Inverse Of Correlation Matrix Research Articles

Решение оптимизационной задачи оценивания моделей полносвязной линейной регрессии

<p>This article is devoted to the problem of estimating fully connected linear regression models using the maximum likelihood method. Previously, a special numerical method was developed for this purpose, based on solving a nonlinear system using the method of simple iterations. At the same time, the issues of choosing initial approximations and fulfilling sufficient conditions for convergence were not studied. This article proposes a new method for solving the optimization problem of estimating fully connected regressions, similar to the method of estimating orthogonal regressions. It has been proven that, with equal error variances of interconnected variables, estimates of b-parameters of fully connected regression are equal to the components of the eigenvector corresponding to the smallest eigenvalue of the inverse covariance matrix. And if the ratios of the error variances of the variables are equal to the ratios of the variances of the variables, then the b-parameter estimates are equal to the components of the eigenvector corresponding to the smallest eigenvalue of the inverse correlation matrix, multiplied by the specific ratios of the standard deviations of the variables. A numerical experiment was carried out to confirm the correctness of the developed mathematical apparatus. The proposed method for solving the optimization problem of estimating fully connected regressions can be effectively used when solving problems of constructing multiple fully connected linear regressions.</p>

Enhanced Kriging leave-one-out cross-validation in improving model estimation and optimization

Leave-one-out cross-validation (LOOCV) is a widely used technique in model estimation and selection of the Kriging surrogate model for engineering problems, such as structural optimization and reliability analysis. However, the traditional LOOCV method has some disadvantages in terms of accuracy and efficiency. This paper proposes an enhanced-LOOCV method that incorporates hyperparameters from the Kriging model based on the complete training dataset (i.e., the complete Kriging model) into the LOOCV error calculation. By keeping the model hyperparameters in LOOCV consistent with the complete Kriging model, it reduces the number of hyperparameter optimizations and significantly increases the accuracy and efficiency of the LOOCV process. Additionally, a decremental calculation is proposed to reduce the computational costs of the correlation matrix inversion without sacrificing accuracy, resulting in an improved time complexity of the traditional LOOCV from O(n4) to O(n3). Experimental results with thirty test functions verify that the enhanced-LOOCV has better estimation performance than the Kriging model with significantly higher efficiency compared to the traditional LOOCV. Numerical experiments and an engineering case in optimization demonstrate that the enhanced-LOOCV can reduce the number of samples needed for infilling in the Kriging model, and it is more suitable for expensive optimizations in engineering.

Developing a New Filtered-X Recursive Least Squares Adaptive Algorithm Based on a Robust Objective Function for Impulsive Active Noise Control Systems

It is well-known that performance of the classical algorithms for active noise control (ANC) systems severely degrades when implemented for controlling the impulsive sources. The objective of this paper is to propose a new recursive least squares (RLS) algorithm (and its variant) for being implemented in the framework of ANC systems. The proposed RLS-based adaptive algorithm employs an objective function designed to achieve robustness against the impulse type sources. The derivation of the algorithm is quite straightforward; however, a few modifications have been incorporated to address the application at hand. In order to improve upon the numerical stability issue of RLS-based adaptation, it is suggested to employ smoothing while updating the inverse correlation matrix. Furthermore, it is proposed to introduce a step size in the update equation of the adaptive algorithm. This results in the fixed step-size modified filtered-x (MFx) robust RLS (FSS-MFxRRLS) algorithm. As expected, a fixed value step size results in a trade-off situation for convergence speed and steady-state misalignment. In order to address this issue of a trade-off situation, the idea of a convex combined step size (CCSS) is introduced into the adaptive procedure to develop the CCSS-MFxRRLS algorithm. When the ANC is started, the CCSS strategy (automatically) selects a large-valued step size to achieve a fast initial convergence. As the ANC system converges at the steady-state, the CCSS is automatically tuned to a small value which improves the steady-state performance of the proposed CCSS-MFxRRLS algorithm. Extensive simulations have been designed to mimic many scenarios for practical applications of ANC for impulsive sources. The simulation results demonstrate that the proposed CCSS-MFxRRLS algorithm is very effective in many practical scenarios involving ANC of impulsive sources.

Optimal data processing in the ballistic laser gravimeter under the effect of correlated interference

Abstract
 In order to develop optimal data processing algorithms in ballistic laser gravimeters under the effect of correlated interference, the method of generalized least squares is applied. In this case, to describe the interference, a mathematical model of the autoregression process is used, for which the inverse correlation matrix has a band type and is expressed through the values of the autoregression coefficients. To convert the “path-time” data from the output of the coincidence circuit of ballistic laser gravimeters to a process uniform in time, their local quadratic interpolation is used.
 Algorithms for data processing in a ballistic gravimeter, developed on the basis of a method of weighted least squares using orthogonal Hahn polynomials, are considered. To implement a symmetric measurement method, the symmetric Hahn polynomials, characterized by one parameter, are used.
 The method of mathematical modelling is used to study the gain in the accuracy of measuring the gravitational acceleration by the synthesized algorithms in comparison with the algorithm based on the method of least squares. It is shown that auto seismic interference in ballistic laser gravimeters with a symmetric measurement method can be significantly reduced by using a mathematical model of the second-order autoregressive process in the method of generalized least squares. A comparative analysis of the characteristics of the algorithms developed using the method of generalized least squares, the method of weighted least squares and the method of ordinary least squares is carried out.

A Meta-Theoretical Approach into the Determinants of Internal Psychological Resources for Entrepreneurs

This study, which was conducted in the context of a Small Island Developing state economy, adopts exploratory, meta-theoretical, and inter-disciplinary stances to examine determinants of internal psychological resources for entrepreneurs. It contributes to existing literature and methodology through its innovative interdisciplinary theoretical framework and the use of Exploratory Factor Analysis (EFA) in the field of entrepreneurship. Questionnaires were randomly distributed among 711 entrepreneurs, of which 539 were deemed useful for analytical purposes. EFA was used to identify factors that determine fundamental internal psychological resources for entrepreneurs. The Kaiser-Meyer Olkin coefficient of 0.85 justified the sample size for the use of EFA. The highly significant Barlett’s test (p<0.0001) showed the presence of adequately correlated items to form clusters. A coefficient of 0.00033 on the inverse of correlation matrix ruled out the possibility of multicollinearity issues among the six key EFA constructs of internal psychological resources for entrepreneurs. Inner Strength which originates from the field of medicine is surprisingly revealed as the leading internal psychological resource valued by entrepreneurs, followed by Entrepreneurial Aspirations, Entrepreneurial Alertness, Entrepreneurial Orientation, Self-leadership, and Risk Orientation. Two other concepts (Psychological capital and Sense of Coherence) which were initially included in the theoretical framework were eliminated during the EFA because the Scree plot did not support their retention and contributed to multicollinearity issues. This study has several practical and policy implications which will enable governments and entrepreneurs to contribute more effectively and more accurately to the entrepreneurial process.

Information loss resulting from statistical disclosure control of output data

The most important methods of assessing information loss caused by statistical disclosure control (SDC) are presented in the paper. The aim of SDC is to protect an individual against identification or obtaining any sensitive information relating to them by anyone unauthorised. The application of methods based either on the concealment of specific data or on their perturbation results in information loss, which affects the quality of output data, including the distributions of variables, the forms of relationships between them, or any estimations. The aim of this paper is to perform a critical analysis of the strengths and weaknesses of the particular types of methods of assessing information loss resulting from SDC. Moreover, some novel ideas on how to obtain effective and well-interpretable measures are proposed, including an innovative way of using a cyclometric function (arcus tangent) to determine the deviation of values from the original ones, as a result of SDC. Additionally, the inverse correlation matrix was applied in order to assess the influence of SDC on the strength of relationships between variables. The first presented method allows obtaining effective and well- -interpretable measures, while the other makes it possible to fully use the potential of the mutual relationships between variables (including the ones difficult to detect by means of classical statistical methods) for a better analysis of the consequences of SDC. Among other findings, the empirical verification of the utility of the suggested methods confirmed the superiority of the cyclometric function in measuring the distance between the curved deviations and the original data, and also heighlighted the need for a skilful correction of its flattening when large value arguments occur.

Regularized Dawid–Sebastiani score for multivariate ensemble forecasts

AbstractThe Dawid–Sebastiani score (DSS) is a theoretically attractive tool for evaluating the accuracy of multivariate ensemble forecasts, wherein each ensemble member produces a vector of forecasts. It has been little used to date mostly because its computation requires calculation and inversion of the ensemble covariance matrix for each forecast occasion. These matrices are not invertible unless the ensemble size is larger than the dimension of the forecast vectors. Moreover, these matrices are poorly estimated unless the ensemble size is quite large relative to the dimension of the vectors. This article describes application to the inverse correlation matrix in the DSS of a relatively recently developed regularization procedure called the graphical lasso (“glasso”), which not only suppresses the sampling variability of the score for relatively small ensemble sizes but also allows its computation even when the ensemble size is smaller than the dimension of the forecast and observation vectors. Use of glasso regularization with the DSS, and its performance in comparison to the Energy Score and the Variogram Score, are illustrated using a novel statistical model for multivariate ensemble forecasts which allows separate manipulation of bias, univariate calibration, multivariate calibration, and multivariate correlation characteristics.

Забезпечення завадозахищеності приймачів сигналів GNSS шляхом використання алгоритмів просторової фільтрації

Здійснюється оцінка потрібного рівня радіо-електронного захисту приймачів сигналів супутникових радіонавігаційних систем (СРНС), що забезпечують застосування наземних платформ озброєння та військової техніки, з урахуванням можливого радіоелектронного подавлення з боку противника. Розглядається адаптивний алгоритм просторової фільтрації сигналів СРНС в умовах впливу спеціально організованих завад з боку противника, побудований на основі рекурентного методу формування оцінки зворотної кореляційної матриці. На основі даного алгоритму створюється модель функціонування завадозахищеного приймача сигналів СРНС в умовах впливу активних завад. За допомогою створеної моделі оцінюється ефективність функціонування завадозахищеного приймача сигналів СРНС в умовах радіоелектронного подавлення.

Enhancing noise performance of decorrelator detectors in multiuser systems using pulse position modulation signature codes

Multiuser systems suffer from multiple access interference (MAI) due to the correlations between users signature codes. The decorrelator detector uses the inverse correlation matrix of the signature codes to eliminate the MAI. The major disadvantage of the decorrelator detector is the enhancement of the noise power at its outputs as mentioned in many previous works. This statement is not always true for non-orthogonal correlation matrix. The decorrelator detector can reduce the noise power at its outputs at certain conditions for non-orthogonal correlation matrix. If the sum of the eigenvalues of the non-orthogonal correlation matrix is greater than the sum of the eigenvalues of its inverse, the decorrelator detector will not enhance the noise power at its output. Moreover, the exponential of the determinant of the correlation matrix should be greater than the exponential of the determinant of its inverse. These two conditions are presented and proved in this work. A new family of signatures codes is also proposed to match the proposed conditions for the correlation matrix. The new signature codes are based on pulse position modulation (PPM). The paper shows that the new codes have three degrees of freedom to change the correlation coefficients between them.

Big Data in Portfolio Allocation: A New Approach to Successful Portfolio Optimization

In the classic mean-variance portfolio theory as proposed by Harry Markowitz, the weights of the optimized portfolios are directly proportional to the inverse of the asset correlation matrix. However, most contemporary portfolio optimization research focuses on optimizing the correlation matrix itself, and not its inverse. In this article, the author demonstrates that this is a mistake. Specifically, from the Big Data perspective, she proves that the inverse of the correlation matrix is much more unstable and sensitive to random perturbations than is the correlation matrix itself. As such, optimization of the inverse of the correlation matrix adds more value to optimal portfolio selection than does optimization of the correlation matrix. The author further shows the empirical results of portfolio reallocation under different common portfolio composition scenarios. The technique outperforms traditional portfolio allocation techniques out of sample, delivering nearly 400% improvement over the equally weighted allocation over a 20-year investment period on the S&P 500 portfolio with monthly reallocation. In general, the author demonstrates that the correlation inverse optimization proposed in this article significantly outperforms the other core portfolio allocation strategies, such as equally weighted portfolios, vanilla mean-variance optimization, and techniques based on the spectral decomposition of the correlation matrix. The results presented in this article are novel in the data science space, extend far beyond financial data, and are applicable to any data correlation matrixes and their inverses, whether in advertising, healthcare, or genomics.

Big Data in Portfolio Allocation

In the classic mean-variance portfolio theory as proposed by Harry Markowitz, the weights of the optimized portfolios are directly proportional to the inverse of the asset correlation matrix. However, most of contemporary portfolio optimization research focuses on optimizing the correlation matrix itself, and not its inverse. In this article, the author demonstrates that this is a mistake. Specifically, from the Big Data perspective, she proves that the inverse of the correlation matrix is much more unstable and sensitive to random perturbations than the correlation matrix itself. As such, optimization of the inverse of the correlation matrix adds more value to optimal portfolio selection than that of the correlation matrix. The author further shows the empirical results of portfolio reallocation under different common portfolio composition scenarios, and outperforms traditional portfolio allocation techniques out-of-sample, delivering nearly 400% improvement over the equally-weighted allocation over a 20-year investment period on the S&P 500 portfolio with monthly reallocation. In general, the author demonstrates that the correlation inverse optimization proposed in this article significantly outperforms the other core portfolio allocation strategies, such as equally-weighted portfolios, vanilla mean-variance optimization, and the techniques based on the spectral decomposition of the correlation matrix. The results presented in this article are novel in Data Science space, extend far beyond financial data, and are applicable to any data correlation matrices and their inverses, whether in advertising, healthcare or genomics.

Enhanced RLS in Smart Antennas for Long Range Communication Networks

The utilisation of smart antenna (SA) techniques in future wireless and cellular networks is expected to have an impact on the efficient use of the spectrum and the optimization of service quality. This is because SAs can enhance the maximization of output power of the signal in desired directions amongst a whole lot of functions. Despite these benefits of SAs, long range communications still face unsolved challenges such as signal fading. Therefore, this paper focuses on enhancing the recursive least squares (RLS) in SA design for long range communication networks. The conventional RLS algorithm does not need any matrix inversion computations because the inverse correlation matrix is determined directly. Therefore, the RLS saves computational power. Hence, we have enhanced the RLS algorithm by introducing a constant m to the gain factor in order to yield an improved gain vector. Results from our simulations show that the enhanced RLS reduces mean square error (MSE), smoothens filter output and improves signal-to-noise ratio (SNR). These benefits further result in the antenna’s gain improvement leading to an increased range and directivity of the smart antenna over a long range communication networks.

Імпульсна характеристика адаптивної антени мережевих супутникових систем для оцінки кореляційної матриці перешкоди

Мета: На основі просторової фільтрації запропонувати метод прямого обчислення зворотної кореляційної матриці перешкоди при невідомих параметрах вхідного впливу для управління діаграмою спрямованості адаптивної антенної решітки, використовуючи імпульсну характеристику просторового фільтра. Методи: підхід базується на теорії випадкових процесів і адаптивної обробки сигналів. Результати: запропонований метод прямого обчислення зворотної кореляційної матриці показав можливість проводити такі обчислення без апріорних знань про направлення приходу перешкоди, про кореляційної функції перешкоди, а також про спектральні характеристики перешкоди. Метод дозволяє зменшити час обчислення зворотної кореляційної матриці і виключити похибки, які викликаються конструктивними розбіжностями радіоканалів адаптивної антенної решітки, що в свою чергу знижує помилку вимірювання напрямку на джерело перешкод. Обговорення: метод пропонується для забезпечення доступності та цілісності (підвищення завадостійкості) навігаційних даних мережевих супутникових систем.

Blind multipath time varying channel estimation using recursive Cholesky update

This paper proposes a simple and high performance least square solver using recursive update of modified Cholesky factors. While most of the methods require inversion of correlation matrix, the proposed method is based on recursive updating of the modified Cholesky factors of correlation matrix and linear prediction error to estimate time varying channel coefficient, without finding the correlation matrix. Blind channel estimation of time varying channel is considered for a SIMO system using only second order statistics (SoS) of the data. The time varying channel is described by complex exponential basis expansion model (CE-BEM). The performance of the proposed method is evaluated by simulation results to demonstrate its effectiveness.

Ratio improved adaptive systems moving target autoregressive type

The comparative analysis of the effectiveness of methods for implementing adaptive systems moving target based on autoregression approach. AR model correlated noise can effectively deal with clutter, without resorting to the algorithm based on the correlation matrix inversion. Considered several methods of weight factor of adaptive systems moving target, which is used as the coefficients of the autoregression. One of the main parameters that determine the effectiveness of the systems being compared, is the improvement factor, which was used in this study.

VLSI Architecture for Broadband MVDR Beamformer

Background/Objectives: The main objective of this proposed work is to investigate the significance of adaptive beamforming technique and to develop an efficient VLSI architecture for broadband MVDR beamformer in the field of medical ultrasound imaging. Methods/Statistical Analysis: The proposed algorithm is Minimum Variance Distortionless Response (MVDR) for near field beamforming of broadband data which gives better contrast and resolution compared to conventional Delay and Sum (DAS) beamformers and is implemented in frequency domain. MVDR beamformer minimizes the output power by allowing the desired signal to pass undistorted with unity gain. The solution for this optimization problem, involves correlation matrix inversion, which is the challenging part of MVDR algorithm. Findings: MVDR algorithm is applied by finding the inverse of correlation matrix which is a complex matrix. Here four elements are used for simplicity. Calculation of inverse complex matrix is the challenging part of MVDR algorithm where different methods are being used. Here QR decomposition is used which follows givens rotation algorithm. The paper demonstrates the formal verification of the proposed work. Final result is compared with the golden reference model which is designed using FIELD II scanner in Matlab. From the results it’s seen that, MVDR beamformer gives a pencil like beamform which shows high resolution and better contrast when compared to DAS. The timing constraints and device utilization parameters are obtained from synthesis report of final architecture designed in FPGA. Conclusion/Improvements: MVDR algorithm gives a pencil like beamformer output with reduced main lobe width and reduced side lobe level. By upgrading number of elements from 4 to 64, it can be made real time.

Adaptive processing of signals on a background of clutter and noise

Suppression of clutter and noise is one of the most important problems of radio location signals processing. It is shown proposed algorithm of division of processing vector into sub-vectors of non-recursive noise suppression filter allows to increase average by signals Doppler velocities probability of correct detection on 6–28% in compare to known non-adaptive whitening filter. Proposed algorithm does not require the noise correlation matrix inversion in case of modification of power of clutter noise that reduces computational burden 1.8–7 times on its realization in compare to optimal adaptive algorithm.

Distributed estimation of the inverse of the correlation matrix for privacy preserving beamforming

In this paper, we consider a privacy preserving scenario where users in the network want to perform distributed target source estimation with a wireless acoustic sensor network (WASN), without revealing the actual source of interest to other entities in the network. This implies that users do not share the steering vector of the beamformer with any other party. For distributed multi-channel noise reduction in WASNs, distributed estimation of the inverse noise or noise+target correlation matrix is an important aspect and in general a challenging problem.To make both privacy preservation and distributed multi-channel noise reduction possible, we make use of the fact that recursive estimation of the inverse correlation matrix can be structured as a consensus problem and can be realized in a distributed manner via the randomized gossip algorithm. This makes it possible to compute the MVDR in distributed manner without revealing the steering vector to any of the other entities in the network, and providing privacy about the actual source of interest. We provide theoretical analysis and numerical simulations to investigate the convergence error between the gossip-based estimated correlation matrix and the centralized estimated correlation matrix. It is shown that the convergence error accumulates across time without using a sufficient number of transmissions in the gossip-based algorithm. To eliminate this convergence error, we propose in addition a clique-based algorithm for distributed estimation of the inverse correlation matrix (CbDECM). Theoretical analysis shows that the CbDECM algorithm converges to the centralized estimate of the matrix inverse.We investigate the performance of the presented clique-based distributed framework in combination with a distributed privacy preserving MVDR beamformer, where information about the actual source of interest is kept private. Simulations show that the proposed algorithm converges to the centralized MVDR beamformer.

Hybrid 1-opt Local Search Polynomial-Expanded Linear Multiuser Detectors

This work proposes hybrid multiuser detector based on Polynomial Expansion (PE-MuD) as a way to reduce computational complexity inherent to correlation matrix inversion, followed by the low complexity Local Search (LS) procedure, aiming to obtain a near-optimum multiuser Bit-Error-Rate (BER) performance, however with reduced computational complexity. The proposed hybrid PE-LS-MuD receiver topology is analyzed under realistic wireless mobile channels, as well as useful system operation scenarios. Simulation results indicate a suitable improvement in the performance-complexity trade-off regarding the classical linear multiuser detectors, particularly the MMSE.

Measuring linkage disequilibrium by the partial correlation coefficient

Measuring linkage disequilibrium by the partial correlation coefficient