I am fairly new to machine learning, so I apologize if this is a bad and/or repeat question. It does seem like questions of this nature have been asked at least for linear relationships. Let's say that I have a collection of noisy data that roughly resembles some function. For clarity's sake, take this function to be sine, so that we have data that goes like
where $\epsilon(x)$ is some noise function that generates the noise in the data and $a,b$ are two parameters. Now suppose that we have no idea what a sine function is. That, or we know what it is, but we don't know the values of $a$ or $b$ that would allow us to train a neural network or BDT to fish out the sine function from all of the noise.
This is where my question comes in. Is there a way that I could use ML to still find a curve that models the data (and, if we are lucky, it happens to approximate sine from the noise correctly without knowing that it was a sine to start off with)?
Secondary question: If it happens to not be possible, is there a way to use ML to estimate $a$ and $b$ without resorting to conventional curve fitting techniques, such as least-squares? This is primarily a curiosity as to whether ML methods can be used to search the space of parameters for a given function (model) that best describes the data (perhaps more efficient, better at finding correlations in the data that would be typically accounted for via the use of a covariance matrix if one used something like least-squares, etc.).