Polynomials orthogonal on the unit circle

In the past decade, sparse and low-rank recovery has drawn much attention in many areas such as signal/image processing, statistics, bioinformatics, and machine learning. To achieve sparsity and/or low-rankness inducing, the $\ell _{1}$ norm and nuclear norm are of the most popular regularization penalties due to their convexity. While the $\ell _{1}$ and nuclear norm are convenient as the related convex optimization problems are usually tractable, it has been shown in many applications that a nonconvex penalty can yield significantly better performance. In recent, nonconvex regularization-based sparse and low-rank recovery is of considerable interest and it in fact is a main driver of the recent progress in nonconvex and nonsmooth optimization. This paper gives an overview of this topic in various fields in signal processing, statistics, and machine learning, including compressive sensing, sparse regression and variable selection, sparse signals separation, sparse principal component analysis (PCA), large covariance and inverse covariance matrices estimation, matrix completion, and robust PCA. We present recent developments of nonconvex regularization based sparse and low-rank recovery in these fields, addressing the issues of penalty selection, applications and the convergence of nonconvex algorithms. Code is available at https://github.com/FWen/ncreg.git .

A Survey on Nonconvex Regularization-Based Sparse and Low-Rank Recovery in Signal Processing, Statistics, and Machine Learning

This paper addresses the problem of obtaining an estimate of a particular module of interest that is embedded in a dynamic network with known interconnection structure. In this paper it is shown that there is considerable freedom as to which variables can be included as inputs to the predictor, while still obtaining consistent estimates of the particular module of interest. This freedom is encoded into sufficient conditions on the set of predictor inputs that allow for consistent identification of the module. The conditions can be used to design a sensor placement scheme, or to determine whether it is possible to obtain consistent estimates while refraining from measuring particular variables in the network. As identification methods the Direct and Two Stage Prediction-Error methods are considered. Algorithms are presented for checking the conditions using tools from graph theory.

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Identification of Dynamic Models in Complex Networks With Prediction Error Methods: Predictor Input Selection

Sparse network identifiability via Compressed Sensing

https://hal.archives-ouvertes.fr/hal-01355011/document

Errors-in-variables identification in dynamic networks - Consistency results for an instrumental variable approach

http://www.cell.com/article/S1535610822002744/pdf

Pan-cancer proteomic map of 949 human cell lines

This paper addresses the problem of identifying the topology of a sparsely connected network of dynamic systems. The goal is to identify the links, the direction of information flow and the transfer function of each dynamic system. The output of each system is affected by the incoming data of the directly connected systems and noise. In contrast to the related existing work we use causal Laguerre basis functions to expand the transfer functions. Since the network is sparsely connected we estimate the system topology using an algorithm which optimizes the l 0 penalized least squares criterion with grouped variables. This also contrasts with previous work which usually uses and l 1 penalty. The l 0 penalty has the potential to generate greater sparsity. We present simulation results to demonstrate the effectiveness of this method.

Topology identification of a sparse dynamic network

The scalar sparse under-determined linear regression problem has had a rapid development with the multivariate version being of more recent interest. In this paper we pose a vector l0 penalized multivariate regression problem to generate coefficient vectors with shared sparsity profile and then solve the problem with a new cyclic descent algorithm. We give optimality conditions and also discuss penalty parameter selection. Finally we present simulation results that compare our algorithm with alternatives.

On vector L0 penalized multivariate regression

The distributed source inverse problem for Magnetoencephalography (MEG) requires regularisation in order to calculate a stable and accurate solution. Recently there has been interest in source reconstruction via the l 1 penalised least squares problem. Although this gives some sparseness the ideal measure for sparsity is the l 0 norm. Here we develop a cyclic descent algorithm to solve the grouped-variable l 0 penalised least squares problem for an underdetermined linear system. We demonstrate the utility of this method on real MEG data and show an increase in sparsity achieved using the l 0 instead of the l 1 penalty.

Grouped L 0 least squares penalised Magnetoencephalography

Motivation The output of electrospray ionisation - liquid chromatography mass spectrometry (ESI-LC-MS) is influenced by multiple sources of noise and major contributors can be broadly categorised as baseline, random and chemical noise. Noise has a negative impact on the identification and quantification of peptides, which influences the reliability and reproducibility of MS-based proteomics data. Most attempts at denoising have been made on either spectra or chromatograms independently, thus important two-dimensional information is lost because the mass-to-charge ratio and retention time dimensions are not considered jointly. Results This paper presents a novel technique for denoising raw ESI-LC-MS data via two-dimensional undecimated wavelet transform, which is applied to proteomics data acquired by data-independent acquisition MS (DIA-MS). We demonstrate that denoising DIA-MS data results in the improvement of peptide identification and quantification in complex biological samples. Availability The software is available on Github (https://github.com/CMRI-ProCan/CRANE). The datasets were obtained from ProteomeXchange (Identifiers-PXD002952 and PXD008651). Preliminary data and intermediate files are available via ProteomeXchange (Identifiers-PXD020529 and PXD025103). Supplementary information Supplementary information is available at Bioinformatics online.

Akila J. Seneviratne

Papers

Pan-cancer proteomic map of 949 human cell lines

Topology identification of a sparse dynamic network

On vector L0 penalized multivariate regression

Grouped L 0 least squares penalised Magnetoencephalography

Improved identification and quantification of peptides in mass spectrometry data via chemical and random additive noise elimination (CRANE).