# How could I go about finding the weights or importance of inputs based on outputs?

I have a table who's inputs (sfm, fr, and doc) all affect the outputs (mmr and ra). How could I go about finding the input importance on the outputs? Basically, I'd like to be able to have a goal output in mmr and ra and have a good idea of starting parameters for sfm, fr, and doc. Does anyone have insight into something like this? Below is a sample of the data.

sfm    fr    doc    mmr      ra

60     0.15  0.1    449.6    1.85
60     0.15  0.2    896.78   0.86
60     0.15  0.25   1116.34  1.28
60     0.2   0.1    593.46   1.42
60     0.2   0.2    1183.62  0.91
60     0.2   0.25   1473.34  1.91
60     0.25  0.1    734.26   1.59
60     0.25  0.2    1464.41  1.52
60     0.25  0.25   1822.79  1.07
70     0.15  0.1    503.3    1.42
70     0.15  0.2    1003.74  0.89
70     0.15  0.25   750.31   0.99
70     0.2   0.1    665.35   1.12
70     0.2   0.2    1326.9   1.96
70     0.2   0.25   1651.5   1.73
70     0.25  0.1    822.97   0.99
70     0.25  0.2    1641.19  1.17
70     0.25  0.25   2042.57  0.85

• I think you want a [reverse] prediction from x:(mmr, ra) to y:(sfm, fr, doc)? you what a y for a given x? – Esmailian Mar 15 '19 at 20:59
• Yes, exactly! I'll collect data points in the real world as the basis, but I can't test every possible outcome, so I'd like to know how I can figure out the "ideal" inputs from target outputs based on this collected data – 55thSwiss Mar 15 '19 at 22:37
• This can be done we a standard neural network that has 2 dimensional input for (mmr, a) and 3 dimensional output for (sfm, fr, doc), done! After model is trained, you input an arbitrary (mmr, a) and it gives (sfm, fr, doc). If it works let me know to put it into an answer – Esmailian Mar 15 '19 at 22:43
• Yes, I've been fooling around with that a little, unfortunately it's not yielding great results (and by not great I mean not even in the ballpark). Would you have any suggestion as to the type of neural net? CNN, RNN, LSTM, etc? Or attributes? – 55thSwiss Mar 15 '19 at 23:57
• Did you calculate the correlation between each of the input columns and the outputs? – Alireza Zolanvari Mar 16 '19 at 13:06

Pearson correlation can be used for this purpose. The Pearson correlation between two entity shows that how mush the values of these two are linearly related to each other.

According to the Cauchy–Schwarz inequality it has a value between +1 and −1, where 1 is total positive linear correlation, 0 is no linear correlation, and −1 is total negative linear correlation.

According to the values you reported here, there is a strong correlation between doc and mrr so the role of doc in the prediction of mrr is more important than others.

But on the other hand none of the features doesn't have any considerable linear correlation with ra. In this case you can test some other correlation methods.

For further information visit here. It can be helpful to you.

Conclusion: the most important feature in predicting an output is the most correlated one with it which has a considerable correlation.

• I'll mark this as an accepted answer because you're trying to help. I really haven't gotten much further though. I do understand what you're saying of course, but without a practical example it is still grey. Thank you tho for trying – 55thSwiss Mar 18 '19 at 19:36