Identifying the best n points from a dataset The problem I am trying solve involves identifying the best n data points from a dataset. For example if I have dataset with x1,x2,x3 independent variables and y1,y2 dependent variables I want to find the best data points (not variables) that could predict y1, y2 (multi-output) or any interaction effect etc. The reason why I am looking for technique to identify the best n (lets say 50) data points among m data points (i.e 600 - the entire dataset) is due to experimentation cost. As performing more experiments is costly, it is ideal to perform experiments close to the data points which show some relevance to predicting the dependent variables. Is there any techniques to achieve such a tasks?
I was looking at factor analysis in design of experiments but not too sure if this could do this.
Thanks
 A: I think this paper might help: https://proceedings.neurips.cc/paper/2020/hash/373e4c5d8edfa8b74fd4b6791d0cf6dc-Abstract.html
Edit:
The paper names "Model Inversion Networks for Model-Based Optimization" on Nips2020
A: Since you are predicting $y$ values from $x$ values, you are doing a regression problem.  In order to find which $x$ values give the best predictions, you should look at the width of the prediction intervals formed using those values.  If you look at the form of the prediction interval for a simple linear regression you will see that it is more accurate (i.e., shorter) for values of $x$ that are closer to the sample mean $\bar{x}$ that was used the fit the regression.  (Graphically, the width of the interval bows outward as we go further from the mean of the explanatory variables.)
Thus, the "best" predictor in the dataset is the one where the $x$ value is closest to the sample mean, the "second best" is the one where the $x$ value is second-closest to the sample mean and so on.
