We refer to collections of mathematical programs with the same structure but different data as slice models. Examples of slice models appear in Data Envelopment Analysis (DEA), 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 and time consuming to solve. However, by incorporating additional information in the solution process, such as the common structure and shared data, we are able to solve these models much more efficiently. This is easily done for linear, mixed-integer and simple quadratic programs under the general purpose modeling language GAMS using the GAMS/DEA (slice) interface that we developed. With the GAMS/DEA interface, we achieve much more efficiency and hence are able to process much larger real-world problems. We are also able to extend DEA efficiency results to confidence intervals using a computationally-intensive smoothed bootstrap procedure.
The GAMS/DEA interface can be downloaded from here.
For more information on slice modeling and the interface, take a look at our papers:
M. C. Ferris and M. M. Voelker (2000). Slice models in general purpose modeling systems: An application to DEA. A revised version of this paper will be appearing in Optimization Methods and Software, 2002.
M. C. Ferris and M. M. Voelker (2001). Slice models in GAMS. A revised version of this paper appeared in P. Chamoni, R. Leisten, A. Martin, J. Minnemann, and H. Stadtler, editors, Operations Research Proceedings 2001, pages 239-246. Springer-Verlag, 2002.
We consider a nonparametric penalized likelihood approach for variable selection and model building, called likelihood basis pursuit (LBP). LBP predicts a probabilty for a {0,1} outcome using a smooth spline ANOVA model, with penalty parameters drawn from basis pursuit ideas. To fit the model, parameters that determine the balance between maximizing the likelihood and minimizing the basis pursuit penalties must be selected. The parameter selection is done by the application of a grid search, which results in hundreds or thousands of solves, depending upon which version of the model is chosen. By applying slice modeling ideas, we were able to speed up the individual solves and so were able to consider more complicated and larger models (for example, those that also incorporated categorical data).
For more information on LBP, please see our papers:
H. Zhang, G. Wahba, Y. Lin, M. Voelker, M. Ferris, R. Klein, and B. Klein (2001). Variable selection via basis pursuit for non-gaussian data. Technical Report 1042, Statistics Department, University of Wisconsin, Madison, Wisconsin, 2001. In Proceedings of the ASA Joint Statistical Meetings, 2001.
H. Zhang, G. Wahba, Y. Lin, M. Voelker, M. Ferris, R. Klein, and B. Klein (2002). Variable selection and model building via likelihood basis pursuit. Technical Report 1059, Statistics Department, University of Wisconsin, Madison, Wisconsin, 2002.
In many cases a radiotherapy treatment is delivered as a series of smaller dosages over a period of time. Currently, it is difficult to determine the actual dose that has been delivered at each stage, precluding the use of adaptive treatment plans. However, new generations of machines will give more accurate information of actual dose delivered, allowing a planner to compensate for errors in delivery. We formulate a model of the day-to-day planning problem as a stochastic linear program and exhibit the gains that can be achieved by incorporating uncertainty about errors during treatment into the planning process. Due to size and time restrictions, the model becomes intractable for realistic instances. We show how neuro-dynamic programming can be used to approximate the stochastic solution, and derive results from our models for realistic time periods. These results allow us to generate practical rules of thumb that can be immediately implemented in current planning technologies.
For more information, please see our paper:
M. C. Ferris and M. M. Voelker. Neuro-dynamic programming for radiation treatment planning. Numerical Analysis Group Research Report NA-02/06, Oxford University Computing Laboratory, Oxford University, 2002.