This paper presents a nonparametric penalized likelihood approach for variable selection and model building, called likelihood basis pursuit (LBP). In the setting of a tensor product reproducing kernel Hilbert space, we decompose the log likelihood into the sum of different functional components such as main effects and interactions, with each component… (More)
Radiotherapy treatment is often delivered in a fractionated manner over a period of time. Emerging delivery devices are able to determine the actual dose that has been delivered at each stage facilitating the use of adaptive treatment plans that compensate for errors in delivery. We formulate a model of the day-today planning problem as a stochastic program… (More)
Slice models are collections of mathematical programs with the same structure but different data. Examples of slice models appear in Data Envelopment Analysis, where they are used to evaluate efficiency, and cross-validation, where they are used to measure generalization ability. Because they involve multiple programs, slice models tend to be data-intensive… (More)
Dedicated to Olvi Mangasarian on the occasion of his 70th birthday We consider a non-parametric penalized likelihood approach for model building called likelihood basis pursuit (LBP) that determines the probabilities of binary outcomes given explanatory vectors while automatically selecting important features. The LBP model involves parameters that balance… (More)
We show how to implement the cross-validation technique used in machine learning as a slice model. We describe the formulation in terms of support vector machines and extend the GAMS/DEA interface to allow for efficient solutions of linear, mixed integer and simple quadratic slice models under GAMS.