Statistical Learning in Multiple Instance Problems

TL;DR: This thesis categorizes current MI methods into a new framework, and proposes a new assumption for MI learning, called the “collective assumption”, which states that “An example is positive if at least one of its instances is positive and negative otherwise”.

Abstract: Multiple instance (MI) learning is a relatively new topic in machine learning. It is concerned with supervised learning but differs from normal supervised learning in two points: (1) it has multiple instances in an example (and there is only one instance in an example in standard supervised learning), and (2) only one class label is observable for all the instances in an example (whereas each instance has its own class label in normal supervised learning). In MI learning there is a common assumption regarding the relationship between the class label of an example and the “unobservable” class labels of the instances inside it. This assumption, which is called the “MI assumption” in this thesis, states that “An example is positive if at least one of its instances is positive and negative otherwise”. In this thesis, we first categorize current MI methods into a new framework. According to our analysis, there are two main categories of MI methods, instancebased and metadata-based approaches. Then we propose a new assumption for MI learning, called the “collective assumption”. Although this assumption has been used in some previous MI methods, it has never been explicitly stated,1 and this is the first time that it is formally specified. Using this new assumption we develop new algorithms — more specifically two instance-based and one metadata-based methods. All of these methods build probabilistic models and thus implement statistical learning algorithms. The exact generative models underlying these methods are explicitly stated and illustrated so that one may clearly understand the situations 1As a matter of fact, for some of these methods, it is actually claimed that they use the standard MI assumption stated above.