A Statistically and Numerically Efficient Independence Test Based on Random Projections and Distance Covariance

Testing for independence plays a fundamental role in many statistical techniques. Among the nonparametric approaches, the distance-based methods (such as the distance correlation-based hypotheses testing for independence) have many advantages, compared with many other alternatives. A known limitation of the distance-based method is that its computational complexity can be high. In general, when the sample size is n, the order of computational complexity of a distance-based method, which typically requires computing of all pairwise distances, can be O(n2). Recent advances have discovered that in the univariate cases, a fast method with O(n log n) computational complexity and O(n) memory requirement exists. In this paper, we introduce a test of independence method based on random projection and distance correlation, which achieves nearly the same power as the state-of-the-art distance-based approach, works in the multivariate cases, and enjoys the O(nK log n) computational complexity and O( max{n, K}) memory requirement, where K is the number of random projections. Note that saving is achieved when K < n/ log n. We name our method a Randomly Projected Distance Covariance (RPDC). The statistical theoretical analysis takes advantage of some techniques on the random projection which are rooted in contemporary machine learning. Numerical experiments demonstrate the efficiency of the proposed method, relative to numerous competitors.

Low Latency Based Convolutional Recurrent Neural Network Model for Speech Command Recognition

The presented paper proposes a new speech command recognition model for novel engineering applications with limited resources. We built the proposed model with the help of a Convolutional Recurrent Neural Network (CRNN). The use of CRNN instead of Convolutional Neural Network (CNN) helps us to reduce the model parameters and memory requirement as per resource constraints. Furthermore, we insert transmute and curtailment layer between the layers of CRNN. By doing this we further reduce model parameters and float number of operations to half of the CRNN requirement. The proposed model is tested on Google’s speech command dataset. The obtained result shows that the proposed CRNN model requires 1/3 parameters as compared to the CNN model. The number of parameters of the CRNN model is further reduced by 45% and the float numbers of operations between 2% to 12 % in different recognition tasks. The recognition accuracy of the proposed model is 96% on Google’s speech command dataset, and on laboratory recording, its recognition accuracy is 89%.

Gaussian exponential regression method for modeling open circuit voltage of lithium-ion battery as a function of state of charge

Purpose The purpose of the article is to develop an equation to accurately represent OCV as a function of SoC with reduced computational burden. Dependency of open circuit voltage (OCV) on state of charge (SoC) is often represented by either a look-up table or an equation developed by regression analysis. The accuracy is increased by either a larger data set for the look-up table or using a higher order equation for the regression analysis. Both of them increase the memory requirement in the controller. In this paper, Gaussian exponential regression methodology is proposed to represent OCV and SoC relationships accurately, with reduced memory requirement. Design/methodology/approach Incremental OCV test under constant temperature provides a data set of OCV and SoC. This data set is subjected to polynomial, Gaussian and the proposed Gaussian exponential equations. The unknown coefficients of these equations are obtained by least residual algorithm and differential evolution–based fitting algorithms for charging, discharging and average OCV. Findings Root mean square error (RMSE) of the proposed equation for differential evolution–based fitting technique is 35% less than second-order Gaussian and 74% less than a fifth-order polynomial equation for average OCV with a 16.66% reduction in number of coefficients, thereby reducing memory requirement. Originality/value The knee structure in the OCV and SoC relationship is accurately represented by Gaussian first-order equation, and the exponential equation can accurately describe the linear relation. Therefore, this paper proposes a Gaussian exponential equation that accurately represents the OCV as a function of SoC. The results obtained from the proposed regression methodology are compared with the polynomial and Gaussian regression in terms of RMSE, mean average, variance and number of coefficients.

Accelerating the charge inversion algorithm with hierarchical matrices for gas insulated systems

Surface charges accumulating on dielectrics during long-time operation of Gas Insulated High Voltage Direct Current (HVDC-GIS) equipments may affect the stable operation and could possibly trigger surface flashovers. In industrial applications, to quantify and identify the location of the surface charge accumulation from experimental measurements, the surface potential distribution is evaluated using, e.g., electrostatic probes, then the charge density is determined by solving an electrostatic problem based on an inversion procedure known as Charge Inversion Algorithm. The major practical limitation of such procedure is the inversion and the storage of the fully dense matrix arising from the representation via Integral Equations of the electrostatic phenomenon, resulting in O(N 3) computational complexity and O(N 2) memory requirement. In this paper it is shown how hierarchical matrices can be efficiently used to accelerate the charge inversion algorithm and, more importantly, reduce the overall memory requirement.

A 3D Optimized Frequency–Wavenumber (FK), Time–Space Optimized Symplectic (TSOS) Hybrid Method for Teleseismic Wave Modeling

ABSTRACT Although teleseismic waveform tomography can provide high-resolution images of the deep mantle, it is still unrealistic to numerically simulate the whole domain of seismic wave propagation due to the huge amount of computation. In this article, we develop a new three-dimensional hybrid method to address this issue, which couples the modified frequency–wavenumber (FK) method with the 3D time–space optimized symplectic (TSOS) method. First, the FK method, which is used to calculate the semianalytical incident wavefields in the layered reference model, is modified to compute the wavefields efficiently with a significantly low-memory requirement. Second, 3D TSOS method is developed to model the seismic wave propagating in the local 3D heterogeneous domain. The low memory requirement of the modified FK method and the high accuracy of the TSOS method make it feasible to obtain highly accurate synthetic seismograms efficiently. A crust–upper mantle model for P-, SV-, and SH-wave incidences is calculated to benchmark the accuracy and efficiency of the 3D optimized FK-TSOS method. Numerical experiments for 3D models with heterogeneities, undulated discontinuous interfaces, and realistic model in eastern Tibet, illustrate the capability of hybrid method to accurately capture the scattered waves caused by heterogeneities in 3D medium. The 3D optimized FK-TSOS method developed shows low-memory requirement, high accuracy, and high efficiency, which makes it be a promising forward method to further apply to high-resolution mantle structure images beneath seismic array.

Fast Numerical Optimization for Genome Sequencing Data in Population Biobanks

We develop two efficient solvers for optimization problems arising from large-scale regularized regressions on millions of genetic variants sequenced from hundreds of thousands of individuals. These genetic variants are encoded by the values in the set {0, 1, 2, NA}. We take advantage of this fact and use two bits to represent each entry in a genetic matrix, which reduces memory requirement by a factor of 32 compared to a double precision floating point representation. Using this representation, we implemented an iteratively reweighted least square algorithm to solve Lasso regressions on genetic matrices, which we name snpnet-2.0. When the dataset contains many rare variants, the predictors can be encoded in a sparse matrix. We utilize the sparsity in the predictor matrix to further reduce memory requirement and computational speed. Our sparse genetic matrix implementation uses both the compact 2-bit representation and a simplified version of compressed sparse block format so that matrix-vector multiplications can be effectively parallelized on multiple CPU cores. To demonstrate the effectiveness of this representation, we implement an accelerated proximal gradient method to solve group Lasso on these sparse genetic matrices. This solver is named sparse-snpnet, and will also be included as part of snpnet R package. Our implementation is able to solve group Lasso problems on sparse genetic matrices with more than 1, 000, 000 columns and almost 100, 000 rows within 10 minutes and using less than 32GB of memory.

Error analysis of nonlinear time fractional mobile/immobile advection-diffusion equation with weakly singular solutions

In this paper, a weighted and shifted Grünwald-Letnikov difference (WSGD) Legendre spectral method is proposed to solve the two-dimensional nonlinear time fractional mobile/immobile advection-dispersion equation. We introduce the correction method to deal with the singularity in time, and the stability and convergence analysis are proven. In the numerical implementation, a fast method is applied based on a globally uniform approximation of the trapezoidal rule for the integral on the real line to decrease the memory requirement and computational cost. The memory requirement and computational cost are O(Q) and O(QK), respectively, where K is the number of the final time step and Q is the number of quadrature points used in the trapezoidal rule. Some numerical experiments are given to confirm our theoretical analysis and the effectiveness of the presented methods.