Second order cone programming approaches for handling missing and uncertain data

We propose a novel second order cone programming formulation for designing robust classifiers which can handle uncertainty in observations. Similar formulations are also derived for designing regression functions which are robust to uncertainties in the regression setting. The proposed formulations are independent of the underlying distribution, requiring only the existence of second order moments. These formulations are then specialized to the case of missing values in observations for both classification and regression problems. Experiments show that the proposed formulations outperform imputation

Learning from Distributions via Support Measure Machines

This paper presents a kernel-based discriminative learning framework on probability measures. Rather than relying on large collections of vectorial training examples, our framework learns using a collection of probability distributions that have been constructed to meaningfully represent training data. By representing these probability distributions as mean embeddings in the reproducing kernel Hilbert space (RKHS), we are able to apply many standard kernel-based learning techniques in straightforward fashion. To accomplish this, we construct a generalization of the support vector machine (SVM) called a support measure machine (SMM). Our analyses of SMMs provides several insights into their relationship to traditional SVMs. Based on such insights, we propose a flexible SVM (Flex-SVM) that places different kernel functions on each training example. Experimental results on both synthetic and real-world data demonstrate the effectiveness of our proposed framework.Comment: Advances in Neural Information Processing Systems 2

Robustness and Generalization

We derive generalization bounds for learning algorithms based on their robustness: the property that if a testing sample is "similar" to a training sample, then the testing error is close to the training error. This provides a novel approach, different from the complexity or stability arguments, to study generalization of learning algorithms. We further show that a weak notion of robustness is both sufficient and necessary for generalizability, which implies that robustness is a fundamental property for learning algorithms to work

Early identification of mild cognitive impairment using incomplete random forest-robust support vector machine and FDG-PET imaging

Alzheimer’s disease (AD) is the most common type of dementia and will be an increasing health problem in society as the population ages. Mild cognitive impairment (MCI) is considered to be a prodromal stage of AD. The ability to identify subjects with MCI will be increasingly important as disease modifying therapies for AD are developed. We propose a semi-supervised learning method based on robust optimization for the identification of MCI from [18F]Fluorodeoxyglucose PET scans. We extracted three groups of spatial features from the cortical and subcortical regions of each FDG-PET image volume. We measured the statistical uncertainty related to these spatial features via transformation using an incomplete random forest and formulated the MCI identification problem under a robust optimization framework. We compared our approach to other state-of-the-art methods in different learning schemas. Our method outperformed the other techniques in the ability to separate MCI from normal controls