23,417 research outputs found
Robustness Verification of Support Vector Machines
We study the problem of formally verifying the robustness to adversarial
examples of support vector machines (SVMs), a major machine learning model for
classification and regression tasks. Following a recent stream of works on
formal robustness verification of (deep) neural networks, our approach relies
on a sound abstract version of a given SVM classifier to be used for checking
its robustness. This methodology is parametric on a given numerical abstraction
of real values and, analogously to the case of neural networks, needs neither
abstract least upper bounds nor widening operators on this abstraction. The
standard interval domain provides a simple instantiation of our abstraction
technique, which is enhanced with the domain of reduced affine forms, which is
an efficient abstraction of the zonotope abstract domain. This robustness
verification technique has been fully implemented and experimentally evaluated
on SVMs based on linear and nonlinear (polynomial and radial basis function)
kernels, which have been trained on the popular MNIST dataset of images and on
the recent and more challenging Fashion-MNIST dataset. The experimental results
of our prototype SVM robustness verifier appear to be encouraging: this
automated verification is fast, scalable and shows significantly high
percentages of provable robustness on the test set of MNIST, in particular
compared to the analogous provable robustness of neural networks
Robustness Verification of k-Nearest Neighbor Classifiers by Abstract Interpretation
openAbstract interpretation is an established mathematical framework introduced by Cousot and Cousot in 1977 and ubiquitously used in static program analysis. In recent years, many noteworthy works have shown how abstract interpretation can be successfully applied to formally verify robustness properties of some major machine learning techniques like (deep) neural networks, decision trees and support vector machines.
This research work aims to pursue this line of research by proposing a novel abstract interpretation-based framework for designing a sound abstract version of the k-Nearest Neighbors (kNN) algorithm, a well-known non-parametric supervised learning method widely used for classification and regression tasks, which is then instantiated to the standard interval domain approximating the range of numerical features, to verify its robustness and stability properties. This verification approach has been fully implemented and evaluated on several datasets, including standard benchmark datasets for individual fairness verification, and then compared with some related works finding adversarial examples on kNNs. The experimental results turned out to be very promising and showed high percentages of provable robustness and stability in most of the reference datasets, thus making a step forward in the current state-of-the-art of formal verification of machine learning models.Abstract interpretation is an established mathematical framework introduced by Cousot and Cousot in 1977 and ubiquitously used in static program analysis. In recent years, many noteworthy works have shown how abstract interpretation can be successfully applied to formally verify robustness properties of some major machine learning techniques like (deep) neural networks, decision trees and support vector machines.
This research work aims to pursue this line of research by proposing a novel abstract interpretation-based framework for designing a sound abstract version of the k-Nearest Neighbors (kNN) algorithm, a well-known non-parametric supervised learning method widely used for classification and regression tasks, which is then instantiated to the standard interval domain approximating the range of numerical features, to verify its robustness and stability properties. This verification approach has been fully implemented and evaluated on several datasets, including standard benchmark datasets for individual fairness verification, and then compared with some related works finding adversarial examples on kNNs. The experimental results turned out to be very promising and showed high percentages of provable robustness and stability in most of the reference datasets, thus making a step forward in the current state-of-the-art of formal verification of machine learning models
Closed-Loop Statistical Verification of Stochastic Nonlinear Systems Subject to Parametric Uncertainties
This paper proposes a statistical verification framework using Gaussian
processes (GPs) for simulation-based verification of stochastic nonlinear
systems with parametric uncertainties. Given a small number of stochastic
simulations, the proposed framework constructs a GP regression model and
predicts the system's performance over the entire set of possible
uncertainties. Included in the framework is a new metric to estimate the
confidence in those predictions based on the variance of the GP's cumulative
distribution function. This variance-based metric forms the basis of active
sampling algorithms that aim to minimize prediction error through careful
selection of simulations. In three case studies, the new active sampling
algorithms demonstrate up to a 35% improvement in prediction error over other
approaches and are able to correctly identify regions with low prediction
confidence through the variance metric.Comment: 8 pages, submitted to ACC 201
Qualitative Robustness of Support Vector Machines
Support vector machines have attracted much attention in theoretical and in
applied statistics. Main topics of recent interest are consistency, learning
rates and robustness. In this article, it is shown that support vector machines
are qualitatively robust. Since support vector machines can be represented by a
functional on the set of all probability measures, qualitative robustness is
proven by showing that this functional is continuous with respect to the
topology generated by weak convergence of probability measures. Combined with
the existence and uniqueness of support vector machines, our results show that
support vector machines are the solutions of a well-posed mathematical problem
in Hadamard's sense
Wild Patterns: Ten Years After the Rise of Adversarial Machine Learning
Learning-based pattern classifiers, including deep networks, have shown
impressive performance in several application domains, ranging from computer
vision to cybersecurity. However, it has also been shown that adversarial input
perturbations carefully crafted either at training or at test time can easily
subvert their predictions. The vulnerability of machine learning to such wild
patterns (also referred to as adversarial examples), along with the design of
suitable countermeasures, have been investigated in the research field of
adversarial machine learning. In this work, we provide a thorough overview of
the evolution of this research area over the last ten years and beyond,
starting from pioneering, earlier work on the security of non-deep learning
algorithms up to more recent work aimed to understand the security properties
of deep learning algorithms, in the context of computer vision and
cybersecurity tasks. We report interesting connections between these
apparently-different lines of work, highlighting common misconceptions related
to the security evaluation of machine-learning algorithms. We review the main
threat models and attacks defined to this end, and discuss the main limitations
of current work, along with the corresponding future challenges towards the
design of more secure learning algorithms.Comment: Accepted for publication on Pattern Recognition, 201
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