Biblio

In this paper, we propose a new regularization scheme for the well-known Support Vector Machine (SVM) classifier that operates on the training sample level. The proposed approach is motivated by the fact that Maximum Margin-based classification defines decision functions as a linear combination of the selected training data and, thus, the variations on training sample selection directly affect generalization performance. We show that the exploitation of the proposed regularization scheme is well motivated and intuitive. Experimental results show that the proposed regularization scheme outperforms standard SVM in human action recognition tasks as well as classical recognition problems.

Machine learning is widely used in security-sensitive settings like spam and malware detection, although it has been shown that malicious data can be carefully modified at test time to evade detection. To overcome this limitation, adversary-aware learning algorithms have been developed, exploiting robust optimization and game-theoretical models to incorporate knowledge of potential adversarial data manipulations into the learning algorithm. Despite these techniques have been shown to be effective in some adversarial learning tasks, their adoption in practice is hindered by different factors, including the difficulty of meeting specific theoretical requirements, the complexity of implementation, and scalability issues, in terms of computational time and space required during training. In this work, we aim to develop secure kernel machines against evasion attacks that are not computationally more demanding than their non-secure counterparts. In particular, leveraging recent work on robustness and regularization, we show that the security of a linear classifier can be drastically improved by selecting a proper regularizer, depending on the kind of evasion attack, as well as unbalancing the cost of classification errors. We then discuss the security of nonlinear kernel machines, and show that a proper choice of the kernel function is crucial. We also show that unbalancing the cost of classification errors and varying some kernel parameters can further improve classifier security, yielding decision functions that better enclose the legitimate data. Our results on spam and PDF malware detection corroborate our analysis.

This brief presents a methodology to develop recursive filters in reproducing kernel Hilbert spaces. Unlike previous approaches that exploit the kernel trick on filtered and then mapped samples, we explicitly define the model recursivity in the Hilbert space. For that, we exploit some properties of functional analysis and recursive computation of dot products without the need of preimaging or a training dataset. We illustrate the feasibility of the methodology in the particular case of the γ-filter, which is an infinite impulse response filter with controlled stability and memory depth. Different algorithmic formulations emerge from the signal model. Experiments in chaotic and electroencephalographic time series prediction, complex nonlinear system identification, and adaptive antenna array processing demonstrate the potential of the approach for scenarios where recursivity and nonlinearity have to be readily combined.