Please help me find an approach to solving the following problem: Let X is a matrix X_mxn = (x1,…,xn), xi is a time series and a vector Y_mx1. To predict values from Y_mx1, let's train some model, let linear regression. We get Y = f (X). Now we need to find X for some given value of Y. The most naive thing is brute force, but what are the competent ways to solve such problems? Perhaps there is a use of the scipy.optimize package here, please enlighten me.
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Most scipy-optimize algorithm use gradient method, for those optimization problem, we could apply these into re-engineering of data (find the best date to invest in the stock market...)
If you want to optimize the result, you should choose a good step size and suitable optimize method.
However, we should not classify tge problem as "predict" of xi because what we are doing is to find local/global maximum/minimum. For example Newton-CG, your data/equation should contain all the information needed/a simulation, but no prediction is made from the method.
If you want to do a pretiction on "time", you could categorize the time data in "year,month..." then using unsupervise learning to "group" the data. If trend is obtained, then we can re-enginning the result to know the time
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