non-Gaussian Models Research Articles

Blind receiver design-based multi-dimensional stable distribution model using the EM algorithm

Multi-antenna receivers are a key technology for modern communication systems. Signal attenuation in the very low frequency (VLF) channel is a serious problem. In addition to high signal attenuation, the resulting noise on the VLF channel is non-Gaussian. Hence, to analyze and address the issue of the normal operation of the multi-antenna receiver in the VLF channel, we must study the signal detection problem in a multi-dimensional non-Gaussian fading channel. Motivated by the existing blind receiver in an underwater submarine single-antenna receiver, we study the signal detection and estimation algorithm under the fading channel for a multi-dimensional non-Gaussian noise model. In this study, we propose a blind receiver based on the expectation-maximization (EM) algorithm. The proposed blind receiver can reduce non-Gaussian noise. In addition, we propose a nonlinear receiver that can accurately receive the transmitted signal over the high-attenuation VLF communication systems. Numerical and simulation results over uncorrelated and correlated non-Gaussian channels confirm that the design of the proposed blind receiver is close to optimal, with low computation complexity.

Accelerating High b-Value Diffusion-Weighted MRI Using a Convolutional Recurrent Neural Network (CRNN-DWI).

To develop a novel convolutional recurrent neural network (CRNN-DWI) and apply it to reconstruct a highly undersampled (up to six-fold) multi-b-value, multi-direction diffusion-weighted imaging (DWI) dataset. A deep neural network that combines a convolutional neural network (CNN) and recurrent neural network (RNN) was first developed by using a set of diffusion images as input. The network was then used to reconstruct a DWI dataset consisting of 14 b-values, each with three diffusion directions. For comparison, the dataset was also reconstructed with zero-padding and 3D-CNN. The experiments were performed with undersampling rates (R) of 4 and 6. Standard image quality metrics (SSIM and PSNR) were employed to provide quantitative assessments of the reconstructed image quality. Additionally, an advanced non-Gaussian diffusion model was employed to fit the reconstructed images from the different approaches, thereby generating a set of diffusion parameter maps. These diffusion parameter maps from the different approaches were then compared using SSIM as a metric. Both the reconstructed diffusion images and diffusion parameter maps from CRNN-DWI were better than those from zero-padding or 3D-CNN. Specifically, the average SSIM and PSNR of CRNN-DWI were 0.750 ± 0.016 and 28.32 ± 0.69 (R = 4), and 0.675 ± 0.023 and 24.16 ± 0.77 (R = 6), respectively, both of which were substantially higher than those of zero-padding or 3D-CNN reconstructions. The diffusion parameter maps from CRNN-DWI also yielded higher SSIM values for R = 4 (>0.8) and for R = 6 (>0.7) than the other two approaches (for R = 4, <0.7, and for R = 6, <0.65). CRNN-DWI is a viable approach for reconstructing highly undersampled DWI data, providing opportunities to reduce the data acquisition burden.

Bayesian multivariate nonlinear state space copula models

A novel flexible class of multivariate nonlinear non-Gaussian state space models, based on copulas, is proposed. Specifically, it is assumed that the observation equation and the state equation are defined by copula families that are not necessarily equal. Inference is performed within the Bayesian framework, using the Hamiltonian Monte Carlo method. Simulation studies show that the proposed copula-based approach is extremely flexible, since it is able to describe a wide range of dependence structures and, at the same time, allows us to deal with missing data. The application to atmospheric pollutant measurement data shows that the approach is suitable for accurate modeling and prediction of data dynamics in the presence of missing values. Comparison to a Gaussian linear state space model and to Bayesian additive regression trees shows the superior performance of the proposed model with respect to predictive accuracy.

Investigation of the Static Performance of Hydrostatic Thrust Bearings Considering Non-Gaussian Surface Topography

The dynamic and static characteristics of hydrostatic thrust bearings are significantly affected by the bearing surface topography. Previous studies on hydrostatic thrust bearings have focused on Gaussian distribution models of bearing surface topography. However, based on actual measurements, the non-Gaussianity of the distribution characteristics of bearing surface topography is clear. To accurately characterize the non-Gaussian distribution of bearing surface topography, the traditional probability density function of Gaussian distribution was modified by introducing Edgeworth expansion. The non-Gaussian surface was then reflected by two parameters: kurtosis and skewness. This had an effect on the static characteristics of hydrostatic thrust bearings with both circumferential and radial surface topographies. The comparison between the Gaussian distribution results and those of the non-Gaussian model showed that errors between the two models could reach more than 10%. Therefore, it is important to take into account the non-Gaussianity of bearing surface when discussing static characteristics of hydrostatic thrust bearings considering the surface topography.

Development of a non-Gaussian copula Bayesian network for safety assessment of metro tunnel maintenance

The operation and maintenance of metro systems play a crucial role in urban development, with a focus on ensuring the serviceability and safety of metro tunnels. Accurate evaluation of the condition of these tunnel states requires investigating the complex interaction of multiple factors that impact their safety state. This study developed a hybrid model that integrates pair copula constructions (PCCs) and Bayesian networks (BN) to assess the safety state of metro tunnels, considering complex dependencies among these factors. First, key performance indicators (KPIs) were selected to assess tunnel safety, based on six failure modes. Then, an improved copula-based PC algorithm was employed to learn the non-Gaussian bayesian network model, which eliminated the normality assumption in the marginal densities of the KPIs. Finally, a combination of forward reasoning and GM(1,1) was utilized to predict the safety state of the metro tunnel in time series, facilitating the formulation of effective operation and maintenance plans. Furthermore, the proposed approach was applied to a real case study of the Wuhan metro system to demonstrate its effectiveness and applicability. The results highlighted the significant influence of some KPIs, such as convergence deformation, dislocation displacement, and stripping area, on metro tunnel safety. These KPIs emerged as key factors requiring focused attention in the operation and maintenance of metro tunnels.

Breast cancer diagnosis and prognosis using a high b-value non-Gaussian continuous-time random-walk model

To compare the diagnostic performance of mono-exponential model-derived apparent diffusion coefficient (ADC), continuous-time random-walk (CTRW) model-derived Dm, α, β and their combinations in discriminating malignancy of breast lesions, and investigate the association between model-derived parameters and prognosis-related immunohistochemical indices. A total of 85 patients with breast lesions (51 malignant, 34 benign) were analysed in this retrospective study. Clinical characteristics include oestrogen receptor (ER), progesterone receptor (PR), human epidermal receptor 2 (HER2), and Ki-67. The ADC was fitted using a mono-exponential model (b-values=0, 800 s/mm2), while Dm, α, and β were fitted using a CTRW model. Independent Student's t-test and the Mann-Whitney U-test were used for the comparison of parameters. Discrimination performance was accomplished by receiver operating characteristic (ROC) analysis, and Spearman's correlation analysis was used to explore the association between immunohistochemical indices and diffusion parameters, the statistical significance level was p<0.05. Dm and ADC demonstrated similar performance in differentiating malignant and benign lesions (AUC=0.928 versus 0.930), while the combination of Dm, α, and β could improve the AUC to 0.969. The combined parameter generated by ADC, Dm, α, and β was effective in identifying the ER+/ER- and PR+/PR- patients. Temporal heterogeneity parameter α correlated significantly with the expression of PR. Diffusion parameters derived from the CTRW model could effectively discriminate the malignancy of breast lesions. Meanwhile, the hormone receptor expression could be distinguished by combined diffusion parameters, and have the potential to reflect the prognosis.

Impact of gut microbiome on the renin-aldosterone system: Shika-machi Super Preventive Health Examination results.

The renin-angiotensin-aldosterone system (RAAS) is a regulatory mechanism of the endocrine system and is associated with various diseases, including hypertension and renal and cardiovascular diseases. The gut microbiota (GM) have been associated with various diseases, mainly in animal models. However, to our knowledge, no studies have examined the relationship between the RAAS and GM in humans. The present study aimed to assess the association between the systemic RAAS and GM genera and their causal relationships. The study participants were 377 members of the general population aged 40 years or older in Shika-machi, Japan. Plasma renin activity (PRA), plasma aldosterone concentration (PAC), aldosterone-renin ratio (ARR), and GM composition were analyzed using the 16S rRNA method. The participants were divided into high and low groups according to the PRA, PAC, and ARR values. U-tests, one-way analysis of covariance, and linear discriminant analysis of effect size were used to identify the important bacterial genera between the two groups, and binary classification modeling using Random Forest was used to calculate the importance of the features. The results showed that Blautia, Bacteroides, Akkermansia, and Bifidobacterium were associated with the RAAS parameters. Causal inference analysis using the linear non-Gaussian acyclic model revealed a causal effect of Blautia on PAC via SBP. These results strengthen the association between the systemic RAAS and GM in humans, and interventions targeting the GM may provide new preventive measures and treatments for hypertension and renal disease.

Improving hydrodynamic modeling of river networks by incorporating data assimilation using a particle filter

Numerical modeling is a well-recognized method for studying the hydrodynamic processes in river networks. Multi-source measurements also offer abundant information on the patterns and mechanisms within the processes. Therefore, improving hydrodynamic modeling of river networks through the use of data assimilation techniques has become a hot research topic in recent years. The particle filter (PF) is a commonly used data assimilation method and has been proven to be applicable to various nonlinear and non-Gaussian models. In the current study, an improved numerical hydrodynamic model for large-scale river networks is established by incorporating the advanced PF algorithm. Furthermore, the PF method based on the Gaussian likelihood function (GLF) and the method based on the Cauchy likelihood function (CLF) are compared for a complex river network scenario. The feasibility of the PF-based methods was evaluated through application to the Yangtze-Dongting River-lake Network (YDRN) by assimilating water stage data collected at six hydrometric stations during the entire hydrodynamic process in 2003. Additionally, the parameters used in the likelihood function, which affect the assimilation performance, also were explored in the current study. The study results found that the accuracy of the model-derived water stage data was improved when the PF-based methods are utilized, with improvement not only at the data assimilation (calibration) sites but also at three hydrometric stations not used in the data assimilation (i.e., verification sites). The highest average Nash-Sutcliffe Efficiency result for the six assimilation sites were 0.98 while the lowest summed root-mean-square-error result was 1.801 m. The comparison results also indicated that the CLF-based PF outperformed the GLF-based PF when high-accuracy observed data are available. Specifically, the CLF can effectively resolve the filtering failure problem and the dispersion problem of PFs, and further improve the accuracy of the filtering results for a river network scenario. In summary, the CLF-based PF method along with high-accuracy observation data shows promise to provide reliable reference and technical support for hydrodynamic modeling of large-scale river networks.

Non-Gaussian feature distribution forecasting based on ConvLSTM neural network and its application to robust machine condition prognosis

The prognosis of a machine condition becomes a hot topic nowadays, as the condition monitoring installations provide a massive amount of Health Index (HI) data that could be used for machine remaining lifetime prognosis. However, existing methodologies might not be effective since in many cases the real HI datasets exhibit non-Gaussian characteristics. Thus, to improve efficiency, there is a need to introduce novel approaches which take into account the possible non-Gaussian distribution of HI data. In the proposed methodology, several innovative components are considered to form an efficient solution for the HI time series prediction. As HI is a mixture of trend and random non-Gaussian, non-homogeneous noise, we propose to forecast the HI distribution rather than the direct HI value. The Skewed Generalized t (SGT) distribution is considered as the general non-Gaussian model. Moreover, the combination of convolutional neural network (CNN) and long short-term memory (LSTM) are used to predict SGT distribution parameters. By incorporating the standardization module and the modified activation function alongside a custom time series standardization method, the architecture of the ConvLSTM neural network is created to be appropriate for non-stationary time series data with non-Gaussian behavior. Finally, a pre-training of the model has been proposed, which improves the efficiency of the designed procedure, as usually the amount of HI data is limited and insufficient to reliably train an artificial intelligence (AI) system. The proposed solution is shown to be robust and more resilient to outliers than the classical Gaussian-based approach. Using simulated and real HI data (known as a benchmark), we may conclude that the superiority of our method increases with the increasing non-Gaussianity level of the analyzed time series.

ParaLiNGAM: Parallel causal structure learning for linear non-Gaussian acyclic models

One of the key objectives in many fields in machine learning is to discover causal relationships among a set of variables from observational data. In linear non-Gaussian acyclic models (LiNGAM), it can be shown that the true underlying causal structure can be identified uniquely from merely observational data. The DirectLiNGAM algorithm is a well-known solution to learn the true causal structure in a high dimensional setting. DirectLiNGAM algorithm executes in a sequence of iterations and it performs a set of comparisons between pairs of variables in each iteration. Unfortunately, the runtime of this algorithm grows significantly as the number of variables increases. In this paper, we propose a parallel algorithm, called ParaLiNGAM, to learn casual structures based on DirectLiNGAM algorithm. We propose a threshold mechanism that can reduce the number of comparisons remarkably compared with the sequential solution. Moreover, in order to further reduce runtime, we employ a messaging mechanism between workers. We also present an implementation of ParaLiNGAM on GPU, considering hardware constraints. Experimental results on synthetic and real data show that our proposed solution outperforms DirectLiNGAM by a factor up to 4788X, and by a median of 2344X.

Analysis of East Asia Wind Vectors Using Space–Time Cross-Covariance Models

As the risk posed by climate change becomes increasingly evident, countries across the world are constantly seeking alternative energy sources. Wind energy has substantial potential for future energy portfolios without having negative impacts on the environment. In developing nationwide and worldwide energy plans, understanding the spatio-temporal pattern of wind is crucial. We analyze wind vectors in the region of East Asia from the fifth-generation ECMWF atmospheric reanalysis. To model the wind vectors, we consider Tukey g-and-h transformation-based non-Gaussian processes, along with multivariate covariance functions. The proposed model can address non-Gaussian features and nonstationary dependence structures of wind vectors. In addition, a two-step inference scheme coupled with the composite likelihood method is applied to handle the computational issues posed by a large dataset. In the first step, we fit the temporal dependence structures of data with a location-specific non-Gaussian time series model. This allows us to remove substantial amounts of nonstationary variations in both space and time, and thus, relatively simple covariance models can handle large and complicated data in the second step. We show that the proposed method with a covariance structure reflecting the nonstationarity due to the latitude difference and the land–ocean difference leads to better predictions for wind speed as well as wind potential, which is crucial for planning wind power generation.

Estimation of Yu and Meyer bivariate stochastic volatility model by iterated filtering

In financial applications, understanding the asset correlation structure is crucial to tasks such as asset pricing, portfolio optimisation, risk management, and asset allocation. Thus, modelling the volatilities and correlations of multivariate stock market returns is of great importance. This paper proposes the iterated filtering algorithm for estimating the bivariate stochastic volatility model of Yu and Meyer. The iterated filtering method is a frequentist-based approach that utilises particle filters and can be applied to estimating the parameters of non-linear or non-Gaussian state-space models. The paper presents an empirical example that demonstrates the way in which the proposed estimation method might be used to estimate the correlation between the returns of two assets: Standard and Poor’s 500 index and the price of gold in US dollars. This is accompanied by a simulation study that proves the validity of the approach.

Preoperative prediction of VETC in hepatocellular carcinoma using non-Gaussian diffusion-weighted imaging at high b values: a pilot study.

Vessels encapsulating tumor clusters (VETC) have been considered an important cause of hepatocellular carcinoma (HCC) metastasis. To compare the potential of various diffusion parameters derived from the monoexponential model and four non-Gaussian models (DKI, SEM, FROC, and CTRW) in preoperatively predicting the VETC of HCC. 86 HCC patients (40 VETC-positive and 46 VETC-negative) were prospectively enrolled. Diffusion-weighted images were acquired using six b-values (range from 0 to 3000 s/mm2). Various diffusion parameters derived from diffusion kurtosis (DK), stretched-exponential (SE), fractional-order calculus (FROC), and continuous-time random walk (CTRW) models, together with the conventional apparent diffusion coefficient (ADC) derived from the monoexponential model were calculated. All parameters were compared between VETC-positive and VETC-negative groups using an independent sample t-test or Mann-Whitney U test, and then the parameters with significant differences between the two groups were combined to establish a predictive model by binary logistic regression. Receiver operating characteristic (ROC) analyses were used to assess diagnostic performance. Among all studied diffusion parameters, only DKI_K and CTRW_α significantly differed between groups (P=0.002 and 0.004, respectively). For predicting the presence of VETC in HCC patients, the combination of DKI_K and CTRW_α had the larger area under the ROC curve (AUC) than the two parameters individually (AUC=0.747 vs. 0.678 and 0.672, respectively). DKI_K and CTRW_α outperformed traditional ADC for predicting the VETC of HCC.

Tile low-rank approximations of non-Gaussian space and space-time Tukey g-and-h random field likelihoods and predictions on large-scale systems

Large-scale statistical modeling has become necessary with the vast flood of geospace data coming from various sources. In space statistics, the Maximum Likelihood Estimation (MLE) is widely considered for modeling geospace data by estimating a set of statistical parameters related to a predefined covariance function. This covariance function describes the correlation between a set of geospace locations where the main goal is to model given data samples and impute missing data. Climate/weather modeling is a prevalent application for the MLE operation where data interpolation and forecasting are highly required. In the literature, the Gaussian random field is often used to describe geospace data as one of the most popular models for MLE. However, real-life datasets are often skewed and/or have extreme values, and non-Gaussian random field models are more appropriate for capturing such features. In this work, we provide an exact and approximate parallel implementation of the well-known Tukey g-and-h (TGH) non-Gaussian random field in the context of climate/weather applications. The proposed implementation alleviates the computation complexity of the log-likelihood function, which requires O(n2) storage and O(n3) operations, where N is the number of geospace locations, M is the number of time slots, and n=N×M. Based on tile low-rank (TLR) approximations, our implementation of the TGH model can tackle large-scale problems. Furthermore, we rely on task-based programming models and dynamic runtime systems to provide fast execution for the MLE operation in space and space-time cases. We assess the performance and accuracy of the proposed implementations using synthetic space and space-time datasets up to 800K. We also consider a 12-month precipitation dataset in Germany to demonstrate the advantage of using non-Gaussian over Gaussian random field models. We evaluate the prediction accuracy of the TGH model on the precipitation dataset using the Probability Integral Transformation (PIT) tool showing that the TGH model outperforms the Gaussian modeling in the real dataset. Moreover, our performance assessment indicates that TLR computations allow solving larger matrix sizes while preserving the required accuracy for prediction. The TLR-based approximation shows a speedup up to 7.29X and 2.96X over the exact solution.

Probabilistic Assessment of Conservation Voltage Reduction Using Static Load Model Parameter in the Presence of Uncertainties

Higher penetration of solar PV and wind generation in distribution networks may change the conservation voltage reduction (CVR) capabilities. The uncertainties associated with the renewable generations and system loads are neglected in the deterministic CVR assessment. In this paper, a probabilistic framework for CVR assessment has been presented to assess the impact of uncertainties associated with renewable generations and system loads. A theoretical framework has been presented by establishing a mathematical relationship between the probability distribution of renewable generations (solar PV and wind) and the probability distribution of static exponential load model parameters. The simulation results have confirmed that the penetration of non-Gaussian solar PV and wind generation leads to non-Gaussian static exponential load model parameter distribution, which is validated by the normality tests (quantile-quantile plot, skewness, and kurtosis). Subsequently, the magnitude and probability distribution of the CVR capabilities of the network changes with the penetration of renewable generations, where the higher renewable penetration scenarios lead to higher CVR values and non-Gaussian (asymmetric) distribution.

Efficient Data Augmentation Techniques for Some Classes of State Space Models

Data augmentation improves the convergence of iterative algorithms, such as the EM algorithm and Gibbs sampler by introducing carefully designed latent variables. In this article, we first propose a data augmentation scheme for the first-order autoregression plus noise model, where optimal values of working parameters introduced for recentering and rescaling of the latent states, can be derived analytically by minimizing the fraction of missing information in the EM algorithm. The proposed data augmentation scheme is then utilized to design efficient Markov chain Monte Carlo (MCMC) algorithms for Bayesian inference of some non-Gaussian and nonlinear state space models, via a mixture of normals approximation coupled with a block-specific reparametrization strategy. Applications on simulated and benchmark real data sets indicate that the proposed MCMC sampler can yield improvements in simulation efficiency compared with centering, noncentering and even the ancillarity-sufficiency interweaving strategy.

Third-order moment varieties of linear non-Gaussian graphical models

Abstract In this paper, we study linear non-Gaussian graphical models from the perspective of algebraic statistics. These are acyclic causal models in which each variable is a linear combination of its direct causes and independent noise. The underlying directed causal graph can be identified uniquely via the set of second and third-order moments of all random vectors that lie in the corresponding model. Our focus is on finding the algebraic relations among these moments for a given graph. We show that when the graph is a polytree, these relations form a toric ideal. We construct explicit trek-matrices associated to 2-treks and 3-treks in the graph. Their entries are covariances and third-order moments and their $2$-minors define our model set-theoretically. Furthermore, we prove that their 2-minors also generate the vanishing ideal of the model. Finally, we describe the polytopes of third-order moments and the ideals for models with hidden variables.

Application of quantum computing to a linear non-Gaussian acyclic model for novel medical knowledge discovery.

Recently, the utilization of real-world medical data collected from clinical sites has been attracting attention. Especially as the number of variables in real-world medical data increases, causal discovery becomes more and more effective. On the other hand, it is necessary to develop new causal discovery algorithms suitable for small data sets for situations where sample sizes are insufficient to detect reasonable causal relationships, such as rare diseases and emerging infectious diseases. This study aims to develop a new causal discovery algorithm suitable for a small number of real-world medical data using quantum computing, one of the emerging information technologies attracting attention for its application in machine learning. In this study, a new algorithm that applies the quantum kernel to a linear non-Gaussian acyclic model, one of the causal discovery algorithms, is developed. Experiments on several artificial data sets showed that the new algorithm proposed in this study was more accurate than existing methods with the Gaussian kernel under various conditions in the low-data regime. When the new algorithm was applied to real-world medical data, a case was confirmed in which the causal structure could be correctly estimated even when the amount of data was small, which was not possible with existing methods. Furthermore, the possibility of implementing the new algorithm on real quantum hardware was discussed. This study suggests that the new proposed algorithm using quantum computing might be a good choice among the causal discovery algorithms in the low-data regime for novel medical knowledge discovery.

Non-Gaussian model-based diffusion-weighted imaging of oral squamous cell carcinoma: associations with Ki-67 proliferation status.

To investigate possible associations between diffusion-weighted imaging (DWI) parameters derived from a non-Gaussian model fitting and Ki-67 status in patients with oral squamous cell carcinoma (OSCC). Twenty-four patients with newly diagnosed OSCC were prospectively recruited. DWI was performed using six b-values (0-2500). The diffusion-related parameters of kurtosis value (K), kurtosis-corrected diffusion coefficient (DK), diffusion heterogeneity (α), distributed diffusion coefficient (DDC), slow diffusion coefficient (Dslow), and apparent diffusion coefficient (ADC) were calculated from four diffusion fitting models. Ki-67 status was categorized as low (Ki-67 percentage score < 20%), middle (20-50%), or high (> 50%). Kruskal-Wallis tests were performed between each non-Gaussian diffusion model parameters and Ki-67 grade. The Kruskal-Wallis tests revealed that multiple parameters (K, ADC, Dk, DDC and Dslow) showed statistically significant differences between the three levels of Ki-67 status (K: p = 0.020, ADC: p = 0.012, Dk: p = 0.027, DDC: p = 0.007 and Dslow: p = 0.026). Several non-Gaussian diffusion model parameters and ADC values were significantly associated with Ki-67 status and have potential as promising prognostic biomarkers in patients with OSCC.

Thermodynamic and scaling limits of the non-Gaussian membrane model

We characterize the behavior of a random discrete interface $\phi$ on $[-L,L]^d \cap \mathbb{Z}^d$ with energy $\sum V(\Delta \phi(x))$ as $L \to \infty$, where $\Delta$ is the discrete Laplacian and $V$ is a uniformly convex, symmetric, and smooth potential. The interface $\phi$ is called the non-Gaussian membrane model. By analyzing the Helffer-Sj\"ostrand representation associated to $\Delta \phi$, we provide a unified approach to continuous scaling limits of the rescaled and interpolated interface in dimensions $d=2,3$, Gaussian approximation in negative regularity spaces for all $d \geq 2$, and the infinite volume limit in $d \geq 5$. Our results generalize some of those of arXiv:1801.05663.