Classical Gaussian Model Research Articles

On Training Targets and Activation Functions for Deep Representation Learning in Text-Dependent Speaker Verification

Deep representation learning has gained significant momentum in advancing text-dependent speaker verification (TD-SV) systems. When designing deep neural networks (DNN) for extracting bottleneck (BN) features, the key considerations include training targets, activation functions, and loss functions. In this paper, we systematically study the impact of these choices on the performance of TD-SV. For training targets, we consider speaker identity, time-contrastive learning (TCL), and auto-regressive prediction coding, with the first being supervised and the last two being self-supervised. Furthermore, we study a range of loss functions when speaker identity is used as the training target. With regard to activation functions, we study the widely used sigmoid function, rectified linear unit (ReLU), and Gaussian error linear unit (GELU). We experimentally show that GELU is able to reduce the error rates of TD-SV significantly compared to sigmoid, irrespective of the training target. Among the three training targets, TCL performs the best. Among the various loss functions, cross-entropy, joint-softmax, and focal loss functions outperform the others. Finally, the score-level fusion of different systems is also able to reduce the error rates. To evaluate the representation learning methods, experiments are conducted on the RedDots 2016 challenge database consisting of short utterances for TD-SV systems based on classic Gaussian mixture model-universal background model (GMM-UBM) and i-vector methods.

Physics-Guided Reduced-Order Representation of Three-Dimensional Sound Speed Fields with Ocean Mesoscale Eddies

Ocean mesoscale eddies have an important role in the ocean and affect the underwater sound speed field (SSF). Many physical models have been proposed for mesoscale eddy three-dimensional (3D) structure analysis and construction. Here, we propose a model for the reduced-order representation of 3D SSF with ocean mesoscale eddies. Particularly, the radial basis functions (RBFs), which are guided by the universal physics model of mesoscale eddy in horizontal dimensions, are employed. RBF and empirical orthogonal function (EOF) are used as basis functions for 3D representation. The proposed method is an approximation of the classical Gaussian eddy model in the first-order form. Simulation results confirm the reduced-order representation performance and effectiveness in reconstruction using 136 days of HYCOM data in the northwestward of the South China Sea with a warm eddy and a cold eddy. The proposed RBF + EOF method roughly halves the number of coefficients for mesoscale eddy representation, compared with classical methods. The reduced-order representation method can be utilized in ocean acoustic tomography and acoustic remote sensing in a mesoscale area.

Macrodispersion in generalized sub-Gaussian randomly heterogeneous porous media

• Features of log-conductivity, Y , fields are captured by a non-Gaussian (GSG) model. • Expressions of flow and transport moments in three-dimensional GSG fields are derived. • Head and velocity fields are more correlated in GSG than in Gaussian Y structures. • Non-Gaussianity of Y heavily influences pre-asymptotic macrodispersion values. • Late time transport exhibits a Fickian behavior also in non-Gaussian Y fields. In this work, we explore the implications of modeling the logarithm of hydraulic conductivity, Y , as a Generalized Sub-Gaussian (GSG) field on the features of conservative solute transport in randomly heterogeneous, three-dimensional porous media. Hydro-geological properties are often viewed as Gaussian random fields. Nevertheless, the GSG model enables us to capture documented non-Gaussian traits that are not explained through classical Gaussian models. Our formulation yields lead- (or first-) order analytical solutions for key statistical moments of flow and transport variables. These include flow velocities, hydraulic head, and macrodispersion coefficients, as obtained across GSG log-conductivity fields. The analytical model is based on a first-order spectral theory, which constrains the rigorous validity of our results to small values of log-conductivity variance ( σ Y 2 < < 1 ). Analytical results are then compared against detailed numerical estimates obtained through a Monte Carlo scheme encompassing various levels of domain heterogeneity. An asymptotic Fickian transport regime is attained at late times in both Gaussian and GSG Y fields. Convergence to such regime is slower for GSG as compared to Gaussian fields. This suggests a strong impact of the heterogeneity structure on non-Fickian pre-asymptotic behaviors of the kind documented in the literature. The quality of the comparison between analytical and numerical results deteriorates with increasing σ Y 2 . Otherwise, our lead-order solutions frame macrodispersion coefficients in appropriate orders of magnitude also for values of σ Y 2 up to approximately 1.7, which are consistent with the spatial variability of Y across a single geological unit. In this sense, our analytical approach enables one to obtain prior information on solute plume evolution and to grasp the effects of non-Gaussian medium heterogeneity while favoring simplicity. Our findings also enhance the current level of understanding of the nature of mass transfer across heterogeneous media characterized by complex variability structures which cannot be reconciled with classical Gaussian scenarios.

A Gaussian moment method for polydisperse multiphase flow modelling

The accurate prediction of multiphase flow when particles are differentiated by a set of “internal” variables, such as size or temperature, can pose modelling and numerical challenges. Although Lagrangian particle methods can provide predictive simulations of a wide spectrum of complex multiphase problems, they can become prohibitively expensive as the number of particles becomes large. Alternatively, Eulerian approaches have the potential to improve the computational efficiency of multiphase flows, but classical methods produce modelling artifacts or do not properly treat the local statistical dependence between the particle velocities and internal variables, or between the internal variables themselves. In this paper an extension is proposed of the classical Gaussian ten-moment model from gaskinetic theory to a model for the treatment of a dilute particle phase with an arbitrary number of internal variables based on an entropy-maximization argument. Unlike previous formulations, this new model provides a set of first-order robustly-hyperbolic balance laws that include a direct treatment for the local statistical variance of each variable, as well as the covariance between the internal variables or the internal variables and particle velocity. A study of the wave speeds of the general hyperbolic system is presented. To demonstrate an example application, the model is then specialized for polydisperse flows that are subject to viscous fluid drag as well as gravitational and buoyancy forces. The complete eigenstructure of this fifteen-moment polydisperse Gaussian model (PGM) is presented and the PGM is shown to maintain a physically realizable distribution function for all admissible initial conditions. Finally, several illustrative low-dimensional problems are studied to demonstrate the predictive capabilities of the new model.

Weighted Fused Pathway Graphical Lasso for Joint Estimation of Multiple Gene Networks.

Gene regulatory networks (GRNs) are often inferred based on Gaussian graphical models that could identify the conditional dependence among genes by estimating the corresponding precision matrix. Classical Gaussian graphical models are usually designed for single network estimation and ignore existing knowledge such as pathway information. Therefore, they can neither make use of the common information shared by multiple networks, nor can they utilize useful prior information to guide the estimation. In this paper, we propose a new weighted fused pathway graphical lasso (WFPGL) to jointly estimate multiple networks by incorporating prior knowledge derived from known pathways and gene interactions. Based on the assumption that two genes are less likely to be connected if they do not participate together in any pathways, a pathway-based constraint is considered in our model. Moreover, we introduce a weighted fused lasso penalty in our model to take into account prior gene interaction data and common information shared by multiple networks. Our model is optimized based on the alternating direction method of multipliers (ADMM). Experiments on synthetic data demonstrate that our method outperforms other five state-of-the-art graphical models. We then apply our model to two real datasets. Hub genes in our identified state-specific networks show some shared and specific patterns, which indicates the efficiency of our model in revealing the underlying mechanisms of complex diseases.

Multichannel Audio Source Separation With Deep Neural Networks

This article addresses the problem of multichannel audio source separation. We propose a framework where deep neural networks (DNNs) are used to model the source spectra and combined with the classical multichannel Gaussian model to exploit the spatial information. The parameters are estimated in an iterative expectation-maximization (EM) fashion and used to derive a multichannel Wiener filter. We present an extensive experimental study to show the impact of different design choices on the performance of the proposed technique. We consider different cost functions for the training of DNNs, namely the probabilistically motivated Itakura–Saito divergence, and also Kullback–Leibler, Cauchy, mean squared error, and phase-sensitive cost functions. We also study the number of EM iterations and the use of multiple DNNs, where each DNN aims to improve the spectra estimated by the preceding EM iteration. Finally, we present its application to a speech enhancement problem. The experimental results show the benefit of the proposed multichannel approach over a single-channel DNN-based approach and the conventional multichannel nonnegative matrix factorization-based iterative EM algorithm.

Contaminant dispersion prediction and source estimation with integrated Gaussian-machine learning network model for point source emission in atmosphere

Gas dispersion model is important for predicting the gas concentrations when contaminant gas leakage occurs. Intelligent network models such as radial basis function (RBF), back propagation (BP) neural network and support vector machine (SVM) model can be used for gas dispersion prediction. However, the prediction results from these network models with too many inputs based on original monitoring parameters are not in good agreement with the experimental data. Then, a new series of machine learning algorithms (MLA) models combined classic Gaussian model with MLA algorithm has been presented. The prediction results from new models are improved greatly. Among these models, Gaussian-SVM model performs best and its computation time is close to that of classic Gaussian dispersion model. Finally, Gaussian-MLA models were applied to identifying the emission source parameters with the particle swarm optimization (PSO) method. The estimation performance of PSO with Gaussian-MLA is better than that with Gaussian, Lagrangian stochastic (LS) dispersion model and network models based on original monitoring parameters. Hence, the new prediction model based on Gaussian-MLA is potentially a good method to predict contaminant gas dispersion as well as a good forward model in emission source parameters identification problem.

Formulation of stability-dependent empirical relations for turbulent intensities from surface layer turbulence measurements for dispersion parameterization in a lagrangian particle dispersion model

Season- and stability-dependent turbulence intensity (σu/u*, σv/u*, σw/u*) relationships are derived from experimental turbulence measurements following surface layer scaling and local stability at the tropical coastal site Kalpakkam, India for atmospheric dispersion parameterization. Turbulence wind components (u′, v′, w′) measured with fast response UltraSonic Anemometers during an intense observation campaign for wind field modeling called Round Robin Exercise are used to formulate the flux–profile relationships using surface layer similarity theory and Fast Fourier Transform technique. The new relationships (modified Hanna scheme) are incorporated in a Lagrangian Particle Dispersion model FLEXPART-WRF and tested by conducting simulations for a field tracer dispersion experiment at Kalpakkam. Plume dispersion analysis of a ground level hypothetical release indicated that the new turbulent intensity formulations provide slightly higher diffusivity across the plume relative to the original Hanna scheme. The new formulations for σu, σv, σw are found to give better agreement with observed turbulent intensities during both stable and unstable conditions under various seasonal meteorological conditions. The simulated concentrations using the two methods are compared with those obtained from a classical Gaussian model and the observed SF6 concentration. It has been found that the new relationships provide comparatively higher diffusion across the plume relative to the model default Hanna scheme and provide downwind concentration results in better agreement with observations.

Land Cover Classification for Polarimetric SAR Images Based on Mixture Models

In this paper, two mixture models are proposed for modeling heterogeneous regions in single-look and multi-look polarimetric SAR images, along with their corresponding maximum likelihood classifiers for land cover classification. The classical Gaussian and Wishart models are suitable for modeling scattering vectors and covariance matrices from homogeneous regions, while their performance deteriorates for regions that are heterogeneous. By comparison, the proposed mixture models reduce the modeling error by expressing the data distribution as a weighted sum of multiple component distributions. For single-look and multi-look polarimetric SAR data, complex Gaussian and complex Wishart components are adopted, respectively. Model parameters are determined by employing the expectation-maximization (EM) algorithm. Two maximum likelihood classifiers are then constructed based on the proposed mixture models. These classifiers are assessed using polarimetric SAR images from the RADARSAT-2 sensor of the Canadian Space Agency (CSA), the AIRSAR sensor of the Jet Propulsion Laboratory (JPL) and the EMISAR sensor of the Technical University of Denmark (DTU). Experiment results demonstrate that the new models fit heterogeneous regions preferably to the classical models and are especially appropriate for extremely heterogeneous regions, such as urban areas. The overall accuracy of land cover classification is also improved due to the more refined modeling.

Pollution models and inverse distance weighting: Some critical remarks

When evaluating the impact of pollution, measurements from remote stations are often weighted by the inverse of distance raised to some nonnegative power (IDW). This is derived from Shepard’s method of spatial interpolation (1968). The paper discusses the arbitrary character of the exponent of distance and the problem of monitoring stations that are close to the reference point. From elementary laws of physics, it is determined which exponent of distance should be chosen (or its upper bound) depending on the form of pollution encountered, such as radiant pollution (including radioactivity and sound), air pollution (plumes, puffs, and motionless clouds by using the classical Gaussian model), and polluted rivers. The case where a station is confused with the reference point (or zero distance) is also discussed: in real cases this station imposes its measurement on the whole area regardless of the measurements made by other stations. This is a serious flaw when evaluating the mean pollution of an area. However, it is shown that this is not so in the case of a continuum of monitoring stations, and the measurement at the reference point and for the whole area may differ, which is satisfactory.

Novel Linear Image Denoising Approach Based on a Modified Gaussian Filter Kernel

A Gaussian noise reduction technique for grayscale images is proposed in this article. It uses a modified Gaussian filter kernel based on a hyperbolic second-order equation. The introduced mathematical model differs from the classic Gaussian model provided by the heat equations, by a localization property. Our filtering approach reduces the amount of Gaussian noise and also enhances the image contrast. Some image denoising experiments that prove the effectiveness of the proposed method are also described in this article.

On Inverse Distance Weighting in Pollution Models

When evaluating the impact of pollution, measurements from remote stations are often weighted by the inverse of distance raised to some nonnegative power (IDW). This is derived from Shepard's method of spatial interpolation (1968). The paper discusses the arbitrary character of the exponent of distance and the problem of monitoring stations that are close to the reference point. From elementary laws of physics, it is determined which exponent of distance should be chosen (or its upper bound) depending on the form of pollution encountered, such as radiant pollution (including radioactivity and sound), air pollution (plumes, puffs, and motionless clouds by using the classical Gaussian model), and polluted rivers. The case where a station is confused with the reference point (or zero distance) is also discussed: in real cases this station imposes its measurement on the whole area regardless of the measurements made by other stations. This is a serious flaw when evaluating the mean pollution of an area. However, it is shown that this is not so in the case of a continuum of monitoring stations, and the measurement at the reference point and for the whole area may differ, which is satisfactory.

Repeat sampling of extreme observations: regression to the mean revisited

The phenomenon of classical regression to the mean was described by Sir Francis Galton in a series of prestigious works in the 19th century. This phenomenon refers to the fact that, in the presence of measurement error, experimental units which give rise to extreme values upon first sampling typically produce less extreme values upon a second independent (or repeat) sampling. This shift from the tails toward the population mean occurs even though there has been no intervention or change in the underlying population or error distributions. The mathematical ideas used to explain this shift typically appeal to correlation arguments and the classical Gaussian model. In this paper we study repeat sampling effects in the tails of arbitrary distributions. Perhaps surprisingly, we are able to show that there are actually three distinct asymptotic repeat sampling effects, of which only one corresponds to Galton’s classical result. These three effects depend on the heaviness of the population tails. In particular, for population distributions with relatively heavy tails the maximum shift occurs in the interior of the distribution. In this case the classical regression effect of Galton actually disappears out in the tails.

Gas diffusion in a pulmonary acinus model: experiments with hyperpolarized helium-3

Diffusion of hyperpolarized helium-3 in epoxy phantoms was experimentally studied by pulsed-gradient nuclear magnetic resonance (NMR). One phantom with a dichotomic branching structure densely filling a cubic volume was built using the Kitaoka algorithm to model a healthy human acinus. Two other phantoms, one with a different size and the other one with a partial destruction of the branched structure, were built to simulate changes occurring at the early stages of emphysema. Gas pressure and composition (mixture with nitrogen) were varied, thus exploring different diffusion regimes. Preliminary measurements in a cylindrical glass cell allowed us to calibrate the gradient intensity with 1% accuracy. Measurements of NMR signal attenuation due to gas diffusion were compared to a classical Gaussian model and to Monte Carlo simulations. In the slow diffusion regime, the Gaussian model was in reasonable agreement with experiments for low gradient intensity, but there was a significant systematic deviation at larger gradient intensity. An apparent diffusion coefficient Dapp was deduced, and in agreement with previous findings, a linear decrease of Dapp/D0 with D0(1/2) was observed, where D0 is the free diffusion coefficient. In the regime of intermediate diffusion, experimental data could be described by the Gaussian model for very small gradient intensities only. The corresponding Dapp/D0 values seemed to reach a constant value. Monte Carlo simulations were generally in fair agreement with the measurements in both regimes. Our results suggest that, for diffusion times typical of medical magnetic resonance imaging, an increase in alveolar size has more impact on signal attenuation than a partial destruction of the branched structure at equivalent surface-to-volume ratio.

The Oklahoma Dispersion Model: Using the Gaussian Plume Model as an Operational Management Tool for Determining Near-Surface Dispersion Conditions across Oklahoma

Abstract The Oklahoma Dispersion Model (ODM) represents a current innovative application of the classic Gaussian plume model in an operational setting. Utilizing a statewide mesoscale automated weather station network (the Oklahoma Mesonet) for current weather conditions and 60-h gridded Nested Grid Model (NGM) model output statistics (MOS) forecasts for future conditions, the ODM is an Internet-based management tool that can be used to qualitatively assess current and future atmospheric dispersion conditions across Oklahoma for near-surface releases of gases and small particulates. The ODM is designed to qualitatively assess concentrations at ground level near the plume centerline at downwind distances of up to 4000 m. The Gaussian plume model is used in conjunction with rural Briggs sigma-y and sigma-z coefficients to estimate horizontal and vertical dispersion. Pasquill stability class is calculated in two ways: for current conditions, Oklahoma Mesonet weather data are used in conjunction with algorithms recommended by the Environmental Protection Agency; for forecast conditions, the Turner method is used. A method is employed that breaks the atmosphere into six dispersion categories, ranging from excellent to very poor. The ODM generates both graphical and text output. Statewide colored maps showing current conditions for dispersion (dilution of plume) and transport (direction of plume movement) are generated every 15 and 5 min, respectively. Similar maps for future conditions are generated every 12 h using gridded 60-h NGM MOS forecasts. In addition to graphical output, tabular output for future conditions at specific MOS locations is available. The ODM has been used as a management tool in the agriculture and natural resources arenas in conjunction with prescribed burning (smoke), pesticide application, and odors associated with animal agriculture.

Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance

The classical Gaussian model, a parametric family of the Gaussian distribution, is known to be a space of constant negative curvature if one regards the Fisher information on the model as a Riemannian metric. Constant curvature reflects the scale invariance of the classical Gaussian model, which is well known in information geometry. However, it is shown that if the Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model is adopted as a Riemannian metric, then this scale invariance on the Gaussian model is broken due to the quantum effect. In the present study, the connection between the geometry of the classical Gaussian model and its quantum counterpart is clarified using the Taylor expansion with respect to the Planck constant. It is further shown that such a method is not applicable to a finite-dimensional system such as the spin system.

A STUDY OF STABLE MODELS OF STOCK MARKETS

Since the middle of the last century, financial engineering has become very popular among mathema-ticians and analysts. Stochastic methods were widely applied in financial engineering. Gaussian models were the first to be applied, but it has been noticed out that they inadequately describe the behavior of financial series. Since the classical Gaussian models were taken with more and more criticism and eventually have lost their positions, new models were proposed. Stable models attracted special attention; however their adequacy in real market should be justified. Nowadays, they have become an extremely powerful and versatile tool in financial modeling. Stock market modeling problems are considered in this paper. Adequacy and efficiency of the chosen model are demonstrated. The parameters of stable laws are estimated by the maximal likelihood method. Multifractality and self-similarity hypo-theses are tested and the Hurst analysis is made as well.

Different parameterisation of a Gaussian scheme: intercomparison study

The aim of this work is to define the most efficient parameterisation of the PBL (planetary boundary layer) by using the simulation with a simple Gaussian dispersion model of the plume type and comparing it with the improved OML model. A different type of σy and σz parameterisation in a Gaussian dispersion scheme was introduced. The old Pasquill–Gifford scheme and the new boundary layer parameterisation based on Monin–Obukhov length and other convective scaling parameters were compared, using a classical Gaussian model. For this comparison, the hourly average concentration and the long-term concentrations generated by these models, using same input data, were computed. These computed values and the field observations clearly show the importance of the parameterisations used by the models and the necessity of improving them. With this new parameterisation, we can easily add in new phenomena, such as dry and wet deposition, building effects and stack tip downwash penetration.

Understanding the elastomeric properties of polymer networks

It is shown that Monte-Carlo (MC) simulations of the elastic behaviour of chains in networks using realistic rotational-isomeric-state (RIS) chain models are able to reproduce experimentally observed deviations from Gaussian network behaviour in uniaxial extension and also to interpret, quantitatively, stress-optical properties. In stress-strain behaviour, an increase in the proportion of fully extended chains with increasing macroscopic strain gives rise to a steady decrease in the rate of change of the Helmholtz energy of a network, causing a reduction in network modulus at moderate macroscopic strains. There is no need to invoke a transition from affine to phantom chain behaviour as deformation increases. To evaluate stress-optical properties, the average orientation of segments with respect to the deformation axis is calculated, taking into account the interdependence of segment orientation and chain orientation as chains become more extended and aligned under uniaxial stress. The MC method gives, in agreement with experiment, values of stress-optical coefficient that are dependent upon both deformation ratio and network-chain length. The method highlights serious shortcomings in the classical Gaussian model of stress-optical behaviour. Applications of the simulation methods to the quantitative modelling of the stress-strain behaviour of poly(dimethyl siloxane) networks and the stress-optical behaviour of polyethylene networks are described.

Critical behavior of the Gaussian model on fractal lattices in external magnetic field

For inhomogeneous lattices we generalize the classical Gaussian model, i.e. it is proposed that the Gaussian type distribution constant and the external magnetic field of site i in this model depend on the coordination number q i of site i , and that the relation b q i /b q j =q i q j holds among b q i 's, where b q i is the Gaussian type distribution constant of site i . Using the decimation real-space renormalization group following the spin-rescaling method, the critical points and critical exponents of the Gaussian model are calculated on some Koch type curves and a family of the diamond-type hierarchical (or DH) lattices. At the critical points, it is found that the nearest-neighbor interaction and the magnetic field of site i can be expressed in the form K * = b q i / q i and h q 1 * =0, respectively. It is also found that most critical exponents depend on the fractal dimensionality of a fractal system. For the family of the DH lattices, the results are identical with the exact results on translation symmetric lattices, and if the fractal dimensionality d f =4, the Gaussian model and the mean field theories give the same results.