The group fused Lasso for multiple change-point detection

Finding the place (or time) where most or all of a set of one-dimensional signals (or profiles) jointly change in some specific way is an important question in several fields. A common situation is when we want to find change-points in a multidimensional signal, e.g., in audio and image processing [1, 2], to detect intrusion in computer networks [3, 4], or in financial and economics time series analysis [5]. Another important situation is when we are confronted with several 1-dimensional signals which we believe share common changepoints, e.g., genomic profiles of a set of patients. The latter application is increasingly important in biology and medicine, in particular for the detection of copy-number variation along the genome [6], or the analysis of microarray and genetic linkage studies [7]. The common thread in biological applications is the search for data patterns shared by a set of individuals, such as cancer patients, at precise places on the genome; in particular, sudden changes in measured values. As opposed to the segmentation of multidimensional signals such as speech, where the dimension is fixed and collecting more data means having longer profiles, the length of signals in genomic studies (i.e., the number of probes measured along the genome) is fixed for a given technology while the number of signals (i.e., the number of individuals) can increase when we collect data about more patients. From a statistical point of view, it is therefore of interest to develop methods that identify multiple change-points shared by several signals that can benefit from increasing the number of signals. There exists a vast literature on the change-point detection problem [8, 9]. Here we focus on computationally efficient methods to segment a multidimensional signal by approximating it with a piecewiseconstant one, using quadratic error criteria.