Aspects of discrete mathematics and probability in the theory of machine learning
This paper concerns developments in the use of probabilistic and combinatorial techniques in the analysis of machine learning. Initially, probabilistic models of learning addressed binary classification (or pattern classification). More recently, analysis has been extended to regression problems, and to classification problems in which the classification is achieved by using real-valued functions (where the concept of a large margin has proven useful). Another development, important in obtaining more applicable models, has been the derivation of data-dependent bounds. Here, we discuss some of the main probabilistic and combinatorial techniques and results.