  In this paper, we analyze the impact of information freshness on supervised
learning based forecasting. In these applications, a neural network is trained
to predict a time-varying target (e.g., solar power), based on multiple
correlated features (e.g., temperature, humidity, and cloud coverage). The
features are collected from different data sources and are subject to
heterogeneous and time-varying ages. By using an information-theoretic
approach, we prove that the minimum training loss is a function of the ages of
the features, where the function is not always monotonic. However, if the
empirical distribution of the training data is close to the distribution of a
Markov chain, then the training loss is approximately a non-decreasing age
function. Both the training loss and testing loss depict similar growth
patterns as the age increases. An experiment on solar power prediction is
conducted to validate our theory. Our theoretical and experimental results
suggest that it is beneficial to (i) combine the training data with different
age values into a large training dataset and jointly train the forecasting
decisions for these age values, and (ii) feed the age value as a part of the
input feature to the neural network.
