Suppose I have two time series, $x(t)$ and $y(t)$: $x$ is the output of a sine wave generator, and $y$ is the generator's frequency setting. Given a training set of $(x, y)$ pairs, Is it possible to formulate a convex/quasi-convex optimization problem to build a predictor of some new $y$ given $x$?
The system is certainly non-linear, since you can double the signal amplitude without changing the output (the frequency). It seems like you need to perform an
argmax in the frequency domain, which I believe is a quasi-convex operation. This limits what functions you can compose, so something like computing residuals may no longer be convex. My hunch though is there may be a clever recasting of the problem, or a duality argument, etc.
I'm sure neural nets are capable of it, but for sake of discussion assume I don't have the data/processing power.