Multiple instance learning with generalized support vector machines

In pattern classification it is usually assumed that a training set of labeled patterns is available. Multiple-Instance Learning (MIL) generalizes this problem setting by making weaker assumptions about the labeling information. While each pattern is still believed to possess a true label, training labels are associated with sets or bags of patterns rather than individual patterns. More formally, given is a set of patterns x1,. . . , xn grouped into bags X1,. . . , Xm, with Xj = xi: i ∈ Ij and Ij ⊆ 1,. . . , n. With each bag Xj is associated a label Yj ∈ −1, 1. These labels are interpreted in the following way: if a bag has a negative label Yj = −1, all patterns in that bag inherit the negative label. If on the other hand, Yj = 1, then at least one pattern xi ∈ Xj is a positive example of the underlying concept. The MIL scenario has many interesting applications: One prominent application is the classification of molecules in the context of drug design (Dietterich, Lathrop, Auer 1997; Long Zhang & Goldman 2002) ) have focused on specially tailored machine learning algorithms that do not compare favorably in the limiting case of bags of size 1 (the standard classification setting). A notable exception is (Ramon & Raedt 2000).