Structure Of Covariance Matrix Research Articles

Adaptive Detection of Radar Range-Doppler Dual-Spread Targets in Lognormal-Texture Clutter

This paper investigates the problem of adaptive detection of radar targets in non-Gaussian clutter, where the target to be detected is considered to behave the dual-spread in the Doppler frequency dimension and the range dimension. The clutter is assumed to follow the compound Gaussian model with lognormal texture and unknown covariance matrix structure. The multi-rank linear subspace model and the range-spread model are employed to depict the Doppler and range spread characteristics of target echoes. Then, the range-Doppler dual-spread adaptive radar target detector with lognormal-texture is proposed using the two-step generalized likelihood ratio criteria, which replaces the true values of the unknown parameters with their maximum likelihood and maximum a posteriori estimates. Experimental results on simulated and measured data demonstrate that the proposed detector shows superior performance in different clutter and target parameters compared to the competitors.

SEMbap: Bow-free covariance search and data de-correlation.

Large-scale studies of gene expression are commonly influenced by biological and technical sources of expression variation, including batch effects, sample characteristics, and environmental impacts. Learning the causal relationships between observable variables may be challenging in the presence of unobserved confounders. Furthermore, many high-dimensional regression techniques may perform worse. In fact, controlling for unobserved confounding variables is essential, and many deconfounding methods have been suggested for application in a variety of situations. The main contribution of this article is the development of a two-stage deconfounding procedure based on Bow-free Acyclic Paths (BAP) search developed into the framework of Structural Equation Models (SEM), called SEMbap(). In the first stage, an exhaustive search of missing edges with significant covariance is performed via Shipley d-separation tests; then, in the second stage, a Constrained Gaussian Graphical Model (CGGM) is fitted or a low dimensional representation of bow-free edges structure is obtained via Graph Laplacian Principal Component Analysis (gLPCA). We compare four popular deconfounding methods to BAP search approach with applications on simulated and observed expression data. In the former, different structures of the hidden covariance matrix have been replicated. Compared to existing methods, BAP search algorithm is able to correctly identify hidden confounding whilst controlling false positive rate and achieving good fitting and perturbation metrics.

End-to-end, decision-based, cardinality-constrained portfolio optimization

Portfolios employing a (factor) risk model are usually constructed using a two step process: first, the risk model parameters are estimated, then the portfolio is constructed. Recent works have shown that this decoupled approach may be improved using an integrated framework that takes the downstream portfolio optimization into account during parameter estimation. In this work we implement an integrated, end-to-end, predict-&-optimize framework to the cardinality-constrained portfolio optimization problem. To the best of our knowledge, we are the first to implement the framework to a nonlinear mixed integer programming problem. Since the feasible region of the problem is discontinuous, we are unable to directly differentiate through it. Thus, we compare three different continuous relaxations of increasing tightness to the problem which are placed as an implicit layers in a neural network. The parameters of the factor model governing the problem’s covariance matrix structure are learned using a loss function that directly corresponds to the decision quality made based on the factor model’s predictions. Using real world financial data, our proposed end-to-end, decision based model is compared to two decoupled alternatives. Results show significant improvements over the traditional decoupled approaches across all cardinality sizes and model variations while highlighting the need of additional research into the interplay between experimental design, problem size and structure, and relaxation tightness in a combinatorial setting.

Testing the hypothesis of a nested block covariance matrix structure with applications to medicine and natural sciences

This paper addresses the challenge of testing the hypothesis of what the authors call a nested block circular‐compound symmetric (NBCCS) covariance structure for the population covariance matrix. This is a covariance structure which has an outer block compound symmetric structure, where the diagonal blocks are themselves block circular matrices, while the off‐diagonal blocks are formed by all equal matrices. The NBCCS null hypothesis is decomposed into sub‐hypotheses, allowing this way for a simpler way to obtain a likelihood ratio test and its associated statistic. The exact moments of this statistic are derived, and its distribution is carefully examined. Given the complicated nature of this distribution, highly precise near‐exact distributions were developed. Numerical studies are conducted to assess the proximity between these near‐exact distributions and the exact distribution, highlighting the performance of these approximations, even in the case of very small sample sizes. Furthermore, three datasets, on bone mineral content, metabolic rates of glucose, and soil moisture are used to exemplify the practical application of the methodology derived in this study.

Adaptive detection of distributed targets in heterogeneous Gaussian clutter without secondary data

This paper addresses the problem of detecting distributed targets in heterogeneous Gaussian clutter without assuming the presence of secondary data. Specifically, the clutter is modeled as a spherically invariant random process with unknown texture components and covariance matrix structure (CMS). In contrast to existing approaches that are based on the estimate-and-plug techniques, we introduce an approximation of the generalized likelihood ratio test that leverages an alternating estimation procedure to obtain at least a local likelihood maximum. We also prove that the proposed method achieves the constant false alarm rate with respect to clutter parameters when appropriately initialized. Finally, a comprehensive performance analysis is carried out by Monte Carlo simulation and in comparison with the non-scatterer density dependent generalized likelihood ratio test (NSDD-GLRT) in the cases of known and unknown CMS. The results show that the proposed solution is more robust and effective than NSDD-GLRT when the CMS is unknown while exhibiting only a modest performance degradation with respect to the benchmark when the CMS is known.

Towards a new standard for seismic moment tensor inversion containing 3-D earth structure uncertainty

SUMMARY Moment tensor (MT) inversion is a classical geophysical inverse problem that infers a force-equivalent model of a seismic source from seismological observations. Like other inverse problems, the accuracy of the inversion depends on the reliability of the forward problem simulating waveforms from the source location through an Earth structural model. Apart from errors in data, the error in forward waveform simulation, also known as theory error, is a significant source of error contributing to the misfit function between the predicted and observed waveforms. Here, we set up numerical experiments to comprehensively probe the sensitivity of the linearized MT inversion to 3-D regional earth model errors, a known predominant factor of the theory error. Using the Monte Carlo method, we estimate the empirical structural covariance matrices to characterize the waveform mismatch due to the imperfect knowledge of Earth's structure. First, although the inversion accuracy deteriorates with increasing model errors, incorporating the structural covariance matrices into the misfit function improves the accuracy of inversion results for all theorized error distributions. Secondly, we propose a slightly modified form of the structural covariance matrix, which further enhances the inversion outcome. Lastly, as the true structural errors are likely spatially correlated, we highlight the importance of adequately treating the correlation into the MT inversion because of its significant impact on inversion. Overall, as a preliminary effort in quantifying 3-D structural errors on MT inversion, this study proves the computational feasibility by means of numerical experiments and will hopefully provide a way forward for future work on this topic.

An Adaptive Radar Target Detection Method Based on Alternate Estimation in Power Heterogeneous Clutter

Multichannel radars generally need to utilize a certain amount of training samples to estimate the covariance matrix of clutter for target detection. Due to factors such as severe terrain fluctuations and complex electromagnetic environments, the training samples usually have different statistical characteristics from the data to be detected. One of the most common scenarios is that all data have the same clutter covariance matrix structure, while different data have different power mismatches, called power heterogeneous characteristics. For detection problems in the power heterogeneous clutter environments, we propose detectors based on alternate estimation, using the generalized likelihood ratio test (GLRT) criterion, Rao criterion, Wald criterion, Gradient criterion, and Durbin criterion. Monte Carlo simulation experiments and real data indicate that the detector based on the Rao criterion has the highest probability of detection (PD). Furthermore, when signal mismatch occurs, the detector based on the GLRT criterion has the best selectivity, while the detector based on the Durbin criterion has the most robust detection performance.

Adaptive detectors for mismatched subspace target in clutter with lognormal texture

Due to factors such as array misalignment and waveform distortion, the target echo may not be precisely located within the nominal subspace in practical applications, resulting in mismatch issues. In response to this challenge, this paper investigates adaptive detection methods for detecting mismatched subspace targets amidst lognormal clutter background. To enhance the suppression of mismatched signal, we introduce a fictitious signal into the null hypothesis, which is situated within a subspace orthogonal to the nominal subspace in the whitened observation space. Following convention, we allow for the existence of a training dataset that shares the same covariance matrix (CM) structure as the main dataset. Subsequently, we propose two adaptive subspace detectors based on a two-step Generalized Likelihood Ratio Test (GLRT) and a two-step maximum a posteriori (MAP) GLRT. Both novel detectors have been validated to have constant false alarm rate (CFAR) properties for speckle CM. Numerical experiments are carried out using simulation data and measured sea clutter data, which demonstrate that our proposed methods exhibit robustness against non-mismatched signal and effective suppression of mismatches.

Clustering Mixed-Type Data via Dirichlet Process Mixture Model with Cluster-Specific Covariance Matrices

Many studies have shown successful applications of the Dirichlet process mixture model (DPMM) for clustering continuous data. Beyond continuous data, in practice, one can expect to see different data types, including ordinal and nominal data. Existing DPMMs for clustering mixed-type data assume a strict covariance matrix structure, resulting in an overfit model. This article explores a DPMM for mixed-type data that allows the covariance matrix to differ from one cluster to another. We assume an underlying latent variable framework for ordinal and nominal data, which is then modeled jointly with the continuous data. The identifiability issue on the covariance matrix poses computational challenges, thus requiring a nonstandard inferential algorithm. The applicability and flexibility of the proposed model are illustrated through simulation examples and real data applications.

Joint regression analysis of multiple traits based on genetic relationships.

Polygenic scores (PGSs) are widely available and employed in genomic data analyses for predicting and understanding genetic architectures. Existing approaches either require information on SNP level, do not infer clusters of traits sharing genetic characteristic, or do not have any immediate predictive properties. Here, we present geneJAM, which is a novel clustering and estimation method using PGSs for inferring a genetic relationship among multiple, simultaneously measured and potentially correlated traits in a multivariate GWAS.Using graphical lasso, we estimate a sparse covariance matrix of the PGSs and obtain clusters of traits sharing genetic characteristics. We use the clusters to specify the structure of the error covariance matrix of a generalized least squares (GLS) model and use the feasible GLS estimator for estimating a linear regression model with a certain unknown degree of correlation between the residuals.The method suits many biology studies well with traits embedded in some genetic functioning groups and facilitates development of the PGS research. We compare the method with fully parametric techniques on simulated data and illustrate the utility of the methods by examining a heterogeneous stock mouse data set from the Wellcome Trust Centre for Human Genetics. We demonstrate that the method successfully identifies clusters of traits and increases precision, power, and computational efficiency. GeneJAM is implemented in R and available at: https://github.com/abuchardt/geneJAM.

A Low‐Complexity Expectation Propagation Detector for OTFS

In this paper, we propose a low‐complexity expectation propagation (EP) detector for orthogonal time frequency space (OTFS) system with practical rectangular waveforms. In the high‐mobility scenario, OTFS is becoming a potential scheme for the sixth‐generation (6G) wireless communication system. However, the large size of the effective delay‐Doppler (DD) domain channel matrix brings unbearable computational complexity to the signal detection algorithm based on the matrix inversion. We propose a low‐complexity EP detector based on the sparsity and the block circulant structure of the effective channel covariance matrix in the DD domain. The proposed algorithm only requires log‐linear complexity. In addition, simulation results show that the proposed algorithm not only has the advantage of low complexity but also has good performance, which achieves a tradeoff between performance and complexity.

A new test for detecting specification errors in Gaussian linear mixed-effects models

<p>Linear mixed-effects models (LMEMs) are widely used in medical, engineering, and social applications. The accurate specification of the covariance matrix structure within the error term is known to impact the estimation and inference procedures. Thus, it is crucial to detect the source of errors in LMEMs specifications. In this study, we propose combining a user-friendly computational test with an analytical method to visualize the source of errors. Through statistical simulations under different scenarios, we evaluate the performance of the proposed test in terms of the Power and Type I error rate. Our findings indicate that as the sample size $ n $ increases, the proposed test effectively detects misspecification in the systematic component, the number of random effects, the within-subject covariance structure, and the covariance structure of the error term in the LMEM with high Power while maintaining the nominal Type I error rate. Finally, we show the practical usefulness of our proposed test with a real-world application.</p>

Discrepancy between structured matrices in the power analysis of a separability test

An important task in the analysis of multivariate data is testing of the covariance matrix structure. In particular, for assessing separability, various tests have been proposed. However, the development of a method of measuring discrepancy between two covariance matrix structures, in relation to the study of the power of the test, remains an open problem. Therefore, a discrepancy measure is proposed such that for two arbitrary alternative hypotheses with the same value of discrepancy, the power of tests remains stable, while for increasing discrepancy the power increases. The basic hypothesis is related to the separable structure of the observation matrix under a doubly multivariate normal model, as assessed by the likelihood ratio and Rao score tests. It is shown that the particular one-parameter method and the Frobenius norm fail in the power analysis of tests, while the entropy and quadratic loss functions can be efficiently used to measure the discrepancy between separable and non-separable covariance structures for a multivariate normal distribution.

Regularized estimation of Kronecker structured covariance matrix using modified Cholesky decomposition

In this paper, we study a Kronecker structured model for covariance matrices when data are matrix-valued. Using the modified Cholesky decomposition for Kronecker structured covariance matrix, we propose a regularized covariance estimator by imposing shrinkage and smoothing penalties on the Cholesky factors. A regularized flip-flop (RFF) algorithm is developed to produce a statistically efficient estimator for a large covariance matrix of matrix-valued data. Asymptotic properties are investigated and the performance of the estimator is evaluated by simulations. The results presented are applied to real data example.

Estimation methods for a linearly structured covariance matrix

Summary Covariance matrices with a linear structure are widely used in multivariate analysis. The choice of the most appropriate covariance structure can be made from a class of possible linear structures. Once we have made the choice, an important question is how we can estimate the covariance matrix for a given covariance structure. This article describes methods used to estimate the structured covariance matrix, and indicates the advantages and disadvantages of the selected methods.

Structure identification for a linearly structured covariance matrix: part II

Summary Covariance matrices with a linear structure are widely used in multivariate analysis. The choice of covariance structure can be made from a set of possible linear structures. As a result, the most appropriate structure is determined by minimizing the discrepancy function. This paper is a continuation of previous work on identifying linear structures with an entropy loss function as a discrepancy function. We present extensive simulation studies on the correctness of identification with the assumed pentagonal banded Toeplitz structure.

Estimation of clutter covariance matrix in stap based on knowledge-aided and geometric methods

The insufficient number of available samples can cause inaccurate estimation of the clutter covariance matrix (CCM) in space-time adaptive processing (STAP), resulting in degraded clutter suppression performance. To tackle this problem, a CCM estimation approach based on knowledge-aided (KA) and geometric methods is proposed in this paper. A combination of environmental as well as structural (Persymmetric or Symmetric structure) knowledge information is utilized to model the covariance matrix of each sample as a knowledge-aided Hermitian positive definite (KA-HPD) covariance matrix. The estimation problem is introduced into the Riemannian manifold composed of the KA-HPD covariance matrices, and the geometric method is used for nonlinear processing. Based on the Kullback-Leibler (KL) divergence and the KL mean, the final estimated CCM is designed as a weighted combination of each KA-HPD covariance matrix. Experiment results show that the two designed structural covariance matrix estimators possess superior clutter suppression performance.

Non-stationary astrophysical stochastic gravitational-wave background: a new probe to the high-redshift population of binary black holes

ABSTRACTThe astrophysical stochastic gravitational-wave background (SGWB) originates from the mergers of compact binary objects that are otherwise undetected as individual events, along with other sources such as supernovae, magnetars, etc. The individual gravitational-wave (GW) signal is time-varying over a time-scale that depends on the chirp mass of the coalescing binaries. Another time-scale that plays a role is the time-scale at which the sources repeat, which depends on the merger rate. The combined effect of these two leads to a breakdown of the time translation symmetry of the observed SGWB and a correlation between different frequency modes in the signal covariance matrix of the SGWB. Using an ensemble of SGWB due to binary black hole coalescence, calculated using simulations of different black hole mass distributions and merger rates, we show how the structure of the signal covariance matrix varies. This structure in the signal covariance matrix brings additional information about the sources on top of the power spectrum. We show that there is a significant improvement in the figure of merit by using this additional information in comparison to only power spectrum estimation for the LIGO–Virgo–KAGRA (LVK) network of detectors with the design sensitivity noise with 2 yr of observation. The inclusion of the off-diagonal correlation in the covariance of the SGWB in the data analysis pipelines will be beneficial in the quest for the SGWB signal in LVK frequency bands as well as in lower frequencies and in getting an insight into its origin.

A novel sparse recovery‐based space‐time adaptive processing algorithm based on gridless sparse Bayesian learning for non‐sidelooking airborne radar

AbstractNon‐sidelooking airborne radar encounters significant non‐stationary and heterogeneous clutter environments, resulting in a severe shortage of samples. Sparse recovery‐based space‐time adaptive processing (SR‐STAP) methods can achieve good clutter suppression performance with limited samples. Nonetheless, grid‐based SR‐STAP algorithms encounter off‐grid effects in non‐sidelooking arrays, which can severely degrade the clutter suppression performance. In this study, the authors propose a novel gridless SR‐STAP method in the continuous spatial‐temporal domain to address the issue of off‐grid effects. Inspired by the fact that sparse Bayesian learning (SBL) framework implicitly performs a structured covariance matrix estimation, the authors reparameterise its cost function to directly estimate the block‐Toeplitz structured matrix from the measurements in a gridless manner. Since the proposed cost function is non‐convex, we utilise a majorisation‐minimisation‐based iterative procedure to estimate the clutter covariance matrix. Finally, using the standard concept of semidefinite programming, the authors derive a convex gridless implementation of the SBL cost function for uniformly sampled radar systems. Extensive simulation experiments demonstrate the exceptional clutter suppression and target detection performance of the proposed algorithm.

Persymmetric Structured Covariance Matrix Estimation Based on Whitening for Airborne STAP

Persymmetric Structured Covariance Matrix Estimation Based on Whitening for Airborne STAP