  Time series data have grown at an explosive rate in numerous domains and have
stimulated a surge of time series modeling research. A comprehensive comparison
of different time series models, for a considered data analytics task, provides
useful guidance on model selection for data analytics practitioners. Data
scarcity is a universal issue that occurs in a vast range of data analytics
problems, due to the high costs associated with collecting, generating, and
labeling data as well as some data quality issues such as missing data. In this
paper, we focus on the temporal classification/regression problem that attempts
to build a mathematical mapping from multivariate time series inputs to a
discrete class label or a real-valued response variable. For this specific
problem, we identify two types of scarce data: scarce data with small samples
and scarce data with sparsely and irregularly observed time series covariates.
Observing that all existing works are incapable of utilizing the sparse time
series inputs for proper modeling building, we propose a model called sparse
functional multilayer perceptron (SFMLP) for handling the sparsity in the time
series covariates. The effectiveness of the proposed SFMLP under each of the
two types of data scarcity, in comparison with the conventional deep sequential
learning models (e.g., Recurrent Neural Network, and Long Short-Term Memory),
is investigated through mathematical arguments and numerical experiments.
