Multidimensional sparse recovery for MIMO channel parameter estimation

Multipath propagation is a common phenomenon in wireless communication. Knowledge of propagation path parameters such as complex channel gain, propagation delay or angle-of-arrival provides valuable information on the user position and facilitates channel response estimation. A major challenge in channel parameter estimation lies in its multidimensional nature, which leads to large-scale estimation problems which are difficult to solve. Current approaches of sparse recovery for multidimensional parameter estimation aim at simultaneously estimating all channel parameters by solving one large-scale estimation problem. In contrast to that we propose a sparse recovery method which relies on decomposing the multidimensional problem into successive one-dimensional parameter estimation problems, which are much easier to solve and less sensitive to off-grid effects, while providing proper parameter pairing. Our proposed decomposition relies on convex optimization in terms of nuclear norm minimization and we present an efficient implementation in terms of the recently developed STELA algorithm

Structural Analysis of Network Traffic Matrix via Relaxed Principal Component Pursuit

The network traffic matrix is widely used in network operation and management. It is therefore of crucial importance to analyze the components and the structure of the network traffic matrix, for which several mathematical approaches such as Principal Component Analysis (PCA) were proposed. In this paper, we first argue that PCA performs poorly for analyzing traffic matrix that is polluted by large volume anomalies, and then propose a new decomposition model for the network traffic matrix. According to this model, we carry out the structural analysis by decomposing the network traffic matrix into three sub-matrices, namely, the deterministic traffic, the anomaly traffic and the noise traffic matrix, which is similar to the Robust Principal Component Analysis (RPCA) problem previously studied in [13]. Based on the Relaxed Principal Component Pursuit (Relaxed PCP) method and the Accelerated Proximal Gradient (APG) algorithm, we present an iterative approach for decomposing a traffic matrix, and demonstrate its efficiency and flexibility by experimental results. Finally, we further discuss several features of the deterministic and noise traffic. Our study develops a novel method for the problem of structural analysis of the traffic matrix, which is robust against pollution of large volume anomalies.Comment: Accepted to Elsevier Computer Network

Detecting structural breaks in seasonal time series by regularized optimization

Real-world systems are often complex, dynamic, and nonlinear. Understanding the dynamics of a system from its observed time series is key to the prediction and control of the system's behavior. While most existing techniques tacitly assume some form of stationarity or continuity, abrupt changes, which are often due to external disturbances or sudden changes in the intrinsic dynamics, are common in time series. Structural breaks, which are time points at which the statistical patterns of a time series change, pose considerable challenges to data analysis. Without identification of such break points, the same dynamic rule would be applied to the whole period of observation, whereas false identification of structural breaks may lead to overfitting. In this paper, we cast the problem of decomposing a time series into its trend and seasonal components as an optimization problem. This problem is ill-posed due to the arbitrariness in the number of parameters. To overcome this difficulty, we propose the addition of a penalty function (i.e., a regularization term) that accounts for the number of parameters. Our approach simultaneously identifies seasonality and trend without the need of iterations, and allows the reliable detection of structural breaks. The method is applied to recorded data on fish populations and sea surface temperature, where it detects structural breaks that would have been neglected otherwise. This suggests that our method can lead to a general approach for the monitoring, prediction, and prevention of structural changes in real systems.Comment: Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures (Edited by George Deodatis, Bruce R. Ellingwood and Dan M. Frangopol), CRC Press 2014, Pages 3621-362

Physical Primitive Decomposition

Objects are made of parts, each with distinct geometry, physics, functionality, and affordances. Developing such a distributed, physical, interpretable representation of objects will facilitate intelligent agents to better explore and interact with the world. In this paper, we study physical primitive decomposition---understanding an object through its components, each with physical and geometric attributes. As annotated data for object parts and physics are rare, we propose a novel formulation that learns physical primitives by explaining both an object's appearance and its behaviors in physical events. Our model performs well on block towers and tools in both synthetic and real scenarios; we also demonstrate that visual and physical observations often provide complementary signals. We further present ablation and behavioral studies to better understand our model and contrast it with human performance.Comment: ECCV 2018. Project page: http://ppd.csail.mit.edu

A Generative Product-of-Filters Model of Audio

We propose the product-of-filters (PoF) model, a generative model that decomposes audio spectra as sparse linear combinations of "filters" in the log-spectral domain. PoF makes similar assumptions to those used in the classic homomorphic filtering approach to signal processing, but replaces hand-designed decompositions built of basic signal processing operations with a learned decomposition based on statistical inference. This paper formulates the PoF model and derives a mean-field method for posterior inference and a variational EM algorithm to estimate the model's free parameters. We demonstrate PoF's potential for audio processing on a bandwidth expansion task, and show that PoF can serve as an effective unsupervised feature extractor for a speaker identification task.Comment: ICLR 2014 conference-track submission. Added link to the source cod