The development of robust classification model is among the important issues in computer vision. This paper deals with weakly supervised learning that generalizes the supervised and semi-supervised learning. In weakly supervised learning training data are given as the priors of each class for each sample. We first propose a weakly supervised strategy for learning soft decision trees. Besides, the introduction of class priors for training samples instead of hard class labels makes natural the formulation of an iterative learning procedure. We report experiments for UCI object recognition datasets. These experiments show that recognition performance close to the supervised learning can be expected using the propose framework. Besides, an application to semi-supervised learning, which can be regarded as a particular case of weakly supervised learning, further demonstrates the pertinence of the contribution. We further discuss the relevance of weakly supervised learning for computer vision applications.