A modified information criterion for tuning parameter selection in 1d fused LASSO for inference on multiple change points

摘要

Inference about multiple change points has been an interesting topic in the statistics literature. Recently, the high throughput technologies became the most popularly used tools in genomic studies and yielded massive data. In particular, when the concern is searching for heterogenous segments in a massive data set, it becomes an interesting problem in statistical change point analysis. That is, one tries to determine if there are multiple change points that separate the data into different parts. Such data have a 'sparsity' feature (within each part, the data points are homogenous), and hence penalized regression, such as the 1d fused LASSO, has been recently used for detecting multiple change points in high throughput data. One of the main challenges for detecting change points is to estimate the number of change points which then becomes the problem of how to select an optimal tuning parameter in the LASSO methods for change point problems. Therefore, in this work, we propose to use a modified Bayesian information criterion to estimate the optimal tuning parameter in the 1d fused LASSO for multiple change points detection. We show theoretically that the proposed JMIC consistently identifies the true number of change points via providing the optimal tuning parameter for 1d fused LASSO. Simulation studies and application to a next-generation sequencing data of a breast cancer tumour cell line illustrated the usefulness of the proposed method.