Approximate message passing for nonconvex sparse regularization with stability and asymptotic analysis

We analyse a linear regression problem with nonconvex regularization called smoothly clipped absolute deviation (SCAD) under an overcomplete Gaussian basis for Gaussian random data. We propose an approximate message passing (AMP) algorithm considering nonconvex regularization, namely SCAD-AMP, and analytically show that the stability condition corresponds to the de Almeida--Thouless condition in spin glass literature. Through asymptotic analysis, we show the correspondence between the density evolution of SCAD-AMP and the replica symmetric solution. Numerical experiments confirm that for a sufficiently large system size, SCAD-AMP achieves the optimal performance predicted by the replica method. Through replica analysis, a phase transition between replica symmetric (RS) and replica symmetry breaking (RSB) region is found in the parameter space of SCAD. The appearance of the RS region for a nonconvex penalty is a significant advantage that indicates the region of smooth landscape of the optimization problem. Furthermore, we analytically show that the statistical representation performance of the SCAD penalty is better than that of L1-based methods, and the minimum representation error under RS assumption is obtained at the edge of the RS/RSB phase. The correspondence between the convergence of the existing coordinate descent algorithm and RS/RSB transition is also indicated

A Prediction-Based Replication Algorithm for Improving Data Availability in Frid Environment

Data replication is a key optimization technique for reducing access latency and managing large data by storing replica of data in a wisely manner. In this paper, we propose a data replication algorithm, called the Prediction-Base Dynamic Replication (PBDR) algorithm that improves file access time. Restricted by the storage capacity, it is essential to design an effective strategy for the replication replacement task. PBDR deletes files by considering four important factors: the number of requests for the replica in the future times, availability, the size of the replica and the last time the replica was requested. Also, it can minimize access latency by selecting the best replica when various sites hold replicas of datasets. The algorithm is simulated using a data grid simulator, OptorSim, developed by European Data Grid projects. The experiment results show that PBDR strategy gives better performance compared to the other algorithms and prevents unnecessary creation of replica which leads to efficient storage usage

3D Point Capsule Networks

In this paper, we propose 3D point-capsule networks, an auto-encoder designed to process sparse 3D point clouds while preserving spatial arrangements of the input data. 3D capsule networks arise as a direct consequence of our novel unified 3D auto-encoder formulation. Their dynamic routing scheme and the peculiar 2D latent space deployed by our approach bring in improvements for several common point cloud-related tasks, such as object classification, object reconstruction and part segmentation as substantiated by our extensive evaluations. Moreover, it enables new applications such as part interpolation and replacement.Comment: As published in CVPR 2019 (camera ready version), with supplementary materia

3D Point Capsule Networks

In this paper, we propose 3D point-capsule networks, an auto-encoder designed to process sparse 3D point clouds while preserving spatial arrangements of the input data. 3D capsule networks arise as a direct consequence of our novel unified 3D auto-encoder formulation. Their dynamic routing scheme and the peculiar 2D latent space deployed by our approach bring in improvements for several common point cloud-related tasks, such as object classification, object reconstruction and part segmentation as substantiated by our extensive evaluations. Moreover, it enables new applications such as part interpolation and replacement

The Sampling Rate-Distortion Tradeoff for Sparsity Pattern Recovery in Compressed Sensing

Recovery of the sparsity pattern (or support) of an unknown sparse vector from a limited number of noisy linear measurements is an important problem in compressed sensing. In the high-dimensional setting, it is known that recovery with a vanishing fraction of errors is impossible if the measurement rate and the per-sample signal-to-noise ratio (SNR) are finite constants, independent of the vector length. In this paper, it is shown that recovery with an arbitrarily small but constant fraction of errors is, however, possible, and that in some cases computationally simple estimators are near-optimal. Bounds on the measurement rate needed to attain a desired fraction of errors are given in terms of the SNR and various key parameters of the unknown vector for several different recovery algorithms. The tightness of the bounds, in a scaling sense, as a function of the SNR and the fraction of errors, is established by comparison with existing information-theoretic necessary bounds. Near optimality is shown for a wide variety of practically motivated signal models

Replica Creation Algorithm for Data Grids

Data grid system is a data management infrastructure that facilitates reliable access and sharing of large amount of data, storage resources, and data transfer services that can be scaled across distributed locations. This thesis presents a new replication algorithm that improves data access performance in data grids by distributing relevant data copies around the grid. The new Data Replica Creation Algorithm (DRCM) improves performance of data grid systems by reducing job execution time and making the best use of data grid resources (network bandwidth and storage space). Current algorithms focus on number of accesses in deciding which file to replicate and where to place them, which ignores resources’ capabilities. DRCM differs by considering both user and resource perspectives; strategically placing replicas at locations that provide the lowest transfer cost. The proposed algorithm uses three strategies: Replica Creation and Deletion Strategy (RCDS), Replica Placement Strategy (RPS), and Replica Replacement Strategy (RRS). DRCM was evaluated using network simulation (OptorSim) based on selected performance metrics (mean job execution time, efficient network usage, average storage usage, and computing element usage), scenarios, and topologies. Results revealed better job execution time with lower resource consumption than existing approaches. This research contributes replication strategies embodied in one algorithm that enhances data grid performance, capable of making a decision on creating or deleting more than one file during same decision. Furthermore, dependency-level-between-files criterion was utilized and integrated with the exponential growth/decay model to give an accurate file evaluation

Composite CDMA - A statistical mechanics analysis

Code Division Multiple Access (CDMA) in which the spreading code assignment to users contains a random element has recently become a cornerstone of CDMA research. The random element in the construction is particular attractive as it provides robustness and flexibility in utilising multi-access channels, whilst not making significant sacrifices in terms of transmission power. Random codes are generated from some ensemble, here we consider the possibility of combining two standard paradigms, sparsely and densely spread codes, in a single composite code ensemble. The composite code analysis includes a replica symmetric calculation of performance in the large system limit, and investigation of finite systems through a composite belief propagation algorithm. A variety of codes are examined with a focus on the high multi-access interference regime. In both the large size limit and finite systems we demonstrate scenarios in which the composite code has typical performance exceeding sparse and dense codes at equivalent signal to noise ratio.Comment: 23 pages, 11 figures, Sigma Phi 2008 conference submission - submitted to J.Stat.Mec