Machine learning algorithms take a training set, form hypotheses or models, and make predictions about the future. Because the training set is finite and the future is uncertain, learning theory usually does not yield absolute guarantees of performance of the algorithms. Instead, probabilistic bounds on the performance of machine learning algorithms are quite common.
There are several difference branches of learning theory, which are often mathematically incompatible. This incompatibility arises from using different inference principles: principles which tell you how to generalize from limited data.
Examples of different branches of learning theory include: