  Tasking machine learning to predict segments of a time series requires
estimating the parameters of a ML model with input/output pairs from the time
series. Using the equivalence between statistical data assimilation and
supervised machine learning, we revisit this task. The training method for the
machine utilizes a precision annealing approach to identifying the global
minimum of the action (-log[P]). In this way we are able to identify the number
of training pairs required to produce good generalizations (predictions) for
the time series. We proceed from a scalar time series $s(t_n); t_n = t_0 + n
\Delta t$ and using methods of nonlinear time series analysis show how to
produce a $D_E > 1$ dimensional time delay embedding space in which the time
series has no false neighbors as does the observed $s(t_n)$ time series. In
that $D_E$-dimensional space we explore the use of feed forward multi-layer
perceptrons as network models operating on $D_E$-dimensional input and
producing $D_E$-dimensional outputs.
