Support vector machines with a reject option

This paper studies $\ell_1$ regularization with high-dimensional features for support vector machines with a built-in reject option (meaning that the decision of classifying an observation can be withheld at a cost lower than that of misclassification). The procedure can be conveniently implemented as a linear program and computed using standard software. We prove that the minimizer of the penalized population risk favors sparse solutions and show that the behavior of the empirical risk minimizer mimics that of the population risk minimizer. We also introduce a notion of classification complexity and prove that our minimizers adapt to the unknown complexity. Using a novel oracle inequality for the excess risk, we identify situations where fast rates of convergence occur.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ320 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

On Reject and Refine Options in Multicategory Classification

In many real applications of statistical learning, a decision made from misclassification can be too costly to afford; in this case, a reject option, which defers the decision until further investigation is conducted, is often preferred. In recent years, there has been much development for binary classification with a reject option. Yet, little progress has been made for the multicategory case. In this article, we propose margin-based multicategory classification methods with a reject option. In addition, and more importantly, we introduce a new and unique refine option for the multicategory problem, where the class of an observation is predicted to be from a set of class labels, whose cardinality is not necessarily one. The main advantage of both options lies in their capacity of identifying error-prone observations. Moreover, the refine option can provide more constructive information for classification by effectively ruling out implausible classes. Efficient implementations have been developed for the proposed methods. On the theoretical side, we offer a novel statistical learning theory and show a fast convergence rate of the excess $\ell$-risk of our methods with emphasis on diverging dimensionality and number of classes. The results can be further improved under a low noise assumption. A set of comprehensive simulation and real data studies has shown the usefulness of the new learning tools compared to regular multicategory classifiers. Detailed proofs of theorems and extended numerical results are included in the supplemental materials available online.Comment: A revised version of this paper was accepted for publication in the Journal of the American Statistical Association Theory and Methods Section. 52 pages, 6 figure

Is Deep Learning Safe for Robot Vision? Adversarial Examples against the iCub Humanoid

Deep neural networks have been widely adopted in recent years, exhibiting impressive performances in several application domains. It has however been shown that they can be fooled by adversarial examples, i.e., images altered by a barely-perceivable adversarial noise, carefully crafted to mislead classification. In this work, we aim to evaluate the extent to which robot-vision systems embodying deep-learning algorithms are vulnerable to adversarial examples, and propose a computationally efficient countermeasure to mitigate this threat, based on rejecting classification of anomalous inputs. We then provide a clearer understanding of the safety properties of deep networks through an intuitive empirical analysis, showing that the mapping learned by such networks essentially violates the smoothness assumption of learning algorithms. We finally discuss the main limitations of this work, including the creation of real-world adversarial examples, and sketch promising research directions.Comment: Accepted for publication at the ICCV 2017 Workshop on Vision in Practice on Autonomous Robots (ViPAR

Building Gene Expression Profile Classifiers with a Simple and Efficient Rejection Option in R

Background: The collection of gene expression profiles from DNA microarrays and their analysis with pattern recognition algorithms is a powerful technology applied to several biological problems. Common pattern recognition systems classify samples assigning them to a set of known classes. However, in a clinical diagnostics setup, novel and unknown classes (new pathologies) may appear and one must be able to reject those samples that do not fit the trained model. The problem of implementing a rejection option in a multi-class classifier has not been widely addressed in the statistical literature. Gene expression profiles represent a critical case study since they suffer from the curse of dimensionality problem that negatively reflects on the reliability of both traditional rejection models and also more recent approaches such as one-class classifiers. Results: This paper presents a set of empirical decision rules that can be used to implement a rejection option in a set of multi-class classifiers widely used for the analysis of gene expression profiles. In particular, we focus on the classifiers implemented in the R Language and Environment for Statistical Computing (R for short in the remaining of this paper). The main contribution of the proposed rules is their simplicity, which enables an easy integration with available data analysis environments. Since in the definition of a rejection model tuning of the involved parameters is often a complex and delicate task, in this paper we exploit an evolutionary strategy to automate this process. This allows the final user to maximize the rejection accuracy with minimum manual intervention. Conclusions: This paper shows how the use of simple decision rules can be used to help the use of complex machine learning algorithms in real experimental setups. The proposed approach is almost completely automated and therefore a good candidate for being integrated in data analysis flows in labs where the machine learning expertise required to tune traditional classifiers might not be availabl