Spline-Lasso in High-Dimensional Linear Regression

<p>We consider a high-dimensional linear regression problem, where the covariates (features) are ordered in some meaningful way, and the number of covariates <i>p</i> can be much larger than the sample size <i>n</i>. The fused lasso of Tibshirani et al. is designed especially to tackle this type of problems; it yields sparse coefficients and selects grouped variables, and encourages local constant coefficient profile within each group. However, in some applications, the effects of different features within a group might be different and change smoothly. In this article, we propose a new spline-lasso or more generally, spline-MCP to better capture the different effects within the group. The newly proposed method is very easy to implement since it can be easily turned into a lasso or MCP problem. Simulations show that the method works very effectively both in feature selection and prediction accuracy. A real application is also given to illustrate the benefits of the method. Supplementary materials for this article are available online.</p

Additional file 1 of Super-taxon in human microbiome are identified to be associated with colorectal cancer

Additional file 1. Simulation Results under various sparsitiy levels and CRC associated microbes from family level

All-optical spatio-temporal metrology for isolated attosecond pulses

Characterizing an isolated attosecond pulse (IAP) is essential for its potential applications. A complete characterization of an IAP ultimately requires the determination of its electric field in both time and space domains. However, previous methods, like the widely-used RABBITT and attosecond streaking, only measure the temporal profile of the attosecond pulse. Here we demonstrate an all-optical method for the measurement of the space-time properties of an IAP. By introducing a non-collinear perturbing pulse to the driving field, the process of IAP generation is modified both spatially and temporally, manifesting as a spatial and a frequency modulation in the harmonic spectrum. By using a FROG-like retrieval method, the spatio-spectral phases of the harmonic spectrum are faithfully extracted from the induced spatio-spectral modulations, which allows a thoroughgoing characterization of the IAP in both time and space. With this method, the spatio-temporal structures of the IAP generated in a two-color driving field in both the near- and far-field are fully reconstructed, from which a weak spatio-temporal coupling in the IAP generation is revealed. Our approach overcomes the limitation in the temporal measurement in conventional in situ scheme, providing a reliable and holistic metrology for IAP characterization