Dissimilarity-based Ensembles for Multiple Instance Learning

In multiple instance learning, objects are sets (bags) of feature vectors (instances) rather than individual feature vectors. In this paper we address the problem of how these bags can best be represented. Two standard approaches are to use (dis)similarities between bags and prototype bags, or between bags and prototype instances. The first approach results in a relatively low-dimensional representation determined by the number of training bags, while the second approach results in a relatively high-dimensional representation, determined by the total number of instances in the training set. In this paper a third, intermediate approach is proposed, which links the two approaches and combines their strengths. Our classifier is inspired by a random subspace ensemble, and considers subspaces of the dissimilarity space, defined by subsets of instances, as prototypes. We provide guidelines for using such an ensemble, and show state-of-the-art performances on a range of multiple instance learning problems.Comment: Submitted to IEEE Transactions on Neural Networks and Learning Systems, Special Issue on Learning in Non-(geo)metric Space

Mixed-Integer Convex Nonlinear Optimization with Gradient-Boosted Trees Embedded

Decision trees usefully represent sparse, high dimensional and noisy data. Having learned a function from this data, we may want to thereafter integrate the function into a larger decision-making problem, e.g., for picking the best chemical process catalyst. We study a large-scale, industrially-relevant mixed-integer nonlinear nonconvex optimization problem involving both gradient-boosted trees and penalty functions mitigating risk. This mixed-integer optimization problem with convex penalty terms broadly applies to optimizing pre-trained regression tree models. Decision makers may wish to optimize discrete models to repurpose legacy predictive models, or they may wish to optimize a discrete model that particularly well-represents a data set. We develop several heuristic methods to find feasible solutions, and an exact, branch-and-bound algorithm leveraging structural properties of the gradient-boosted trees and penalty functions. We computationally test our methods on concrete mixture design instance and a chemical catalysis industrial instance

Ensembles of random sphere cover classifiers

We propose and evaluate a new set of ensemble methods for the Randomised Sphere Cover (RSC) classifier. RSC is a classifier using the sphere cover method that bases classification on distance to spheres rather than distance to instances. The randomised nature of RSC makes it ideal for use in ensembles. We propose two ensemble methods tailored to the RSC classifier; RSE, an ensemble based on instance resampling and RSSE, a subspace ensemble. We compare RSE and RSSE to tree based ensembles on a set of UCI datasets and demonstrates that RSC ensembles perform significantly better than some of these ensembles, and not significantly worse than the others. We demonstrate via a case study on six gene expression data sets that RSSE can outperform other subspace ensemble methods on high dimensional data when used in conjunction with an attribute filter. Finally, we perform a set of Bias/Variance decomposition experiments to analyse the source of improvement in comparison to a base classifier