On the optimal generalization error for weighted least squares under variable individual supervision times

In this short paper, the trade-off between the number of labeled examples in linear regression and their precision of supervision is investigated and optimized, for the case in which distinct examples can be associated with one among M > 2 different supervision times, and weighted least squares is used for learning. The analysis extends the one made in one section of Gnecco and Nutarelli, Optimization Letters, 2019, https://doi.org/10.1007/s11590-019-01486-x , which was limited to the case M = 2. The results show that, for the specific learning problem, there is no advantage in applying weighted least squares instead of ordinary least squares as the learning algorithm.