Title: 
Change Detection in Multivariate Data: Likelihood and Detectability Loss

Presenter:
Giacomo Boracchi
Politecnico di Milano, DEIB - Dipartimento di Elettronica, Informazione e Bioingegneria


Abstract
We address the problem of detecting changes in multivariate data, and we investigate the intrinsic difficulty that change-detection methods have to face when the data dimension scales. In particular, we consider algorithms that compute at first the data log-likelihood, and then detect changes by comparing the distribution of this latter over different time windows / portions of the dataset. Despite this approach constitutes the frame of several change-detection methods, its effectiveness when data dimension scales has never been investigated, which is indeed the goal of our research.
We show that the magnitude of the change can be naturally measured by the symmetric Kullback-Leibler divergence between the pre- and post-change distributions, and that the detectability of changes of a given magnitude worsens when the data dimension increases. This problem, which we refer to as "detectability loss", is due to the linear relationship between the variance of the log-likelihood and the data dimension. 
We analytically derive the detectability loss on Gaussian-distributed data, and empirically demonstrate that this problem holds also in real-world datasets, where it can be harmful even at low data-dimensions. We finally discuss few implications of detectability loss, illustrating as a case study the detection of defects in SEM images of nanofibers by means of anomaly-detection algorithms based on sparse representations. 


Bio
Giacomo Boracchi received the M.S. degree in Mathematics from the Università Statale degli Studi di Milano, Italy, and the Ph.D. degree in Information Technology at Politecnico di Milano, Italy, in 2004 and 2008, respectively. He was researcher at Tampere International Center for Signal Processing, Finland, during 2004-2005. 
Currently, he is an assistant professor at the Dipartimento di Elettronica, Informazione e Bioingegneria of the Politecnico di Milano. His main research interests include learning methods for nonstationary environments, as well as mathematical and statistical methods for image processing and analysis. In 2015 he received the IBM Faculty Award, and in 2016 the IEEE Trans. on Neural Networks and Learning Systems Outstanding Paper Award.



References
- Cesare Alippi, Giacomo Boracchi, Diego Carrera, Manuel Roveri "Change Detection in Multivariate Datastreams: Likelihood and Detectability Loss", International Joint Conference of Artificial Intelligence (IJCAI) 2016, New York, USA, July 9 - 13, 7 pages.
Preprint: http://arxiv.org/pdf/1510.04850v2
- Diego Carrera, Fabio Manganini, Giacomo Boracchi, Ettore Lanzarone "Defect Detection in Nanostructures", IEEE Transactions on Industrial Informatics -- Submitted, 11 pages.
Preprint: http://bibliograzia.imati.cnr.it/sites/bibliograzia.vp1.it/files/16-03.pdf