  In this paper, we analyze the impact of data freshness on real-time
supervised learning, where a neural network is trained to infer a time-varying
target (e.g., the position of the vehicle in front) based on features (e.g.,
video frames) observed at a sensing node (e.g., camera or lidar). One might
expect that the performance of real-time supervised learning degrades
monotonically as the feature becomes stale. Using an information-theoretic
analysis, we show that this is true if the feature and target data sequence can
be closely approximated as a Markov chain; it is not true if the data sequence
is far from Markovian. Hence, the prediction error of real-time supervised
learning is a function of the Age of Information (AoI), where the function
could be non-monotonic. Several experiments are conducted to illustrate the
monotonic and non-monotonic behaviors of the prediction error. To minimize the
inference error in real-time, we propose a new "selection-from-buffer" model
for sending the features, which is more general than the "generate-at-will"
model used in earlier studies. By using Gittins and Whittle indices,
low-complexity scheduling strategies are developed to minimize the inference
error, where a new connection between the Gittins index theory and Age of
Information (AoI) minimization is discovered. These scheduling results hold (i)
for minimizing general AoI functions (monotonic or non-monotonic) and (ii) for
general feature transmission time distributions. Data-driven evaluations are
presented to illustrate the benefits of the proposed scheduling algorithms.
