Super-Linear Convergence of Dual Augmented-Lagrangian Algorithm for Sparsity Regularized Estimation

We analyze the convergence behaviour of a recently proposed algorithm for regularized estimation called Dual Augmented Lagrangian (DAL). Our analysis is based on a new interpretation of DAL as a proximal minimization algorithm. We theoretically show under some conditions that DAL converges super-linearly in a non-asymptotic and global sense. Due to a special modelling of sparse estimation problems in the context of machine learning, the assumptions we make are milder and more natural than those made in conventional analysis of augmented Lagrangian algorithms. In addition, the new interpretation enables us to generalize DAL to wide varieties of sparse estimation problems. We experimentally confirm our analysis in a large scale $\ell_1$-regularized logistic regression problem and extensively compare the efficiency of DAL algorithm to previously proposed algorithms on both synthetic and benchmark datasets.Comment: 51 pages, 9 figure

Fast Convergence Rate of Multiple Kernel Learning with Elastic-net Regularization

We investigate the learning rate of multiple kernel leaning (MKL) with elastic-net regularization, which consists of an $\ell_1$-regularizer for inducing the sparsity and an $\ell_2$-regularizer for controlling the smoothness. We focus on a sparse setting where the total number of kernels is large but the number of non-zero components of the ground truth is relatively small, and prove that elastic-net MKL achieves the minimax learning rate on the $\ell_2$-mixed-norm ball. Our bound is sharper than the convergence rates ever shown, and has a property that the smoother the truth is, the faster the convergence rate is.Comment: 21 pages, 0 figur

Dual Augmented Lagrangian Method for Efficient Sparse Reconstruction

We propose an efficient algorithm for sparse signal reconstruction problems. The proposed algorithm is an augmented Lagrangian method based on the dual sparse reconstruction problem. It is efficient when the number of unknown variables is much larger than the number of observations because of the dual formulation. Moreover, the primal variable is explicitly updated and the sparsity in the solution is exploited. Numerical comparison with the state-of-the-art algorithms shows that the proposed algorithm is favorable when the design matrix is poorly conditioned or dense and very large.Comment: 10 pages, 3 figure

Ultra-broadband surface-normal coherent optical receiver with nanometallic polarizers

A coherent receiver that can demodulate high-speed in-phase and quadrature signals of light is an essential component for optical communication, interconnects, imaging, and computing. Conventional waveguide-based coherent receivers, however, exhibit large footprints, difficulty in coupling a large number of spatial channels efficiently, and limited operating bandwidth imposed by the waveguide-based optical hybrid. Here, we present a surface-normal coherent receiver with nanometallic-grating-based polarizers integrated directly on top of photodetectors without the need for an optical hybrid circuit. Using a fabricated device with the active section occupying a 70-{\mu}m-square footprint, we demonstrate demodulation of high-speed (up to 64 Gbaud) coherent signals in various formats. Moreover, ultra-broadband operation from 1260 nm to 1630 nm is demonstrated, thanks to the wavelength-insensitive nanometallic polarizers. To our knowledge, this is the first demonstration of a surface-normal homodyne optical receiver, which can easily be scaled to a compact two-dimensional arrayed device to receive highly parallelized coherent signals.Comment: 23 pages, 4 figures (main manuscript) + 4 pages, 2 figures (supporting info

Approach for growth of high-quality and large protein crystals

Three crystallization methods, including crystallization in the presence of a semi-solid agarose gel, top-seeded solution growth (TSSG) and a large-scale hanging-drop method, have previously been presented. In this study, crystallization has been further evaluated in the presence of a semi-solid agarose gel by crystallizing additional proteins. A novel crystallization method combining TSSG and the large-scale hanging-drop method has also been developed