Learning Using Privileged Information: SVM+ and Weighted SVM

Prior knowledge can be used to improve predictive performance of learning algorithms or reduce the amount of data required for training. The same goal is pursued within the learning using privileged information paradigm which was recently introduced by Vapnik et al. and is aimed at utilizing additional information available only at training time -- a framework implemented by SVM+. We relate the privileged information to importance weighting and show that the prior knowledge expressible with privileged features can also be encoded by weights associated with every training example. We show that a weighted SVM can always replicate an SVM+ solution, while the converse is not true and we construct a counterexample highlighting the limitations of SVM+. Finally, we touch on the problem of choosing weights for weighted SVMs when privileged features are not available.Comment: 18 pages, 8 figures; integrated reviewer comments, improved typesettin

Designing Semantic Kernels as Implicit Superconcept Expansions

Recently, there has been an increased interest in the exploitation of background knowledge in the context of text mining tasks, especially text classification. At the same time, kernel-based learning algorithms like Support Vector Machines have become a dominant paradigm in the text mining community. Amongst other reasons, this is also due to their capability to achieve more accurate learning results by replacing standard linear kernel (bag-of-words) with customized kernel functions which incorporate additional apriori knowledge. In this paper we propose a new approach to the design of ‘semantic smoothing kernels’ by means of an implicit superconcept expansion using well-known measures of term similarity. The experimental evaluation on two different datasets indicates that our approach consistently improves performance in situations where (i) training data is scarce or (ii) the bag-ofwords representation is too sparse to build stable models when using the linear kernel

Visual and Contextual Modeling for the Detection of Repeated Mild Traumatic Brain Injury.

Currently, there is a lack of computational methods for the evaluation of mild traumatic brain injury (mTBI) from magnetic resonance imaging (MRI). Further, the development of automated analyses has been hindered by the subtle nature of mTBI abnormalities, which appear as low contrast MR regions. This paper proposes an approach that is able to detect mTBI lesions by combining both the high-level context and low-level visual information. The contextual model estimates the progression of the disease using subject information, such as the time since injury and the knowledge about the location of mTBI. The visual model utilizes texture features in MRI along with a probabilistic support vector machine to maximize the discrimination in unimodal MR images. These two models are fused to obtain a final estimate of the locations of the mTBI lesion. The models are tested using a novel rodent model of repeated mTBI dataset. The experimental results demonstrate that the fusion of both contextual and visual textural features outperforms other state-of-the-art approaches. Clinically, our approach has the potential to benefit both clinicians by speeding diagnosis and patients by improving clinical care

DSL: Discriminative Subgraph Learning via Sparse Self-Representation

The goal in network state prediction (NSP) is to classify the global state (label) associated with features embedded in a graph. This graph structure encoding feature relationships is the key distinctive aspect of NSP compared to classical supervised learning. NSP arises in various applications: gene expression samples embedded in a protein-protein interaction (PPI) network, temporal snapshots of infrastructure or sensor networks, and fMRI coherence network samples from multiple subjects to name a few. Instances from these domains are typically ``wide'' (more features than samples), and thus, feature sub-selection is required for robust and generalizable prediction. How to best employ the network structure in order to learn succinct connected subgraphs encompassing the most discriminative features becomes a central challenge in NSP. Prior work employs connected subgraph sampling or graph smoothing within optimization frameworks, resulting in either large variance of quality or weak control over the connectivity of selected subgraphs. In this work we propose an optimization framework for discriminative subgraph learning (DSL) which simultaneously enforces (i) sparsity, (ii) connectivity and (iii) high discriminative power of the resulting subgraphs of features. Our optimization algorithm is a single-step solution for the NSP and the associated feature selection problem. It is rooted in the rich literature on maximal-margin optimization, spectral graph methods and sparse subspace self-representation. DSL simultaneously ensures solution interpretability and superior predictive power (up to 16% improvement in challenging instances compared to baselines), with execution times up to an hour for large instances.Comment: 9 page

Optimization: A Journal of Mathematical Programming and Operations Research

In this article we study support vector machine (SVM) classifiers in the face of uncertain knowledge sets and show how data uncertainty in knowledge sets can be treated in SVM classification by employing robust optimization. We present knowledge-based SVM classifiers with uncertain knowledge sets using convex quadratic optimization duality. We show that the knowledge-based SVM, where prior knowledge is in the form of uncertain linear constraints, results in an uncertain convex optimization problem with a set containment constraint. Using a new extension of Farkas' lemma, we reformulate the robust counterpart of the uncertain convex optimization problem in the case of interval uncertainty as a convex quadratic optimization problem. We then reformulate the resulting convex optimization problems as a simple quadratic optimization problem with non-negativity constraints using the Lagrange duality. We obtain the solution of the converted problem by a fixed point iterative algorithm and establish the convergence of the algorithm. We finally present some preliminary results of our computational experiments of the metho