I'm dealing with a dataset that has about 300 input features, and about 200 response variables and consists of 25000 samples. These response variables are basically a profile of 200 different values of the same response and these are 200 sequential geometrical points along the 1D line. You can visualize this as a line graph of 200 points for each observation. These points are the different regions/zones across a plate at which the response variable is being measured during manufacturing. The input features are different process conditions set in different processes during the manufacturing of this plate such as thickness, temperature, pressure etc.
There are two objectives:
To build a model/s that predicts the profile of the response variable. In other words, the model should predict the response at 200 different points across the plate.
Determine the important features (predictors) that affect the response variable. Ideally, this response variable should be uniform across the entire profile. So by tweaking the features, I should be able to control the response variable.
Now, predicting these 200 values is equivalent to building 200 models and I'm not sure how to draw inference from these 200 models. I tried doing a PCA on these 200 response variables to reduce them to a reasonable size but the variance is unstable and I'd require about 130 PC's to explain 90% of the variance. So PCA doesn't make sense. The points in a neighborhood seem to be closely correlated with each other. I'm not sure if you can call it spatial correlation because these points are along 1D line as opposed to 2D plane or 3D space. I'd greatly appreciate if someone can point me in the right direction in dealing with this problem.
The layout of the plate is about 7ft*5ft and some of the process parameters(input features) also are set and measured at different geometrical points across the plate like the target variable. After building the model and extracting significant predictors, I probably have to do some kind of optimization for finding the best combination of all input variables to achieve the uniformity of the target variable across all the measurements.