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There are 3 columns used to train to model, A,B and C. A is the predicted value by a model, B is the target value in the dataset, C is the pre knowledge.

C is the evaluated value to B, the absolute difference is closer to 0, the better, illustrated by column D. the negative and positive sign in column C denote the direction, negative means less than, positive mean greater than.

For instance, ideally the model should predict first row as 10.3, 2nd row as less than 15.1, how much smaller? nobody knows; 3rd row as greater than 11.3.

      A     B     C     D
0  16.0  10.3  0.00  0.00
1  11.6  15.1 -0.08  0.08
2  12.2  11.3  0.31  0.31
3  18.8  14.7 -0.61  0.61
4  18.1  15.2  0.64  0.64
5  10.3  11.3 -0.72  0.72
6  17.2  12.2 -0.75  0.75
7  16.2  10.9 -0.84  0.84
8  12.6  16.3  0.85  0.85
9  11.6  10.8  0.93  0.93

The question is:

How to bring the pre knowledge C into the training?


The following is just a supplement to the question, not part of the question.

Actually, it not "nobody knows".

There is another measurement for the difference between A and B on C, column E. Assume $A_1 = 6.0, B_1 = 6.5, A_2 = 5.5, B_2 = 6.0, E_2>E_1$, then

$|C_1|>|C_2|>0$

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