  In this work, we introduce a novel approach to regularization in
multivariable regression problems. Our regularizer, called DLoss, penalises
differences between the model's derivatives and derivatives of the data
generating function as estimated from the training data. We call these
estimated derivatives data derivatives. The goal of our method is to align the
model to the data, not only in terms of target values but also in terms of the
derivatives involved. To estimate data derivatives, we select (from the
training data) 2-tuples of input-value pairs, using either nearest neighbour or
random, selection. On synthetic and real datasets, we evaluate the
effectiveness of adding DLoss, with different weights, to the standard mean
squared error loss. The experimental results show that with DLoss (using
nearest neighbour selection) we obtain, on average, the best rank with respect
to MSE on validation data sets, compared to no regularization, L2
regularization, and Dropout.
