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I have a dataset of 5-dimensional real-valued vector X^j={x_i: i=1,2,3,4,5} and their corresponding y^j where y^j is a real-valued number and j is the no of samples.

Suppose the X^j vectors are various audio feature vectors and the y^j are corresponding user ratings. Now there will be some (non)linear relationship between X^j and y^j where y^j will denote some degree of importance(quality) of the corresponding vector X^j. Then, I want to derive a X^j vector wherein the user rating values or y^j (quality) is maximized (the most likely to be maximized following the relationship distribution between X^j and y^j).

If I take a weighted average of X^j then the result will be converging towards the mean but how can I make it to converge towards the maximum using some sophisticated statistical technique?

Any hint/help is highly appreciated.

Thanks.

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# Inferring a vector wrt a maximization objective!

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