predict parameters of linear function

My questions seems very trivial, but I can't quite grasp it. I am also aware this post asks for opinions and knowhow, but do not know were else to ask. I do have quite a lot of experience solving even somewhat difficult machine learning problems, but never faced a situation were the target is still a parameter in an other function.

I have a function like:

t = ax + by + cz + bias.

And a database with t, x, y, z, m, n, o, p, etc. I expect the optimal a, b, c etc. to be functions of x, y, z, m, n, o, p. But since I do not know a,b,c, etc and only label/target t instead most machine learning methods from SKlearn do not work out of the box.

I though about first running a linear regression to find a, b, c, etc, that that loses all the information differentiating different datapoints. I guess a self coded SGD would be able to solve my issue, but do not know were to start. I also thought about just dropping my final function completly, but I want to conserve some of the information stored within the function.

For example I do know, that a is dependant on different parameters than b and can give a list to each. My thought is that I reduce possible overfitting by giving as many constraints as possible, espacially since my dataset is not that big.

Topic parameter-estimation

Category Data Science


It might be helpful to map your problem onto conventional linear regression:

$$ y = β_0 + B_1x_1 + B_2+x_2 + ε $$

In your case:

  • $t$ would the numeric target values from the dataset.
  • $a, b, c$ are the the coefficients/weights to estimate.
  • $x, y, z$ are the features values from the dataset.
  • $bias$ is the intercept term $B_0$ to estimate.

Once the dataset is properly formatted, scikit-learn's linear regression can be used to estimate the coefficients.

You are correct that estimating a model "loses all the information differentiating different datapoints". A model is a useful simplification of the data.

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