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Multi-Objective methods and Multi-task learning

Co-Investigator: Kristin P. Bennett

Professor, Department of Mathematical Sciences, Rensselaer Polytechnic Institute

Kernel PLS and SVM QSPR models have shown that inference models can support discovery and understanding of bioseparations and protein/surface interactions (Breneman et al 2003). By developing extensions to these approaches targeted towards ranking and multi- task modeling, we can further accelerate the discovery process. Highly nonlinear ranking methods have been developed by simply changing the loss function used in SVM to a loss function appropriate for ranking. In the past, PLS and K-PLS could not be readily adapted to other loss functions. We have developed a novel dimensionality reduction method called Boosted Latent Factors (BLF) (Momma and Bennett 2005). For any given loss function, BLF creates latent variables or principal components similar to those produced by PLS and PCA. We have extended BLF to ranking loss-function with great success. BLF can use the kernel approach of SVM and K-PLS to construct highly nonlinear ranking functions. For the least squares loss, BLF reduces to PLS, but now we can rapidly create learning methods for any convex loss function that maintains the many benefits of PLS. Simultaneous modeling of a multi-task problem can improve insight into the causal model underlying the methods. PLS was developed for such multi-task and multi-response models but is limited to least squares regression loss functions. Multiple Latent Analysis (MLA) extends BLF to multi-task problems optimized using any convex loss function (Bennett 2005). With MLA, we can model the tasks as interrelated ranking problems in order to determine the experimental conditions likely to achieve a desired outcome. Recently, SVMs have also been extended to multi-task modeling (Evgeniou and Pontil 2004). We have developed and applied the multi- task learning methods for small-molecule chromatographic displacer property prediction as an exemplar of probe design problems. Multi- task modeling is applicable to many problems in cheminformatics (e.g. in drug discovery, we typically want to model and optimize several properties of small molecules related to efficacy, absorption, and toxicity).

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