One-class learning or classification has many applications. For example, in information retrieval, one has a set of documents of interest and wants to identify more such documents [55].

The strong correlation between neurons or filters can significantly weaken the generalization ability of neural networks.

Thefollowing lemma provides moment bounds for a summation of weakly dependent and mean-zero random functions withbounded increments underachange ofanysinglecoordinate [1,10]. The stated bound then follows by combining the above two inequalities together. Note A(S0) is independent ofS and can be considered as a fixed model if we only consider the randomness induced fromS. In this section, we present the proof related to stability and generalization for pairwise learning with convex and smooth loss functions. For anyi [n], define Si as (3.3).

Representative problems include AUC maximization [14, 25, 42, 63, 66], metric learning [8, 31], ranking [1, 13] and learning with minimum error entropy loss functions [29]. For example, in supervised metric learning we wish to find a distance function between pairs of examples so that examples within the same class are relatively close while examples from different classes are far apartfromeachother.

InInternational Journalof Parallel, Emergentand Distributed Systems, volume 27, pages 387-408, 2012.