Sparse Poisson regression via mixed-integer optimization.

We present a mixed-integer optimization (MIO) approach to sparse Poisson regression. The MIO approach to sparse linear regression was first proposed in the 1970s, but has recently received renewed attention due to advances in optimization algorithms and computer hardware. In contrast to many sparse estimation algorithms, the MIO approach has the advantage of finding the best subset of explanatory variables with respect to various criterion functions. In this paper, we focus on a sparse Poisson regression that maximizes the weighted sum of the log-likelihood function and the L2-regularization term. For this problem, we derive a mixed-integer quadratic optimization (MIQO) formulation by applying a piecewise-linear approximation to the log-likelihood function. Optimization software can solve this MIQO problem to optimality. Moreover, we propose two methods for selecting a limited number of tangent lines effective for piecewise-linear approximations. We assess the efficacy of our method through computational experiments using synthetic and real-world datasets. Our methods provide better log-likelihood values than do conventional greedy algorithms in selecting tangent lines. In addition, our MIQO formulation delivers better out-of-sample prediction performance than do forward stepwise selection and L1-regularized estimation, especially in low-noise situations.

Design and synthesis of biotinylated inositol 1,3,4,5-tetrakisphosphate targeting Grp1 pleckstrin homology domain.

A bifunctional molecule containing biotin and d-myo-inositol 1,3,4,5-tetrakisphosphate was synthesized. This molecule was designed on the basis of X-ray structure of the complex of d-myo-inositol 1,3,4,5-tetrakisphosphates, Ins(1,3,4,5)P(4), and Grp1 PH (general receptor of phosphoinositides pleckstrin homology) domain for the application to the widely employed biotin-avidin techniques. The building block of inositol moiety was synthesized starting with myo-inositol and assembled with the biotin-linker moiety through a phosphate linkage. The equilibrium dissociation constant K(D) of biotinylated Ins(1,3,4,5)P(4) binding of original Grp1 PH domain was 0.14 µM in pull-down analysis, which was comparable to that of unmodified Ins(1,3,4,5)P(4). Furthermore, biotinylated Ins(1,3,4,5)P(4) had an ability to distinguish Grp1 PH domain from PLCδ(1) PH domain. Thus, biotinylated Ins(1,3,4,5)P(4) retained the binding affinity and selectivity of original Grp1 PH domain, and realized the intracellular Ins(1,3,4,5)P(4) despite a tethering at the 1-phosphate group of inositol.