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I am planning on using a machine learning algorithm to learn the mapping between sets of four coordinates (x,y,z + a distance d from a reference point) to two numbers (an amplitude A and a time t). In other words, a machine learning algorithm should learn, for each sample i, the mapping

(x[i], y[i], z[i], d[i]) --> (A[i], t[i])

The coordinates x,y,z are integer numbers (because they are actually grid points on a fixed grid). The distance d is a decimal number instead.

The amplitude A is also a decimal number, while t is integer (because again, it represents a shift on a time grid).

What would be the best machine learning technique to use in this case? I thought of Gaussian process, maybe a neural network (if so, which type?)

If that matters, the sizes of my trianing and testing samples are 1500 and 500, respectively.

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Since it's a regression problem I would suggest starting out with a multi output regressor (https://scikit-learn.org/stable/modules/generated/sklearn.multioutput.MultiOutputRegressor.html) to predict multiple target variables. A good first step before doing that would be to visualize your features ie. the coordinates and distance alongside the target variables to see the relationship between the predictors and target variables. That would help you understand what kind of a function would fit best to the problem.

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