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

Linear classification tikhonov regularization knowledge-based support vector machine for tornado forecasting

Knowledge-based model, Linear classification, Knowledge set, Prior knowledge, Tikhonov regularization, Support vector machines,

A data-driven kernel method assimilation technique for geophysical modelling

© 2016 Informa UK Limited, trading as Taylor & Francis Group. Incorporating the quantity and variety of observations in atmospheric and oceanographic assimilation and prediction models has become an increasingly complex task. Data assimilation allows for uneven spatial and temporal data distribution and redundancy to be addressed so that the models can ingest massive data sets. Traditional data assimilation methods introduce Kalman filters and variational approaches. This study introduces a family of algorithms, motivated by advances in machine learning. These algorithms provide an alternative approach to incorporating new observations into the analysis forecast cycle. The application of kernel methods to processing the states of a quasi-geostrophic numerical model is intended to demonstrate the feasibility of the method as a proof-of-concept. The speed, efficiency, accuracy and scalability in recovering unperturbed state trajectories establishes the viability of machine learning for data assimilation

Data selection using support vector regression

© 2015, Chinese National Committee for International Association of Meteorology and Atmospheric Sciences, Institute of Atmospheric Physics, Science Press and Springer-Verlag Berlin Heidelberg. Geophysical data sets are growing at an ever-increasing rate, requiring computationally efficient data selection (thinning) methods to preserve essential information. Satellites, such as WindSat, provide large data sets for assessing the accuracy and computational efficiency of data selection techniques. A new data thinning technique, based on support vector regression (SVR), is developed and tested. To manage large on-line satellite data streams, observations from WindSat are formed into subsets by Voronoi tessellation and then each is thinned by SVR (TSVR). Three experiments are performed. The first confirms the viability of TSVR for a relatively small sample, comparing it to several commonly used data thinning methods (random selection, averaging and Barnes filtering), producing a 10% thinning rate (90% data reduction), low mean absolute errors (MAE) and large correlations with the original data. A second experiment, using a larger dataset, shows TSVR retrievals with MAE −1 and correlations ⩽ 0.98. TSVR was an order of magnitude faster than the commonly used thinning methods. A third experiment applies a two-stage pipeline to TSVR, to accommodate online data. The pipeline subsets reconstruct the wind field with the same accuracy as the second experiment, is an order of magnitude faster than the nonpipeline TSVR. Therefore, pipeline TSVR is two orders of magnitude faster than commonly used thinning methods that ingest the entire data set. This study demonstrates that TSVR pipeline thinning is an accurate and computationally efficient alternative to commonly used data selection techniques

A nonlinear multi-classification knowledge-based kernel machine

Knowledge-based model, Multi-classification, Kernel, Prior knowledge, Tikhonov regularization,

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, 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