Uncertainty of the input data is a common issue in machine learning. In this paper we show how one can incorporate knowledge on uncertainty measure regarding particular points in the training set. This may boost up models accuracy as well as reduce overfitting. We show an approach based on the classical training with jitter for Artificial Neural Networks (ANNs). We prove that our method, which can be applied to a wide class of models, is approximately equivalent to generalised Tikhonov regularisation learning. We also compare our results with some alternative methods. In the end we discuss further prospects and applications.