Higher Order Statistics Research Articles

Multimodal diffusion model for increments of electroencephalogram data

AbstractWe propose a new strictly stationary strong mixing diffusion model with marginal multimodal (three-peak) distribution and exponentially decaying autocorrelation function for modeling of increments of electroencephalogram data collected from Ugandan children during coma from cerebral malaria. We treat the increments as discrete-time observations and construct a diffusion process where the stationary distribution is viewed as a mixture of three non-central generalized Gaussian distributions and we state some important properties related to the moments of this mixture. We estimate the distribution parameters using the expectation-maximization algorithm, where the added shape parameter is estimated using the higher order statistics approach based on an analytical relationship between the shape parameter and kurtosis. The derived estimates are then used for prediction of subsequent neurodevelopment and cognition of cerebral malaria survivors using the elastic net regression. We compare different predictive models and determine whether additional information obtained from multimodality of the marginal distributions can be used to improve the prediction.

Distributed maximum correntropy Kalman filter with state equality constraints in a sensor network with packet drops

This study presents the design of a distributed Kalman filter with excellent performance in a sensor network with packet drops and non-Gaussian noise. The proposed filter incorporates the maximum correntropy criterion and state equality constraint information. The maximum correntropy criterion is employed to handle non-Gaussian noise by utilizing higher-order statistics. To achieve superior estimation performance, the equality constrained filter is obtained by incorporating state equality constraint information. Furthermore, to enhance the consistency in the estimation of each node, the equality constrained distributed maximum correntropy Kalman filter is established through the covariance interaction algorithm. Finally, the effectiveness of the proposed filter is verified by simulation results.

A novel magnetic calibration method based on an extended shaping filter

During maneuvering of high-speed aircraft, the eddy-current magnetic field has a significant impact on the real-time geomagnetic field measurement accuracy. However, it is difficult to estimate the eddy-current component directly when it is considered in the magnetic distortion model. In this paper, we proposed a geomagnetic field estimation method based on a shaping filter. Soft-iron, hard-iron and eddy-current field distortions were considered in the compensation system. In the estimation process, a higher-order shaping filter is designed to coincide the higher-order statistics of the alternative system with the input of the original system. Simulation results showed that our proposed method could accurately estimate the eddy-current field. Compared with methods that do not consider the eddy-current field, the root-mean-square error of the geomagnetic field could be reduced by more than 50%, thus significantly improving the accuracy of geomagnetic field measurement.

Modelling the next-to-leading order matter three-point correlation function using FFTLog

The study of higher-order statistics, particularly 3-point statistics, of the Large Scale Structure (LSS) of the Universe provides us with unique information on the biasing relation between luminous and dark matter and on deviations from primordial Gaussianity. As a result, much effort has been put into improving measurement techniques as well as theoretical modelling, especially in Fourier space. Comparatively, little progress has been made, instead, in configuration space analyses. This work represents a first step towards filling this gap by proposing a new strategy for modelling 3-point statistics at higher perturbative orders in configuration space. Starting from the next-to-leading order model for the matter bispectrum, we use 2D-FFTLog to generate its counterpart in configuration space. We calibrate the procedure using the leading order predictions for which an analytic model for the 3-point correlation function (3PCF) already exists. Then we assess the goodness of the 3PCF model by comparing its predictions with measurements performed on the matter distribution in collisionless cosmological N-body simulation (DEMNUni). We focus on two redshifts (z = 0.49 and z = 1.05) in the range spanned by current and future galaxy redshift surveys. The χ 2 analysis reveals that the next-to-leading order 3PCF models significantly improve over the leading order one for all triangle configurations in both redshifts, increasing the number of matched configurations at redshift z = 1.05 and z = 0.49, respectively. In particular, a significant improvement is also seen on the Baryonic Acoustic Oscillations (BAO) scale for triangle configurations whose smallest side length is well into the nonlinear regime. The computational cost of the model proposed here is high but not prohibitively large — order of five hours in a 48-core computation — and represents the first step towards a complete 3PC model for the galaxies.

Shape-Aware Joint Distribution Alignment for Cross-Domain Image Segmentation.

We present an unsupervised domain adaptation method for image segmentation which aligns high-order statistics, computed for the source and target domains, encoding domain-invariant spatial relationships between segmentation classes. Our method first estimates the joint distribution of predictions for pairs of pixels whose relative position corresponds to a given spatial displacement. Domain adaptation is then achieved by aligning the joint distributions of source and target images, computed for a set of displacements. Two enhancements of this method are proposed. The first one uses an efficient multi-scale strategy that enables capturing long-range relationships in the statistics. The second one extends the joint distribution alignment loss to features in intermediate layers of the network by computing their cross-correlation. We test our method on the task of unpaired multi-modal cardiac segmentation using the Multi-Modality Whole Heart Segmentation Challenge dataset and prostate segmentation task where images from two datasets are taken as data in different domains. Our results show the advantages of our method compared to recent approaches for cross-domain image segmentation. Code is available at https://github.com/WangPing521/Domain_adaptation_shape_prior.

Retail Demand Forecasting Using Spatial-Temporal Gradient Boosting Methods

ABSTRACT With the significant growth of the e-commerce business, the retail industry is experiencing rapid developments, leading to the explosion of the number of stock-keeping units (SKUs). Therefore, it calls for forecasting algorithms to forecast a large number of product-level demands over a short forecasting horizon. We developed a novel machine learning algorithm—the spatial-temporal gradient boosting tree (ST-GBT)—for demand forecasting for the retail industry. By incorporating the cross-section and time-series information in the existing gradient-boosting decision tree algorithm, our new algorithm can accurately forecast tremendous SKUs in one process. Furthermore, we show potential factors related to the retail industry, while new factors, such as higher-order statistics and risk-free interest, are also proposed for demand forecasting tasks. The numerical experiment results based on a large e-commerce company’s historical transaction records support the comparative merits of the new algorithm with superior accuracy and automation ability.

Towards a full wCDM map-based analysis for weak lensing surveys

ABSTRACT The next generation of weak lensing surveys will measure the matter distribution of the local universe with unprecedented precision, allowing the resolution of non-Gaussian features of the convergence field. This encourages the use of higher-order mass-map statistics for cosmological parameter inference. We extend the forward-modelling based methodology introduced in a previous forecast paper to match these new requirements. We provide multiple forecasts for the $w$CDM parameter constraints that can be expected from stage 3 and 4 weak lensing surveys. We consider different survey setups, summary statistics and mass map filters including wavelets. We take into account the shear bias, photometric redshift uncertainties, and intrinsic alignment. The impact of baryons is investigated and the necessary scale cuts are applied. We compare the angular power spectrum analysis to peak and minima counts as well as Minkowski functionals of the mass maps. We find a preference for Starlet over Gaussian filters. Our results suggest that using a survey setup with 10 instead of 5 tomographic redshift bins is beneficial. Adding cross-tomographic information improves the constraints on cosmology and especially on galaxy intrinsic alignment for all statistics. In terms of constraining power, we find the angular power spectrum and the peak counts to be equally matched for stage 4 surveys, followed by minima counts and the Minkowski functionals. Combining different summary statistics significantly improves the constraints and compensates the stringent scale cuts. We identify the most ‘cost-effective’ combination to be the angular power spectrum, peak counts and Minkowski functionals following Starlet filtering.

Exploring Seismic Hazard in the Groningen Gas Field Using Adaptive Kernel Smoothing

The discovery of gas in Groningen in 1959 has been a massive boon to the Dutch economy. From the 1990s onwards, though, gas production has led to induced seismicity. In this paper, we carry out a comprehensive exploratory analysis of the spatio-temporal earthquake catalogue. We develop a non-parametric adaptive kernel smoothing technique to estimate the spatio-temporal hazard map and to interpolate monthly well-based gas production statistics. Second- and higher-order inhomogeneous summary statistics are used to show that the state-of-the-art rate-and-state models for the prediction of seismic hazard fail to capture inter-event interaction in the earthquake catalogue. Based on these findings, we suggest a modified rate-and-state model that also takes into account changes in gas production volumes and uncertainty in the pore pressure field.

Non-stationary non-Gaussian random vibration analysis of Duffing systems based on explicit time-domain method

Non-stationary non-Gaussian random vibration problems of structures are challenging and drawing increasing attention. In the present study, firstly, an explicit time-domain method (ETDM) is proposed to determine the higher-order response statistics of linear systems subjected to non-stationary non-Gaussian random excitations, in which the first four orders of cumulants of dynamic responses are directly formulated through the cumulant operation rule based on the explicit expressions of responses. Secondly, an equivalent linearization – explicit time-domain method (EL-ETDM) is further developed to solve the non-stationary non-Gaussian random vibration problems of Duffing systems, in which the equivalent linear system is derived discarding the assumption of Gaussian response, and the corresponding higher-order cumulant analyses of the linearized system are accomplished by the efficient ETDM. The present approach can account for non-Gaussian random excitations with arbitrary forms, and two specific applications to the Poisson white noise and the square form of Gaussian random process are investigated. Four numerical examples are presented to demonstrate the effectiveness of the proposed methods.

The MillenniumTNG Project: an improved two-halo model for the galaxy–halo connection of red and blue galaxies

ABSTRACT Approximate methods to populate dark-matter haloes with galaxies are of great utility to galaxy surveys. However, the limitations of simple halo occupation models (HODs) preclude a full use of small-scale galaxy clustering data and call for more sophisticated models. We study two galaxy populations, luminous red galaxies (LRGs) and star-forming emission-line galaxies (ELGs), at two epochs, z = 1 and z = 0, in the large-volume, high-resolution hydrodynamical simulation of the MillenniumTNG project. In a partner study we concentrated on the small-scale, one-halo regime down to r ∼ 0.1 h−1 Mpc, while here we focus on modelling galaxy assembly bias in the two-halo regime, r ≳ 1 h−1 Mpc. Interestingly, the ELG signal exhibits scale dependence out to relatively large scales (r ∼ 20 h−1 Mpc), implying that the linear bias approximation for this tracer is invalid on these scales, contrary to common assumptions. The 10–15 per cent discrepancy is only reconciled when we augment our halo occupation model with a dependence on extrinsic halo properties (‘shear’ being the best-performing one) rather than intrinsic ones (e.g. concentration, peak mass). We argue that this fact constitutes evidence for two-halo galaxy conformity. Including tertiary assembly bias (i.e. a property beyond mass and ‘shear’) is not an essential requirement for reconciling the galaxy assembly bias signal of LRGs, but the combination of external and internal properties is beneficial for recovering ELG the clustering. We find that centrals in low-mass haloes dominate the assembly bias signal of both populations. Finally, we explore the predictions of our model for higher order statistics such as nearest neighbour counts. The latter supplies additional information about galaxy assembly bias and can be used to break degeneracies between halo model parameters.

Localization of epileptic surgical area using automated hybrid approach based on higher-order statistics with sensitivity analysis and residual wavelet transform

Epilepsy is a persistent neurological disorder characterized by epileptic seizures. Medication is often unable to regulate epileptic episodes, and surgery is the only cure for epilepsy. Therefore, localizing the epileptic zone is crucial for effective epileptic surgery. This surgical area can be identified through the presence of cerebral intracranial focal electroencephalogram (FEEG) signals. This article proposes a mixed approach based on higher-order statistics (HOS) with sensitivity analysis and residual wavelet transform (RWT). The sensitivity analysis method examines only the portions of the brain signal dominated by transient and burst events, and measuring a set of frequencies associated with underlying nonlinear dynamics. The suggested approach assesses the brain output in two distinct spaces based on these frequency benchmarks. The RWT investigates transient and impulsive changes in a non-stationary time series by evaluating it in time-scale space. Additionally, the HOS explores nonlinear dynamics in higher-dimensional space without loss of generality. The data are then mapped and ranked using a data-reduction method, LSDA (locality sensitivity discrimination analysis). The pertinent and delicate information was decoded using a deep learning method based on bidirectional long-short term memory (bi-LSTM). The results reveal that the presented algorithm has yielded a better discrimination accuracy of 99.76% on the Bern Barcelona EEG database. The proposed algorithm enables a clinician to locate the epileptogenic zone, which is essential for effective brain surgery.

Euclidpreparation

Recent cosmic shear studies have shown that higher-order statistics (HOS) developed by independent teams now outperform standard two-point estimators in terms of statistical precision thanks to their sensitivity to the non-Gaussian features of large-scale structure. The aim of the Higher-Order Weak Lensing Statistics (HOWLS) project is to assess, compare, and combine the constraining power of ten different HOS on a common set ofEuclid-like mocks, derived fromN-body simulations. In this first paper of the HOWLS series, we computed the nontomographic (Ωm,σ8) Fisher information for the one-point probability distribution function, peak counts, Minkowski functionals, Betti numbers, persistent homology Betti numbers and heatmap, and scattering transform coefficients, and we compare them to the shear and convergence two-point correlation functions in the absence of any systematic bias. We also include forecasts for three implementations of higher-order moments, but these cannot be robustly interpreted as the Gaussian likelihood assumption breaks down for these statistics. Taken individually, we find that each HOS outperforms the two-point statistics by a factor of around two in the precision of the forecasts with some variations across statistics and cosmological parameters. When combining all the HOS, this increases to a 4.5 times improvement, highlighting the immense potential of HOS for cosmic shear cosmological analyses withEuclid. The data used in this analysis are publicly released with the paper.

A Graphical method for PQ assessment: EDA tools using traditional indices and Higher-order Statistics

This paper presents a new qualitative method for assessing the power quality (PQ) of electrical systems using both time domain traditional indices and higher-order statistics. The method employs engineering data analysis (EDA) tools to analyse and interpret the PQ data coming from real datasets. Boxplot of each index are considered an essential tool that deserves to be included and studied when an external dataset it is analysed. But this research intends to go a step further, and for this reason a new tool for the spatial visualization of supply quality based on a radar chart is proposed. Each of its vertices constitutes an index, integrating from 3rd to 6 th order statistics with the traditional indicators SNR, SINAD and crest factor. The proposed methodology is applied to the analysis of real available signals and both, boxplot and radarchart, results are compared and commented. Finally, relationships are established between the altered indicators and the type(s) of event found in the signal.

Cosmology from the integrated shear 3-point correlation function: simulated likelihood analyses with machine-learning emulators

The integrated shear 3-point correlation function ζ ± measures the correlation between the local shear 2-point function ξ ± and the 1-point shear aperture mass in patches of the sky. Unlike other higher-order statistics, ζ ± can be efficiently measured from cosmic shear data, and it admits accurate theory predictions on a wide range of scales as a function of cosmological and baryonic feedback parameters. Here, we develop and test a likelihood analysis pipeline for cosmological constraints using ζ ±. We incorporate treatment of systematic effects from photometric redshift uncertainties, shear calibration bias and galaxy intrinsic alignments. We also develop an accurate neural-network emulator for fast theory predictions in MCMC parameter inference analyses. We test our pipeline using realistic cosmic shear maps based on N-body simulations with a DES Y3-like footprint, mask and source tomographic bins, finding unbiased parameter constraints. Relative to ξ ±-only, adding ζ ± can lead to ≈ 10-25% improvements on the constraints of parameters like As (or σ 8) and w 0. We find no evidence in ξ ± + ζ ± constraints of a significant mitigation of the impact of systematics. We also investigate the impact of the size of the apertures where ζ ± is measured, and of the strategy to estimate the covariance matrix (N-body vs. lognormal). Our analysis solidifies the strong potential of the ζ ± statistic and puts forward a pipeline that can be readily used to improve cosmological constraints using real cosmic shear data.

Automatic Classification of Field Winding Faults in Synchronous Motors Based on Bicoherence Image Segmentation and Higher Order Statistics of Stray Flux Signals

In this work, the application of the bicoherence (a squared normalized version of the bispectrum) of the stray flux signal is proposed as a way of detecting faults in the field winding of synchronous motors. These signals are analyzed both under the starting and at steady state regime. Likewise, two quantitative indicators are proposed, the first one based on the maximum values of the asymmetry and the kurtosis of the bicoherence matrix obtained from the flux signals and the second one relying on an algorithm based on the bicoherence image segmentation of the obtained pattern for each analyzed state. The results are analyzed through a comparative study for the two considered motor regimes, obtaining satisfactory results that sustain the potential application of the proposed methodology for the automatic field winding fault detection in real applications.

High-order paired-ASPP for deep semantic segmentation networks

Current semantic segmentation models only exploit first-order information, while rarely exploring high-order semantics. However, traditional first-order statistics are insufficient to support a solid unanimous representation. In this paper, we propose High-Order Paired-ASPP (Atrous Spatial Pyramid Pooling) Network to exploit high-order statistics from various feature levels. The network first introduces a High-Order Representation module to extract the contextual high-order information from all stages of the backbone. They can provide more semantic clues and discriminative information than the first-order ones. Besides, a Paired-ASPP module is proposed to embed high-order statistics of the early stages into the last stage. It can further preserve the boundary-related and spatial context in the low-level features for final prediction. Our experiments show that the high-order semantics significantly boost the performance on confusing objects. Our method achieves competitive performance without bells and whistles on three benchmarks, i.e., Cityscapes, ADE20K and Pascal-Context.

Noise and fluctuations in nanoscale gas flow

We theoretically calculate the fundamental noise that is present in gaseous (dilute fluid) flow in channels in the classical and degenerate quantum regime, where the Fermi–Dirac and Bose–Einstein distribution must be considered. Results for both regimes are analogous to their electrical counterparts. The quantum noise is calculated for a two terminal system and is a complicated function of the thermal and shot noise with the thermal noise dominating when 2k B T ρ ≫ mΔP and vice versa. The cumulant generating function for mass flow, which generates all the higher order statistics related to our mass flow distribution, is also derived and is used to find an expression for the third cumulant of flow across a fluidic channel.

Zero-watermark scheme for medical image protection based on style feature and ResNet

Zero-watermarking technology is of major interest within the field of medical image copyright protection because this embedding method does not cause loss of images. However, the features used to construct the zero-watermark in existing methods are destroyed after geometric attacks, particularly strong geometric attacks. This destruction causes the final extracted watermark image to lose its details and fail copyright protection. This study proposes a zero-watermark medical image protection scheme based on style features and a residual network to solve this concern. The style features extracted based on deep neural networks are high-order statistics of image details and abstract features and have good robustness against geometric attacks, such as rotation and scale. Simultaneously, this study proposes a zero-watermark verification method based on the residual network to replace the traditional XOR11The full name is exclusive OR, abbreviated as xor, which is a common logical operation in the computer field. operation. The residual network can iteratively learn to extract the watermark image from the zero-watermark image and enhance the quality of the watermark image using the designed loss function. We experimentally demonstrated that the residual network outperformed in reconstructing watermark images. This scheme can resist common geometric and strong image attacks, performance is superior to that of similar zero-watermarking schemes.

Cramer-Rao bound investigation of a novel virtually extended nested arc array for 2D DOA estimation

This paper exploits a sparse array representation, a novel nested arc array, to generate a virtual non-uniform circular arrays that have been presented and investigated. To increase the array aperture, the virtual array has been developed using higher-order statistics, namely, the Forth-Order Cumulants (FOC). The extended array contains a combination of physical as well as virtual sensors. The increased degrees of freedom (DOFs) in the resultant virtual array make it suitable for over-and under-determined direction of arrival (DOA) estimation. The Cramer-Rao bound (CRB) and the (DOA) estimation for such an array are developed and investigated for various arrays. The proposed array performance is superior to that of the uniform one. Further, the offered array is suitable for two-dimensional (2D) DOA estimation problems.

Fourth-order cumulants based-least squares methods for fractional Multiple-Input-Single-Output Errors-In-Variables system identification

This paper presents new consistent methods for continuous-time Multiple-Input-Single-Output (MISO) Errors-In-Variables (EIV) systems by fractional models. The proposed idea is to use Higher-Order Statistics (HOS), such as fourth-order cumulants (foc), instead of noisy input and output measurements to obtain unbiased estimates. Firstly, all differentiation orders are assumed to be known a priori and linear coefficients are estimated. The developed estimator is based on minimizing the equation error and it is called fractional fourth-order based-least squares estimator ( $$frac-foc-ls$$ ). Secondly, the global commensurability of the fractional MISO system is considered. The $$frac-foc-ls$$ is combined with a non linear technique to estimate the global commensurate order along with linear coefficients. The developed algorithm is based on minimizing the output error and called fractional fourth-order cumulants based-least squares combined with global commensurate order optimization ( $$frac-foc-gcools$$ ). The consistency of the developed estimators, in presence of high levels of noise corrupting both the input and output measurements, is assessed through a numerical example with the help of Monte Carlo simulations.