Gaussian Assumption Research Articles

Experimental study on dynamic response performance of hydrogen sensor in confined space under ceiling

With the advancement of Fuel Cell Vehicles (FCVs), detecting hydrogen leaks is critically important in facilities such as hydrogen refilling stations. Despite its significance, the dynamic response performance of hydrogen sensors in confined spaces, particularly under ceilings, has not been comprehensively assessed. This study utilizes a catalytic combustion hydrogen sensor to monitor hydrogen leaks in a confined area. It examines the effects of leak size and placement height on the distribution of hydrogen concentrations beneath the ceiling. Results indicate that hydrogen concentration rapidly decreases within a 0.5–1.0 m range below the ceiling and declines more gradually from 1.0 to 2.0 m. The study further explores the attenuation pattern of hydrogen concentration radially from the hydrogen jet under the ceiling. By normalizing the radius and concentration, it was determined that the distribution conforms to a Gaussian model, akin to that observed in open space jet flows. Utilizing this Gaussian assumption, the model is refined by incorporating an impact reflux term, thereby enhancing the accuracy of the predictive formula.

Vine Copula-Based Classifiers with Applications

AbstractThe vine pair-copula construction can be used to fit flexible non-Gaussian multivariate distributions to a mix of continuous and discrete variables. With multiple classes, fitting univariate distributions and a vine to each class lead to posterior probabilities over classes that can be used for discriminant analysis. This is more flexible than methods with the Gaussian and/or independence assumptions, such as quadratic discriminant analysis and naive Bayes. Some variable selection methods are studied to accompany the vine copula-based classifier because unimportant variables can make discrimination worse. Simple numerical performance metrics cannot give a full picture of how well a classifier is doing. We introduce categorical prediction intervals and other summary measures to assess the difficulty of discriminating classes. Through extensive experiments on real data, we demonstrate the superior performance of our approaches compared to traditional discriminant analysis methods and random forests when features have different dependent structures for different classes.

Analysis of the Gaussian assumption of single sound source measured and processed through sound level meter

Machine learning (ML) techniques are constantly growing in acoustics. Such methods exploit large databases to train algorithms and earn complex feature correlations. The primary goal is to obtain inferences and predictions. Thus, ML often exploits statistics, and understanding the data distribution becomes fundamental when analyzing the available data. However, it is well-known that only some common methods can be used with large databases, e.g., normality tests are discouraged. The present work aims to explore the Gaussian assumption underlying a validated clustering technique used in long-term monitoring of sound level meters. The Gaussianity of single sound sources is analyzed through normal tests, normal probability plots, cumulative distribution functions, and high-order moments. The analysis involves a real-world measurement carried out through a sound level meter and speech recordings obtained from a common database used in machine learning. Results show that a single sound source can be deemed Gaussian in sound level meter long-term measurements, leading to important insights concerning the choice of algorithms.

A structurally informed data assimilation approach for nonlinear partial differential equations

Ensemble-based Kalman filtering data assimilation is often used to combine available observations with numerical simulations to obtain statistically accurate and reliable state representations in dynamical systems. However, it is well known that the commonly used Gaussian distribution assumption introduces biases for state variables that admit discontinuous profiles, which are prevalent in nonlinear partial differential equations. This investigation designs a new structurally informed prior that exploits statistical information from the simulated state variables. In particular, based on the second moment information of the state variable gradient, we construct a new weighting matrix for the numerical simulation contribution in the data assimilation objective function. This replaces the typical prior covariance matrix used for this purpose. We further adapt our weighting matrix to include information in discontinuity regions via a clustering technique. Our numerical experiments demonstrate that this new approach yields more accurate estimates than those obtained using standard ensemble-based Kalman filtering on shallow water equations, even when it is enhanced with inflation and localization techniques.

Iterated rational quadratic kernel - High-order unscented Kalman filtering algorithm for spacecraft tracking

The high-speed development of space defense technology demands a high state estimation capacity for spacecraft tracking methods. However, reentry flight is accompanied by complex flight environments, which brings to the uncertain, complex, and strongly coupled non-Gaussian detection noise. As a result, there are several intractable considerations on the problem of state estimation tasks corrupted by complex non-Gaussian outliers for non-linear dynamics systems in practical application. To address these issues, a new iterated rational quadratic (RQ) kernel high-order unscented Kalman filtering (IRQ-HUKF) algorithm via capturing the statistics to break through the limitations of the Gaussian assumption is proposed. Firstly, the characteristic analysis of the RQ kernel is investigated in detail, which is the first attempt to carry out an exploration of the heavy-tailed characteristic and the ability on capturing high-order moments of the RQ kernel. Subsequently, the RQ kernel method is first introduced into the UKF algorithm as an error optimization criterion, termed the iterated RQ kernel-UKF (RQ-UKF) algorithm by derived analytically, which not only retains the high-order moments propagation process but also enhances the approximation capacity in the non-Gaussian noise problem for its ability in capturing high-order moments and heavy-tailed characteristics. Meanwhile, to tackle the limitations of the Gaussian distribution assumption in the linearization process of the non-linear systems, the high-order Sigma Points (SP) as a subsidiary role in propagating the state high-order statistics is devised by the moments matching method to improve the RQ-UKF. Finally, to further improve the flexibility of the IRQ-HUKF algorithm in practical application, an adaptive kernel parameter is derived analytically grounded in the Kullback-Leibler divergence (KLD) method and parametric sensitivity analysis of the RQ kernel. The simulation results demonstrate that the novel IRQ-HUKF algorithm is more robust and outperforms the existing advanced UKF with respect to the kernel method in reentry vehicle tracking scenarios under various noise environments.

Density-driven free convection in heterogeneous aquifers with connectivity features

Free convection usually happens in variable-density groundwater flow systems, and it favors contaminant transport by enlarging length scales and shortening timescales compared to advection and diffusion/dispersion alone. Previous studies have demonstrated that heterogeneity with multi-variate Gaussian distribution for logarithmic permeabilities (log10k) plays an important role in the onset, growth, and/or decay of instability during the density-driven convective process. Nevertheless, the connectivity features (i.e., connected structures of extremely high/low-k values), which are common in natural aquifers, have received little attention. In this study, the classical problem of transient free convection has been modified and numerically simulated by Monte Carlo approach to investigate the effects of connectivity features in heterogeneity on the unstable convective processes. Results show that free convection is promoted by the connected high-k structures and retarded by the connected low-k structures during mainly the early-stage mass loading. The impacts of connectivity features tend to be amplified by higher variation in log10k distributions, and can be secondarily influenced by correlation lengths and anisotropy. Under the multi-variate Gaussian assumption, the existence of connected high-k structures leads to underestimation of density-driven instability, in which the risk differs based on the statistics of permeability fields, metrics of interest and timeframe. This study highlights the importance of understanding connectivity features in heterogeneous geological media when assessing density-dependent solute transport in groundwater systems.

Generating Independent Replicates Directly from the Posterior Distribution for a Class of Spatial Hierarchical Models

Markov chain Monte Carlo (MCMC) allows one to generate dependent replicates from a posterior distribution for effectively any Bayesian hierarchical model. However, MCMC can produce a significant computational burden. This motivates us to consider finding expressions of the posterior distribution that are computationally straightforward to obtain independent replicates from directly. We focus on a broad class of Bayesian hierarchical models for spatially dependent data, which are often modeled via a latent Gaussian process (LGP). First, we derive a new class of distributions referred to as the generalized conjugate multivariate (GCM) distribution. The GCM distribution’s theoretical development follows that of the conjugate multivariate (CM) distribution with two main differences: the GCM allows for latent Gaussian process assumptions, and the GCM explicitly accounts for hyperparameters through marginalization. The development of GCM is needed to obtain independent replicates directly from the exact posterior distribution, which has an efficient regression form. Hence, we refer to our method as Exact Posterior Regression (EPR). Simulation studies with weakly stationary spatial processes and spatial basis function expansions are provided. We provide an analysis of poverty incidence from the U.S. Census Bureau, and an analysis of high-dimensional remote sensing data. Supplementary materials for this article are available online.

A multivariate student-t process model for dependent tail-weighted degradation data

Traditionally, the Gaussian assumption, implied by the Wiener process, is widely admitted for modeling degradation processes. However, when degradation data exhibit heavy tails, this assumption is not suitable. To overcome this limitation, this article proposes a novel class of tail-weighted multivariate degradation model, which is built upon Student-t process. The model is able to account for both between-unit variability and process dependency, while allowing the adjustment of tail heaviness through tuning the parameter of the degree of freedom. For reliability assessment, we derive the system reliability function and present an efficient Monte Carlo method for its evaluation. Further, we introduce an expectation–maximization algorithm for parameter estimation and design a bootstrap method for interval estimation. Comprehensive simulation studies are conducted to validate the effectiveness of the inference method. Finally, the proposed methodology is applied to analyze two real-world degradation datasets.

Neural Operator Variational Inference Based on Regularized Stein Discrepancy for Deep Gaussian Processes.

Deep Gaussian process (DGP) models offer a powerful nonparametric approach for Bayesian inference, but exact inference is typically intractable, motivating the use of various approximations. However, existing approaches, such as mean-field Gaussian assumptions, limit the expressiveness and efficacy of DGP models, while stochastic approximation can be computationally expensive. To tackle these challenges, we introduce neural operator variational inference (NOVI) for DGPs. NOVI uses a neural generator to obtain a sampler and minimizes the regularized Stein discrepancy (RSD) between the generated distribution and true posterior in L2 space. We solve the minimax problem using Monte Carlo estimation and subsampling stochastic optimization techniques and demonstrate that the bias introduced by our method can be controlled by multiplying the Fisher divergence with a constant, which leads to robust error control and ensures the stability and precision of the algorithm. Our experiments on datasets ranging from hundreds to millions demonstrate the effectiveness and the faster convergence rate of the proposed method. We achieve a classification accuracy of 93.56 on the CIFAR10 dataset, outperforming state-of-the-art (SOTA) Gaussian process (GP) methods. We are optimistic that NOVI possesses the potential to enhance the performance of deep Bayesian nonparametric models and could have significant implications for various practical applications.

Most frequent value analysis of distance measurements to M87

Abstract We reanalyze the recent compilation of distance measurements to M87 by collecting the data from published literature. Different from the traditional statistical methods, based on the principle of minimum information loss, we use a robust most frequent value (MFV) procedure to estimate the distance to M87, irrespective of the Gaussian or non-Gaussian distributions. The MFV-based robust estimate for the M87 distance modulus is given by $31.09^{+0.04}_{-0.03}$(statistical)$^{+0.05}_{-0.07}$ (systematic) mag corresponding to a 68.27% confidence interval, whereas the result of combining the two uncertainties in quadrature is $31.09^{+0.06}_{-0.08}$ mag. We also construct the error distributions of M87 distance moduli values according to the weighted mean, median, and MFV, which is non-Gaussian. This demonstrates that the MFV method offers a more accurate and robust estimate of the distance to M87 compared to methods that depend on the unfulfilled assumption of Gaussianity.

Efficient Local Coherent Structure Learning via Self-Evolution Bipartite Graph.

Dimensionality reduction (DR) targets to learn low-dimensional representations for improving discriminability of data, which is essential for many downstream machine learning tasks, such as image classification, information clustering, etc. Non-Gaussian issue as a long-standing challenge brings many obstacles to the applications of DR methods that established on Gaussian assumption. The mainstream way to address above issue is to explore the local structure of data via graph learning technique, the methods based on which however suffer from a common weakness, that is, exploring locality through pairwise points causes the optimal graph and subspace are difficult to be found, degrades the performance of downstream tasks, and also increases the computation complexity. In this article, we first propose a novel self-evolution bipartite graph (SEBG) that uses anchor points as the landmark of subclasses, and learns anchor-based rather than pairwise relationships for improving the efficiency of locality exploration. In addition, we develop an efficient local coherent structure learning (ELCS) algorithm based on SEBG, which possesses the ability of updating the edges of graph in learned subspace automatically. Finally, we also provide a multivariable iterative optimization algorithm to solve proposed problem with strict theoretical proofs. Extensive experiments have verified the superiorities of the proposed method compared to related SOTA methods in terms of performance and efficiency on several real-world benchmarks and large-scale image datasets with deep features.

Multi-Person Pose Regression With Distribution-Aware Single-Stage Models.

Understanding human posture is a challenging topic, which encompasses several tasks, e.g., pose estimation, body mesh recovery and pose tracking. In this article, we propose a novel Distribution-Aware Single-stage (DAS) model for the pose-related tasks. The proposed DAS model estimates human position and localizes joints simultaneously, which requires only a single pass. Meanwhile, we utilize normalizing flow to enable DAS to learn the true distribution of joint locations, rather than making simple Gaussian or Laplacian assumptions. This provides a pivotal prior and greatly boosts the accuracy of regression-based methods, thus making DAS achieve comparable performance to the volumetric-based methods. We also introduce a recursively update strategy to progressively approach the regression target, reducing the difficulty of regression and improving the regression performance. We further adapt DAS to multi-person mesh recovery and pose tracking tasks and achieve considerable performance on both tasks. Comprehensive experiments on CMU Panoptic and MuPoTS-3D demonstrate the superior efficiency of DAS, specifically 1.5 times speedup over previous best method, and its state-of-the-art accuracy for multi-person pose estimation. Extensive experiments on 3DPW and PoseTrack2018 indicate the effectiveness and efficiency of DAS for human body mesh recovery and pose tracking, respectively, which prove the generality of our proposed DAS model.

On the efficiency of misspecified Gaussian inference in nonlinear regression: Application to time-delay and Doppler estimation

Nonlinear regression plays a crucial role in various engineering applications. For the sake of mathematical tractability and ease of implementation, most of the existing inference procedures are derived under the assumption of independent and identically distributed (i.i.d.) Gaussian-distributed data. However, real-world situations often deviate from this assumption, with the true data generating process being a correlated, heavy-tailed and non-Gaussian one. The paper aims at providing the Misspecified Cramér–Rao Bound (MCRB) on the Mean Squared Error (MSE) of any unbiased (in a proper sense) estimator of the parameters of a nonlinear regression model derived under the i.i.d. Gaussian assumption in the place of the actual correlated, non-Gaussian data generating process. As a special case, the MCRB for an uncorrelated, i.i.d. Complex Elliptically Symmetric (CES) data generating process under Gaussian assumption is also provided. Consistency and asymptotic normality of the related Mismatched Maximum Likelihood Estimator (MMLE) will be discussed along with its connection with the Nonlinear Least Square Estimator (NLLSE) inherent to the nonlinear regression model. Finally, the derived theoretical findings will be applied in the well-known problem of time-delay and Doppler estimation for GNSS.

Denoising diffusion delensing: reconstructing the non-Gaussian CMB lensing potential with diffusion models

ABSTRACT Optimal extraction of cosmological information from observations of the cosmic microwave background (CMB) critically relies on our ability to accurately undo the distortions caused by weak gravitational lensing. In this work, we demonstrate the use of denoising diffusion models in performing Bayesian lensing reconstruction. We show that score-based generative models can produce accurate, uncorrelated samples from the CMB lensing convergence map posterior, given noisy CMB observations. To validate our approach, we compare the samples of our model to those obtained using established Hamiltonian Monte Carlo methods, which assume a Gaussian lensing potential. We then go beyond this assumption of Gaussianity, and train and validate our model on non-Gaussian lensing data, obtained by ray-tracing N-body simulations. We demonstrate that in this case, samples from our model have accurate non-Gaussian statistics beyond the power spectrum. The method provides an avenue towards more efficient and accurate lensing reconstruction, which does not rely on an approximate analytical description of the posterior probability. The reconstructed lensing maps can be used as an unbiased tracer of the matter distribution, and to improve delensing of the CMB, resulting in more precise cosmological parameter inference.

Identification of switched gated recurrent unit neural networks with a generalized Gaussian distribution

Due to the limitations of the model itself, the performance of switched autoregressive exogenous (SARX) models will face potential threats when modeling nonlinear hybrid dynamic systems. To address this problem, a robust identification approach of the switched gated recurrent unit (SGRU) model is developed in this paper. Firstly, all submodels of the SARX model are replaced by gated recurrent unit neural networks. The obtained SGRU model has stronger nonlinear fitting ability than the SARX model. Secondly, this paper departs from the conventional Gaussian distribution assumption for noise, opting instead for a generalized Gaussian distribution. This enables the proposed model to achieve stable prediction performance under the influence of different noises. Notably, no prior assumptions are imposed on the knowledge of operating modes in the proposed switched model. Therefore, the EM algorithm is used to solve the problem of parameter estimation with hidden variables in this paper. Finally, two simulation experiments are performed. By comparing the nonlinear fitting ability of the SGRU model with the SARX model and the prediction performance of the SGRU model under different noise distributions, the effectiveness of the proposed approach is verified.

A Bayesian nonparametric approach for causal mediation with a post-treatment confounder.

We propose a new Bayesian nonparametric method for estimating the causal effects of mediation in the presence of a post-treatment confounder. The methodology is motivated by the Rural Lifestyle Intervention Treatment Effectiveness Trial (Rural LITE) for which there is interest in estimating causal mediation effects but is complicated by the presence of a post-treatment confounder. We specify an enriched Dirichlet process mixture (EDPM) to model the joint distribution of the observed data (outcome, mediator, post-treatment confounder, treatment, and baseline confounders). For identifiability, we use the extended version of the standard sequential ignorability (SI) as introduced in Hong etal. along with a Gaussian copula model assumption. The observed data model and causal identification assumptions enable us to estimate and identify the causal effects of mediation, that is, the natural direct effects (NDE) and natural indirect effects (NIE). Our method enables easy computation of NIE and NDE for a subset of confounding variables and addresses missing data through data augmentation under the assumption of ignorable missingness. We conduct simulation studies to assess the performance of our proposed method. Furthermore, we apply this approach to evaluate the causal mediation effect in the Rural LITE trial, finding that there was not strong evidence for the potential mediator.

Comparative analysis of fluctuations in viscoelastic stress: A comparison of the temporary network and dumbbell models

Traditionally, stress fluctuations in flowing and deformed materials are overlooked, with an obvious focus on average stresses in a continuum mechanical approximation. However, these fluctuations, often dismissed as “noise,” hold the potential to provide direct insights into the material structure and its structure-stress coupling, uncovering detailed aspects of fluid transport and relaxation behaviors. Despite advancements in experimental techniques allowing for the visualization of these fluctuations, their significance remains largely untapped as modeling efforts continue to target Newtonian fluids within the confines of Gaussian noise assumptions. In the present work, a comparative analysis of stress fluctuations in two distinct microstructural models is carried out: the temporary network model and the hydrodynamic dumbbell model. Despite both models conforming to the upper convected Maxwell model at a macroscopic level, the temporary network model predicts non-Gaussian fluctuations. We find that stress fluctuations within the temporary network model exhibit more pronounced abruptness at the local scale, with only an enlargement of the control volume leading to a gradual Gaussian-like noise, diminishing the differences between the two models. These findings underscore the heightened sensitivity of fluctuating rheology to microstructural details and the microstructure–flow coupling, beyond what is captured by macroscopically averaged stresses.

A Novel DOA Estimation Algorithm Based on Robust Mixed Fractional Lower-Order Correntropy in Impulsive Noise

The estimation of direction of arrival (DOA) is paramount in the realm of practical array signal processing systems. Nevertheless, traditional estimation methods often rely heavily on the Gaussian noise assumption, rendering them ineffective in achieving high-precision estimates in environments plagued by strong impulsive noise. To address this challenge, this paper introduces a novel DOA estimation algorithm that leverages mixed fractional lower-order correntropy (MFLOCR) in the context of Alpha-stable distributed impulsive noise. Correntropy is used as a measure of the similarity of the signals, using a Gaussian function to smooth extreme values and provide greater robustness against impulsive noise. By utilizing diverse kernel lengths to jointly regulate the kernel function, the concept of correntropy is expanded and implemented in the fractional lower-order moment (FLOM) algorithm for received signals. Subsequently, the MFLOCR is derived by adjusting the resulting form of correntropy. Finally, an enhanced DOA estimation algorithm is proposed that combines the MFLOCR operator with the MUSIC algorithm, specifically tailored for impulsive noise environments. Furthermore, a proof of boundedness is provided to validate the effectiveness of the proposed approach in such noisy conditions. Simulation experiments confirmed that the proposed method outperforms existing DOA estimation methods in the context of intense impulsive noise, a low generalized signal-to-noise ratio (GSNR), and a smaller number of snapshots.

Application of latent variable evolution for channel reservoir characterization using generative adversarial networks and particle swarm optimization

When characterizing channel reservoirs, ensemble-based methods may compromise channel features due to the conflict between the Gaussian distribution assumption of the methods and bimodality of channel reservoirs. To overcome this challenge, one effective approach involves leveraging generative models. Specifically, a generative model trained with channel reservoir models has ability to generate bimodally distributed values from latent vectors whose elements are intentionally designed to conform a Gaussian distribution. Therefore, it resolves the conflict, allowing the ensemble-based methods to update the latent vectors.However, generating initial latent vectors randomly poses an additional challenge and can lead to a suboptimal quality of the initial ensemble. They can significantly influence the unreliability of characterizations, primarily because their impact is strongly tied to the quality of the initial models in the ensemble-based methods.To address this challenge, we propose a novel scheme for channel reservoir characterization using Latent Variable Evolution. In this study, we adopt Generative Adversarial Networks (GAN) and Particle Swarm Optimization (PSO). PSO explores the latent space of GAN trained with channel reservoirs in order to find ones that generate models resembling a true reservoir. Validation on simple and complex reservoir cases demonstrates our proposed method can efficiently provide reliable channel reservoir characterization regardless of the quality of the initial latent vectors. These results are compared to Ensemble Smoother with Multiple Data Assimilation with GAN.

Advances in Radar Signal Processing: Integrating Deep Learning Approaches

In the military, in daily life, and in scientific research, radar technology is widely used. Radar signal processing has long been an essential component in target detection and imaging. The development of deep learning technology in recent years has given radar signal processing new approaches and resources. With its exceptional feature extraction and pattern recognition skills, deep learning has made amazing strides and has been applied to radar signal processing to enhance tasks like target detection, tracking, and recognition. Traditional radar signal processing is based on models. It mainly uses the prior information of the model and related signal processing criteria to design signal processing methods. It uses Gaussian, linear, and stationary assumptions. The deep learning method is a data-based method that does not require prior knowledge of the model and can spontaneously find the relationship between the input of the algorithm and the expected output. This article will review traditional methods and deep learning methods in radar signal processing, focusing on the application and future development direction of deep learning methods in radar signal processing, briefly sorting out the research progress in recent years, and analyze some existing problems or shortcomings of existing methods.