A Scalable and Extensible Framework for Superposition-Structured Models

In many learning tasks, structural models usually lead to better interpretability and higher generalization performance. In recent years, however, the simple structural models such as lasso are frequently proved to be insufficient. Accordingly, there has been a lot of work on "superposition-structured" models where multiple structural constraints are imposed. To efficiently solve these "superposition-structured" statistical models, we develop a framework based on a proximal Newton-type method. Employing the smoothed conic dual approach with the LBFGS updating formula, we propose a scalable and extensible proximal quasi-Newton (SEP-QN) framework. Empirical analysis on various datasets shows that our framework is potentially powerful, and achieves super-linear convergence rate for optimizing some popular "superposition-structured" statistical models such as the fused sparse group lasso

Sparse Regression Codes for Multi-terminal Source and Channel Coding

We study a new class of codes for Gaussian multi-terminal source and channel coding. These codes are designed using the statistical framework of high-dimensional linear regression and are called Sparse Superposition or Sparse Regression codes. Codewords are linear combinations of subsets of columns of a design matrix. These codes were recently introduced by Barron and Joseph and shown to achieve the channel capacity of AWGN channels with computationally feasible decoding. They have also recently been shown to achieve the optimal rate-distortion function for Gaussian sources. In this paper, we demonstrate how to implement random binning and superposition coding using sparse regression codes. In particular, with minimum-distance encoding/decoding it is shown that sparse regression codes attain the optimal information-theoretic limits for a variety of multi-terminal source and channel coding problems.Comment: 9 pages, appeared in the Proceedings of the 50th Annual Allerton Conference on Communication, Control, and Computing - 201

Rainfall frequency analysis for ungauged regions using remotely sensed precipitation information

Rainfall frequency analysis, which is an important tool in hydrologic engineering, has been traditionally performed using information from gauge observations. This approach has proven to be a useful tool in planning and design for the regions where sufficient observational data are available. However, in many parts of the world where ground-based observations are sparse and limited in length, the effectiveness of statistical methods for such applications is highly limited. The sparse gauge networks over those regions, especially over remote areas and high-elevation regions, cannot represent the spatiotemporal variability of extreme rainfall events and hence preclude developing depth-duration-frequency curves (DDF) for rainfall frequency analysis. In this study, the PERSIANN-CDR dataset is used to propose a mechanism, by which satellite precipitation information could be used for rainfall frequency analysis and development of DDF curves. In the proposed framework, we first adjust the extreme precipitation time series estimated by PERSIANN-CDR using an elevation-based correction function, then use the adjusted dataset to develop DDF curves. As a proof of concept, we have implemented our proposed approach in 20 river basins in the United States with different climatic conditions and elevations. Bias adjustment results indicate that the correction model can significantly reduce the biases in PERSIANN-CDR estimates of annual maximum series, especially for high elevation regions. Comparison of the extracted DDF curves from both the original and adjusted PERSIANN-CDR data with the reported DDF curves from NOAA Atlas 14 shows that the extreme percentiles from the corrected PERSIANN-CDR are consistently closer to the gauge-based estimates at the tested basins. The median relative errors of the frequency estimates at the studied basins were less than 20% in most cases. Our proposed framework has the potential for constructing DDF curves for regions with limited or sparse gauge-based observations using remotely sensed precipitation information, and the spatiotemporal resolution of the adjusted PERSIANN-CDR data provides valuable information for various applications in remote and high elevation areas