Finding a vector that minimize the MSE of its linear combination I have been doing a COVID-19 related project. Here is the question:


N = vector of daily new infected cases
D = vector of daily deaths
E[D] = estimation of daily deaths


N is a n-dimensional vector, n is around 60. E[D] is another n-dimensional vector. Under certain assumptions, each entry of E[D] can be calculated as a linear combination of the entries of N.

We want to find the vector N such that the E[D] derived from N has least mean squared error when compared to actual D data. I think a gradient descent algorithm is needed here. However, I am not very familiar with gradient descent.

This seems to be a basic data science problem, but I am kind of lost right now. Does anyone has any idea about which algorithm should I dig into?
If inputs are the same and you expect multiple outputs, I would recommend you to look at multioutput models which can be of two types :


native multioutput algorithms
multiple single output regressors wrapped together. Sklearn’s multioutput does that.