A Review of Multi-Instance Learning Assumptions <s> Multi-Instance Regression <s> As opposed to traditional supervised learning, multiple-instance learning concerns the problem of classifying a bag of instances, given bags that are labeled by a teacher as being overall positive or negative. Current research mainly concentrates on adapting traditional concept learning to solve this problem. In this paper we investigate the use of lazy learning and Hausdorff distance to approach the multiple-instance problem. We present two variants of the K-nearest neighbor algorithm, called Bayesian-KNN and Citation-KNN, solving the multiple-instance problem. Experiments on the Drug discovery benchmark data show that both algorithms are competitive with the best ones conceived in the concept learning framework. Further work includes exploring of a combination of lazy and eager multiple-instance problem classifiers. <s> BIB001 </s> A Review of Multi-Instance Learning Assumptions <s> Multi-Instance Regression <s> We present a Multiple-Instance Learning (MIL) algorithm for determining the salience of each item in each bag with respect to the bag’s real-valued label. We use an alternating-projections constrained optimization approach to simultaneously learn a regression model and estimate all salience values. We evaluate this algorithm on a significant real-world problem, crop yield modeling, and demonstrate that it provides more extensive, intuitive, and stable salience models than Primary-Instance Regression, which selects a single relevant item from each bag. <s> BIB002 </s> A Review of Multi-Instance Learning Assumptions <s> Multi-Instance Regression <s> The multiple-instance learning model has received much attention recently with a primary application area being that of drug activity prediction. Most prior work on multiple-instance learning has been for concept learning, yet for drug activity prediction, the label is a real-valued affinity measurement giving the binding strength. We present extensions of k-nearest neighbors (k-NN), Citation-kNN, and the diverse density algorithm for the real-valued setting and study their performance on Boolean and real-valued data. We also provide a method for generating chemically realistic artificial data. <s> BIB003 </s> A Review of Multi-Instance Learning Assumptions <s> Multi-Instance Regression <s> Refining agents comprising intimate mixtures of finely-divided sulfates and reducing agents are added to vitrifiable charges of glassmaking raw materials prior to melting the raw materials so that, when the charge is melted, the refining agent will evolve bubbles of sulfur dioxide gas which will remove smaller bubbles of other gases from the molten glass as these bubbles rise to the surface of the molten glass. The metal sulfates and reducing agents (preferably carbon) employed in the refining agent have a particle size of less than about 0.1 mm and are formed into homogeneous agglomerates having a size of about 1 to 5 mm. The glassmaking raw materials are also finely-divided and may be used in this form or may be formed into agglomerates of about the same size as, or containing the agglomerated refining agent. The relative amounts of reducing agent to sulfur in the refining agent is such that at least one-fourth of the sulfate present will be reduced to the sulfide form, and the amount of refining agent employed is such that the amount of added sulfur expressed as SO3 is at least 0.05% by weight of the glass to be obtained. <s> BIB004
At the ICML conference in 2001, BIB002 and BIB003 5 independently formulated multiple instance regression, where bags are associated with real-valued labels instead of the usual binary class labels. The task is again to predict these labels. Similarly to MI classification, MI regression is motivated by the drug activity prediction problem. The authors of both papers observe that many drug developers prefer predictions of activity levels of drugs, instead of active / inactive classification predictions. Application areas identified by later authors include aerosol optical depth prediction for climate research BIB004 and crop yield modeling  . Ray and Page assume that the data is generated by a linear model with Gaussian noise on the real-valued labels. Critically, they further assume that for each bag, there is one instance (referred to as the primary instance) that is responsible for the label. Similarly to the standard MI assumption in classification problems, this further assumption is useful for modeling ambiguity, where the instances in a bag represent different views or different states of an object, and it is unknown which of the instances is responsible for the class label. We thus refer to it as the standard MI regression assumption. Amar et al. proposed the direct application of the Citation-KNN algorithm BIB001 and traditional k-NN (using the minimal Hausdorff distance) to data with real-valued labels. These methods depend on the same assumption as the nearest neighbour MI classification methods; namely that bags that are similar according to the bag-level distance measure will have similar labels. The later MI regression algorithms proposed by BIB004 use the assumption that each bag is generated by some random noise around a point in instance space, which they refer to as a prime instance 6 . Bag labels are assumed to be generated from the prime instances via some function (with added noise). Zhang & Zhou (in press) observed that their BARTMIP algorithm (see Section 3.5), which maps bags into a single-instance feature space, can be directly applied to multi-instance regression when a single-instance regression base learner is used -the method works the same way regardless of whether labels are discrete or real-valued. This method could in fact be applied to any other metadata algorithm, such as MILES or Simple MI. Under this approach, the metadata assumption used by the corresponding MI classification algorithm is applied in the regression setting.