In multi-instance (MI) learning, each object (bag) consists of multiple feature vectors (instances), and is most commonly regarded as a set of points in a multidimensional space. A different viewpoint is that the instances are realisations of random vectors with corresponding probability distribution, and that a bag is the distribution, not the realisations. In MI classification, each bag in the training set has a class label, but the instances are unlabelled. By introducing the probability distribution space to bag-level classification problems, dissimilarities between probability distributions (divergences) can be applied. The bag-to-bag Kullback-Leibler information is asymptotically the best classifier, but the typical sparseness of MI training sets is an obstacle. We introduce bag-to-class divergence to MI learning, emphasising the hierarchical nature of the random vectors that makes bags from the same class different. We propose two properties for bag-to-class divergences, and an additional property for sparse training sets.
The feature vector set viewpoint seems to be the most common, but the probabilistic viewpoint was introduces already in 1998, then under the i.i.d. given class assumption @cite_11 . This assumption has been used in approaches such as estimating the expectation by the mean @cite_38 , or estimation of class distribution parameters @cite_29 , but has also been criticised @cite_2 . The hierarchical distribution was introduced for learnability theory under the standard MI assumption for instance classification @cite_22 , and we expand the use for more general assumptions.
@cite_38 @cite_22 @cite_29 @cite_2 @cite_11
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In this paper we upgrade linear logistic regression and boosting to multi-instance data, where each example consists of a labeled bag of instances. This is done by connecting predictions for individual instances to a bag-level probability estimate by simple averaging and maximizing the likelihood at the bag level—in other words, by assuming that all instances contribute equally and independently to a bag’s label. We present empirical results for artificial data generated according to the underlying generative model that we assume, and also show that the two algorithms produce competitive results on the Musk benchmark datasets. We propose a new theoretical framework for analyzing the multiple-instance learning (MIL) setting. In MIL, training examples are provided to a learning algorithm in the form of labeled sets, or "bags," of instances. Applications of MIL include 3-D quantitative structure-activity relationship prediction for drug discovery and content-based image retrieval for web search. The goal of an algorithm is to learn a function that correctly labels new bags or a function that correctly labels new instances. We propose that bags should be treated as latent distributions from which samples are observed. We show that it is possible to learn accurate instance - and bag-labeling functions in this setting as well as functions that correctly rank bags or instances under weak assumptions. Additionally, our theoretical results suggest that it is possible to learn to rank efficiently using traditional, well-studied "supervised" learning approaches. We perform an extensive empirical evaluation that supports the theoretical predictions entailed by the new framework. The proposed theoretical framework leads to a better understanding of the relationship between the MI and standard supervised learning settings, and it provides new methods for learning from MI data that are more accurate, more efficient, and have better understood theoretical properties than existing MI-specific algorithms. Previous studies on multi-instance learning typically treated instances in the bags as independently and identically distributed. The instances in a bag, however, are rarely independent in real tasks, and a better performance can be expected if the instances are treated in an non-i.i.d. way that exploits relations among instances. In this paper, we propose two simple yet effective methods. In the first method, we explicitly map every bag to an undirected graph and design a graph kernel for distinguishing the positive and negative bags. In the second method, we implicitly construct graphs by deriving affinity matrices and propose an efficient graph kernel considering the clique information. The effectiveness of the proposed methods are validated by experiments. Multiple-instance learning is a variation on supervised learning, where the task is to learn a concept given positive and negative bags of instances. Each bag may contain many instances, but a bag is labeled positive even if only one of the instances in it falls within the concept. A bag is labeled negative only if all the instances in it are negative. We describe a new general framework, called Diverse Density, for solving multiple-instance learning problems. We apply this framework to learn a simple description of a person from a series of images (bags) containing that person, to a stock selection problem, and to the drug activity prediction problem.