The cell defense mechanism of RNA interference has applications in gene function analysis and promising potentials in human disease therapy. To effectively silence a target gene, it is desirable to select appropriate initiator siRNA molecules having satisfactory silencing capabilities. Computational prediction for silencing efficacy of siRNAs can assist this screening process before using them in biological experiments. String kernel functions, which operate directly on the string objects representing siRNAs and target mRNAs, have been applied to support vector regression for the prediction and improved accuracy over numerical kernels in multidimensional vector spaces constructed from descriptors of siRNA design rules. To fully utilize information provided by string and numerical data, we propose to unify the two in a kernel feature space by devising a multiple kernel regression framework where a linear combination of the kernels is used. We formulate the multiple kernel learning into a quadratically constrained quadratic programming (QCQP) problem, which although yields global optimal solution, is computationally demanding and requires a commercial solver package. We further propose three heuristics based on the principle of kernel-target alignment and predictive accuracy. Empirical results demonstrate that multiple kernel regression can improve accuracy, decrease model complexity by reducing the number of support vectors, and speed up computational performance dramatically. In addition, multiple kernel regression evaluates the importance of constituent kernels, which for the siRNA efficacy prediction problem, compares the relative significance of the design rules. Finally, we give insights into the multiple kernel regression mechanism and point out possible extensions.

String kernels directly model sequence similarities without the necessity of extracting numerical features in a vector space. Since they better capture complex traits in the sequences, string kernels often achieve better prediction performance. RNA interference is a cell defense mechanism with many biological and therapeutical applications, where strings can be used to represent target messenger RNAs and initiating short RNAs and string kernels can be applied for training and prediction. While most existing string kernels are developed for general purpose sequences and have been applied to text and protein classifications, the RNA string kernel is particularly designed to model mismatches, GU wobbles, and bulges of RNA biology and has been applied to RNAi off-target evaluation. We adapt the RNA string kernel to compute the similarity of siRNA sequences and use it in support vector regression to predict siRNA silencing efficacy. We evaluate the performance of the RNA kernel against the spectrum kernel, the string subsequence kernel of arbitrary mismatch, the randomized string kernel, and numerical kernels computed from numerical features extracted according to siRNA design rules. We also give insights into computational performance and common properties and differences of the RNA kernel as compared to other kernels. Empirical results on biological data sets demonstrate that the RNA string kernel performed favorably than most existing string kernels and achieved significant improvements over kernels computed from numerical descriptors extracted according to structural and thermodynamic rules. Meanwhile, the string kernels achieved favorable results relative to other methods in related work. Furthermore, the RNA string kernel is simple to implement and fast to compute.

While kernel support vector machines are powerful classification algorithms, their computational overhead can be significant, especially for large and high-dimensional data sets. A recent biomedical dataset, for instance, could take as long as 3 weeks to compute its RBF kernel matrix on a modern, single-processor workstation. In this paper, we develop methods for high-performance parallel computation of kernel matrices. There are two key components to a parallel implementation: distribution of the computation across nodes and communication to combine the results. To address the first, we employ a dimension-wise data partition that yields efficient computation and low communication overhead during the initial phase. This partition provides dramatic speedups on large and high-dimensional data, applies to a wide variety of kernel functions, and is an exact computation, producing the same kernel matrix as its sequential implementation. To address communication needs during the second phase, we introduce an approximation specific to the Gaussian RBF kernel that yields sparse partial kernel matrices and, thus, efficient communication. We analyze the approximation error of this method, demonstrating that it falls off exponentially with N, the parameter of the approximation. We also examine the positive definiteness of the approximation with respect to Mercer's condition and show that (a) in the limit of N our approximation becomes positive definite for any data set and (b) for a fixed data set, there exists a finite N yielding a positive definite kernel matrix. We also give a simple iterative method for selecting N to yield a positive definite kernel matrix on any fixed data set. In practice, we find that positive definiteness is achieved on all of the data sets we examine with very small N (2–5). Finally, we test the empirical performance of our two methods on a variety of large, real-world data sets, demonstrating large computational speedups with little or no impact on accuracy.