN is that it encodes an entire distribution in each network node, and this compact representation allows DRN to achieve better accuracies than conventional neural networks. However, the experiments in Kou et al. (2018) focused mainly on non-time series data and there is no systematic study on how DRN performs with limited annotated data. The ability to train well with limited training data is an important feature in the current supervised training paradigm. In this paper, we evaluate DRN for the new task of performing forward prediction on time sequences of probability distributions. We also perform extensive studies on how the test performance varies with the size of training data since for time series, the number of data may be limited given the seasonality of the data. In our experiments, we show that DRN requires two to five times fewer training data than neural networks to achieve similar prediction accuracies. However, DRN is a feedforward network and does not explicitly model time dependencies. Hence we propose a new recurrent architecture for DRN, named recurrent distribution regression network (RDRN). In our experiments involving prediction on sequences of distributions, RDRN and DRN outperform neural network models, with RDRN achieving similar or better accuracies than DRN.
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