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

Machine learning for early detection of traffic congestion using public transport traffic data

The purpose of this project is to provide better knowledge of how the bus travel times is affected by congestion and other problems in the urban traffic environment. The main source of data for this study is second-level measurements coming from all buses in the Linköping region showing the location of each vehicle.The main goal of this thesis is to propose, implement, test and optimize a machine learning algorithm based on data collected from regional buses from Sweden so that it is able to perform predictions on the future state of the urban traffic.El objetivo principal de este proyecto es proponer, implementar, probar y optimizar un algoritmo de aprendizaje automático basado en datos recopilados de autobuses regionales de Suecia para que poder realizar predicciones sobre el estado futuro del tráfico urbano.L'objectiu principal d'aquest projecte és proposar, implementar, provar i optimitzar un algoritme de machine learning basat en dades recollides a partir d'autobusos regionals de Suècia de manera per poder realitzar prediccions sobre l'estat futur del trànsit urbà

Is Your Model Susceptible to Floating-Point Errors?

This paper provides a framework that highlights the features of computer models that make them especially vulnerable to floating-point errors, and suggests ways in which the impact of such errors can be mitigated. We focus on small floating-point errors because these are most likely to occur, whilst still potentially having a major influence on the outcome of the model. The significance of small floating-point errors in computer models can often be reduced by applying a range of different techniques to different parts of the code. Which technique is most appropriate depends on the specifics of the particular numerical situation under investigation. We illustrate the framework by applying it to six example agent-based models in the literature.Floating Point Arithmetic, Floating Point Errors, Agent Based Modelling, Computer Modelling, Replication