We present an extension to the Lasso [9] for binary classification problems with ordered attributes. Inspired by the Fused Lasso [8] and the Group Lasso [10, 4] models, we aim to both discover and model runs (contiguous subgroups of the variables) that are highly predictive. We call the extended model LAPS (the Lasso with Attribute Partition Search). Such problems commonly arise in financial and medical domains, where predictors are time series variables, for example. This paper outlines the formulation of the problem, an algorithm to obtain the model coefficients and experiments showing applicability to practical problems of this type. 1 Predictive Runs We consider regression and classification problems where the predictor variables are ordered and naturally form groups. For example, in predicting whether or not a vaccinated animal survives an anthrax challenge, relevant attributes might include a toxin neutralization assay (TNA) measured at ten different time points (i.e., a gro...