Article
Mathematics
Vladimir E. Bening, Victor Y. Korolev
Summary: This paper introduces a new approach to comparing the distributions of sums of random variables using the notion of deficiency from mathematical statistics. The approach is used to determine the distribution of a separate random variable in the sum that guarantees a desired quantile or probability, with the fewest possible number of summands. The paper also considers the case of comparing distributions when the number of summands is random, and applies the approach to determining the distribution of insurance payments for minimum portfolio size under specified risk or non-ruin probability.
Article
Mathematics
Vladimir Bening, Victor Korolev
Summary: In this paper, a new approach is applied to compare the distributions of sums of random variables, specifically in the case of Poisson random sums. This approach is based on the concept of statistical deficiency and introduces a continuous analog of deficiency. By utilizing this approach, the distribution of a separate term in the Poisson sum can be determined to provide the minimum possible value of the parameter of the Poisson distribution of the number of summands, guaranteeing a prescribed value of the (1-a)-quantile of the normalized Poisson sum. The approach is also applied to the collective risk model and the comparison of approximation accuracy between the sum of independent, identically distributed random variables and the accompanying infinitely divisible distribution.
Article
Mathematics, Applied
Xueying Yu, Chuancun Yin
Summary: The kurtosis and skewness are important measures for shape characterization of distributions. While there have been many results for symmetric distributions, characterizing skew distributions still poses difficulties and challenges. Building on previous work on kurtosis measures for elliptical distributions by Zografos [1], we generalize the results and study measures for both elliptical and skew-elliptical distributions. We derive moment expressions for skew-elliptical distributions using those of skew-normal distributions, and provide examples using skew-t, skew-Pearson type VII, and skew-Pearson type II distributions.
Article
Mathematics
Xiangyu Han, Chuancun Yin
Summary: The study presents general results on the univariate tail conditional moments for a location-scale mixture of elliptical distributions, including the tail variance, skewness, and kurtosis for the generalised hyperbolic distribution and Student-GIG mixture distribution. An illustrative example is given to discuss the TCE, TV, TCS, and TCK for three stocks (Amazon, Google, and Apple).
Article
Statistics & Probability
Nelson Antunes, Shankar Bhamidi, Tianjian Guo, Vladas Pipiras, Bang Wang
Summary: This work focuses on estimating the in-degree distribution of directed networks from sampling network nodes or edges. Two estimation approaches are proposed, based on inversion and asymptotic methods. The performance of these approaches is tested on synthetic and real networks, showing good results.
JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS
(2021)
Article
Automation & Control Systems
Sergii Voronov, Voronov Daniel Jung, Erik Frisk
Summary: The paper introduces a forest-based variable selection algorithm, named Variable Depth Distribution, to measure the importance of variables. The algorithm is developed for datasets with correlated variables and can identify important variables in different applications.
ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE
(2021)
Article
Engineering, Electrical & Electronic
Xiaowei Wang, Fan Zhang, Jie Gao, Liang Guo, Xue Wang, Zhenfeng Liang, Weibo Liu
Summary: This paper proposes a new fault location method for resonant grounding systems based on variable modal decomposition (VMD) and kurtosis calibration. The proposed method accurately calibrates the arrival moment of the fault wave head and achieves precise fault location. The method is not affected by the fault location and the initial angle of the fault, as shown by PSCAD simulation results.
INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS
(2023)
Article
Statistics & Probability
Luca Bagnato, Antonio Punzo, Maria Grazia Zoia
Summary: This article demonstrates the construction of multivariate elliptically contoured distributions from univariate standard symmetric distributions. The concepts of moment-parameterized and leptokurtic MEC distributions are introduced, with the latter characterized by an excess kurtosis parameter. Estimation methods including the method of moments and maximum likelihood are discussed, and the application to financial returns of European stock indexes is presented.
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
(2022)
Article
Computer Science, Artificial Intelligence
Muhammad Aslam
Summary: This paper studies the truncated variable simulation method under the indeterminate environment and introduces the algorithm using the DUS-neutrosophic Weibull distribution as an example. Extensive simulation tables are presented to demonstrate the results for different values of indeterminacy and truncated variables.
COMPLEX & INTELLIGENT SYSTEMS
(2023)
Article
Statistics & Probability
Jimmy Reyes, Diego Gallardo, Filidor Vilca, Hector W. Gomez
Summary: In this paper, a new family of noncentral elliptical distributions is introduced, generated as the quotient of two independent random variables. General properties, including moments, as well as special cases are derived, showing the advantages of this distribution family in parameter estimation. The results and methods are applied to real datasets, demonstrating better fit compared to other models in recent statistical literature.
REVSTAT-STATISTICAL JOURNAL
(2021)
Article
Engineering, Electrical & Electronic
Mayur Dhanaraj, Panos P. P. Markopoulos
Summary: The dominant eigenvector of the covariance matrix represents the line with the maximum variance of the projected data. Principal Component Analysis (PCA) is commonly used to estimate the dominant eigenvector when the true covariance matrix is unknown, but it is sensitive to outliers. L1-PCA, a robust alternative to PCA, has shown resistance against outliers in various applications, but its asymptotic properties as an eigenvector estimator have not been well understood.
IEEE SIGNAL PROCESSING LETTERS
(2022)
Article
Computer Science, Artificial Intelligence
Shengxi Li, Danilo Mandic
Summary: This article introduces a novel approach based on the von-Mises-Fisher (vMF) distribution to obtain an explicit and simple probability representation of skewed elliptical distributions. This method allows for the design and implementation of nonsymmetric learning systems and provides a physically meaningful and intuitive way of generalizing skewed distributions.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2023)
Article
Mathematics
Juan E. Ruiz-Castro, Christian Acal, Ana M. Aguilera, Juan B. Roldan
Summary: A new stochastic process was developed by considering the internal performance of macro-states with phase-type distributed sojourn time, leading to interesting measures and stationary distribution calculation through matrix-algorithmic methods. The analysis of the number of visits distribution to a determine macro-state was done through differential equations and Laplace transform. The results were successfully applied to study random telegraph noise in resistive memories, which is important for both technological applications and physical characterization.
Article
Statistics & Probability
Christian E. Galarza, Larissa A. Matos, Luis M. Castro, Victor H. Lachos
Summary: This paper computes doubly truncated moments for the selection elliptical class of distributions, including some multivariate asymmetric versions of well-known elliptical distributions. The moments for doubly truncated members of this family are addressed, with neat formulation for high-order moments and its first two moments established. Sufficient and necessary conditions for the existence of these truncated moments are established. Optimized methods are proposed to handle extreme settings of parameters and partitions with almost zero volume or no truncation, and are validated with numerical studies. Results have been particularized to the unified skew-t distribution, a complex multivariate asymmetric heavy-tailed distribution which includes several related distributions as special cases.
JOURNAL OF MULTIVARIATE ANALYSIS
(2022)
Article
Mathematics
Zhenduo Sun, Nengneng Qing, Xiangzhi Kong
Summary: Significant progress has been made in incorporating fractional calculus into the projection and lag synchronization of complex networks. However, real-world networks are highly complex, making the fractional derivative used in complex dynamics more susceptible to changes over time. Therefore, it is essential to incorporate variable-order fractional calculus into the asymptotic hybrid projection lag synchronization of complex networks. Firstly, this approach considers nonidentical models with variable-order fractional characteristics, which is more general. Secondly, a class of variable-order fractional sliding mode surfaces is designed, and an accurate formula for calculating finite arriving time is provided, in contrast to traditional sliding mode control methods that use an inequality-based range. Thirdly, sufficient conditions for achieving asymptotic hybrid projection lag synchronization of nonidentical variable-order fractional complex networks are derived. Lastly, the feasibility and effectiveness of our approach are demonstrated through two illustrative examples.
Editorial Material
Engineering, Electrical & Electronic
Michael Muma, Esa Ollila, Frederic Pascal
Article
Engineering, Electrical & Electronic
Elias Raninen, Esa Ollila
Summary: The proposed method provides an approximate bias correction for the eigenvalues of the SSCM, leading to a robust and efficient estimator for high dimensional problems.
IEEE SIGNAL PROCESSING LETTERS
(2022)
Article
Engineering, Electrical & Electronic
Elias Raninen, David E. Tyler, Esa Ollila
Summary: This paper considers the problem of estimating high-dimensional covariance matrices of K-populations or classes when the sample sizes are comparable to the data dimension. It proposes a method to estimate each class covariance matrix as a linear combination of all class sample covariance matrices, which reduces the estimation error when the sample sizes are limited and the true class covariance matrices share a similar structure. The paper develops an effective method for estimating the coefficients in the linear combination and shows how the proposed method can be used for regularization parameter selection in a single class covariance matrix estimation problem. The proposed method is evaluated through numerical simulation studies and an application in global minimum variance portfolio optimization using real stock data.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2022)
Article
Engineering, Electrical & Electronic
Jari Miettinen, Sergiy A. Vorobyov, Esa Ollila
Summary: The paper addresses the importance of modeling errors in adjacency matrices for graph signal processing and introduces practically justifiable graph error models. Through analytical and numerical studies, the effects of graph errors on the performance of GSP methods are explored.
Article
Engineering, Electrical & Electronic
Farshad G. Veshki, Nora Ouzir, Sergiy A. Vorobyov, Esa Ollila
Summary: This paper presents a multimodal image fusion method based on coupled dictionary learning, which effectively preserves texture details and modality-specific information, and achieves excellent performance in both visual and objective evaluations.
Article
Engineering, Electrical & Electronic
Esa Ollila, Daniel P. Palomar, Frederic Pascal
Summary: This paper proposes a method to estimate the scale parameter of the scatter matrix using weights obtained from Tyler's M-estimator. The estimated scale parameter is used to construct an affine equivariant Tyler's M-estimator. Additionally, a unified framework for estimating the tail parameter of elliptical distributions is developed, with a new robust estimate proposed for the degrees of freedom parameter in the multivariate t distribution.
IEEE SIGNAL PROCESSING LETTERS
(2023)
Article
Geochemistry & Geophysics
Matthieu Gallet, Ammar Mian, Guillaume Ginolhac, Esa Ollila, Nickolas Stelzenmuller
Summary: In this article, two algorithms are proposed to improve the interpretability of hyperbolas in B-scans obtained with ground penetrating radar (GPR). These algorithms, based on a sparse convolutional coding model and a low-rank component, are solved using the alternating direction method of multipliers (ADMM) framework. The second algorithm, based on the Huber norm, is designed to handle outliers and artifacts caused by the acquisition process. Experimental results on a real dataset demonstrate the denoising efficiency and robustness of the proposed approach.
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
(2023)
Proceedings Paper
Acoustics
Xinjue Wang, Esa Ollila, Sergiy A. Vorobyov
Summary: This paper investigates the impact of a probabilistic graph error model on the performance of graph convolutional networks (GCNs). The paper proves the upper bound of the adjacency matrix under the error model and analytically specifies the upper bound of a normalized adjacency matrix with self-loop added. Experiments on a synthetic dataset are conducted to illustrate the error bounds and study the sensitivity of a simple GCN under this probabilistic error model on accuracy.
2022 30TH EUROPEAN SIGNAL PROCESSING CONFERENCE (EUSIPCO 2022)
(2022)
Proceedings Paper
Acoustics
Esa Ollila, Hyon-Jung Kim
Summary: Tensor regression models have shown good performance in problems involving tensor covariates like images, by exploiting the temporal and/or spatial structure of the tensors. This paper proposes a robust tensor regression estimation method and demonstrates its superior performance in heavy-tailed noise through simulation studies.
2022 30TH EUROPEAN SIGNAL PROCESSING CONFERENCE (EUSIPCO 2022)
(2022)
Proceedings Paper
Acoustics
Christoph F. Mecklenbraeuker, Peter Gerstoft, Esa Ollila
Summary: Based on the assumption of robustness, we derive a sparse direction estimation method that accurately estimates the direction of arrival in complex noise environments. The method performs well under various loss functions and has similar performance to the classical method for Gaussian noise.
2022 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP)
(2022)
Article
Engineering, Electrical & Electronic
Esa Ollila, Arnaud Breloy
Summary: This paper investigates the problem of covariance matrix estimation in high-dimensional settings and proposes a new estimator called TABASCO. By shrinking the tapered sample covariance matrix, more accurate estimation results can be obtained. Simulation studies and practical application results demonstrate that TABASCO outperforms other competing estimators in various scenarios.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2022)
Article
Engineering, Electrical & Electronic
Jari Miettinen, Eyal Nitzan, Sergiy A. Vorobyov, Esa Ollila
Summary: This paper fills the gap in blind source separation research for graph signals with two contributions. The results show that utilizing both graph structure and non-Gaussianity provides a more robust approach, which is demonstrated to be more efficient in separating non-Gaussian graph signals.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2021)
Article
Engineering, Electrical & Electronic
Esa Ollila, Daniel P. Palomar, Frederic Pascal
Summary: The paper presents a more general approach by replacing SCM with an M-estimator of scatter matrix and proposes a fully automatic data adaptive method for computing the optimal shrinkage parameter. The simulation examples show that the proposed method outperforms SCM estimator in Gaussian data and significantly improves performance in heavy-tailed elliptically symmetric distribution data. Real-world and synthetic stock market data also validate the performance of the proposed method in practical applications.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2021)
Article
Engineering, Electrical & Electronic
Elias Raninen, Esa Ollila, David E. Tyler
Summary: In this study, we investigate the variance-covariance matrix of affine equivariant matrix-valued statistics when sampling from complex elliptical distributions, and derive the variance-covariance matrix of the sample covariance matrix (SCM) along with its theoretical mean squared error (MSE) when finite fourth-order moments exist. Illustrative examples of the formulas are also provided.
IEEE SIGNAL PROCESSING LETTERS
(2021)
Article
Engineering, Electrical & Electronic
Elias Raninen, Esa Ollila
Summary: The article focuses on the estimation of covariance matrices of multiple classes through the use of regularized SCM estimators. By coupling the regularization towards the pooled SCM and scaled identity matrix, the proposed techniques show promising MSE performance in scenarios where class populations follow elliptical distributions. The coupled RSCMs demonstrate comparable performance to cross-validation but with significantly faster computation time when applied on real data sets.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2021)
