High-Low Level Support Vector Regression Prediction Approach (HL-SVR) for Data Modeling with Input Parameters of Unequal Sample Sizes

Support vector regression (SVR) has been widely used to reduce the high computational cost of computer simulation. SVR assumes the input parameters have equal sample sizes, but unequal sample sizes are often encountered in engineering practices. To solve this issue, a new prediction approach based on SVR, namely as high-low level SVR approach (HL-SVR) is proposed for data modeling of input parameters of unequal sample sizes in this paper. The proposed approach consists of low-level SVR models for the input parameters of larger sample sizes and high-level SVR model for the input parameters of smaller sample sizes. For each training point of the input parameters of smaller sample sizes, one low-level SVR model is built based on its corresponding input parameters of larger sample sizes and their responses of interest. The high-level SVR model is built based on the obtained responses from the low-level SVR models and the input parameters of smaller sample sizes. A number of numerical examples are used to validate the performance of HL-SVR. The experimental results indicate that HL-SVR can produce more accurate prediction results than SVR. The proposed approach is applied to the stress analysis of dental implant, in which the structural parameters have massive samples but the material of implant can only be selected from Ti and its alloys. The obtained prediction results of the HL-SVR approach are much better than SVR. The proposed approach can be used for the design, optimization, and analysis of engineering systems with input parameters of unequal sample sizes.

NExUS: Bayesian simultaneous network estimation across unequal sample sizes

Motivation Network-based analyses of high-throughput genomics data provide a holistic, systems-level understanding of various biological mechanisms for a common population. However, when estimating multiple networks across heterogeneous sub-populations, varying sample sizes pose a challenge in the estimation and inference, as network differences may be driven by differences in power. We are particularly interested in addressing this challenge in the context of proteomic networks for related cancers, as the number of subjects available for rare cancer (sub-)types is often limited. Results We develop NExUS (Network Estimation across Unequal Sample sizes), a Bayesian method that enables joint learning of multiple networks while avoiding artefactual relationship between sample size and network sparsity. We demonstrate through simulations that NExUS outperforms existing network estimation methods in this context, and apply it to learn network similarity and shared pathway activity for groups of cancers with related origins represented in The Cancer Genome Atlas (TCGA) proteomic data. Availability and implementation The NExUS source code is freely available for download at https://github.com/priyamdas2/NExUS. Supplementary information Supplementary data are available at Bioinformatics online.