基于Subsampling抽样的厚尾AR(p)序列趋势变点的Ratio检验

文章考虑的是厚尾AR(p)序列趋势变点检验问题。首先,在已有研究的启发下,构造了一个Ratio统计量来检验趋势变点;其次,在原假设下证明统计量的极限分布是列维过程的泛函,在备择假设下得到统计量的一致性;其次,为了避免参数的估计,采用Subsampling方法获得更为准确的临界值,数值模拟结果显示,在大样本下基于Subsampling抽样方法的Ratio检验很好地控制了经验水平,经验势也达到了比较好的效果;最后,通过一组实证数据进一步阐明理论的有效性和可行性。

含有变点的厚尾单位根的subsampling检验

本文研究趋势项含有变点且新息为方差无穷厚尾过程的序列单位根检验问题,通过构造DF型检验,得到了其渐近分布。为避免估计统计量渐近分布中的尾指数,构造subsampling抽样方法来确定统计量渐近分布的百分位数,同时论证了subsampling抽样方法的一致性。最后,用Monte Carlo模拟证实本文所提出统计量以及subsampling抽样方法的可行性。

重尾过程的subsampling协整检验

由于重尾过程协整检验统计量的渐近分布含有不可估计的重尾指数α,本文通过构造subsampling抽样算法,在不估计重尾指数α的情况下,计算该检验统计量的临界值,并且证明该算法在理论上的合理性.最后,通过MonteCalo模拟证明该方法的有效性.

基于稳定分布的ARCH模型均值变点Subsampling检验

讨论了基于稳定分布的ARCH模型的均值变点检验问题,其中特征指数k∈(1,2)。基于残量平方累积和统计量,利用Subsampling抽样方法确定渐近分布的临界值,从而避免特征指数k的估计。结果显示:蒙特卡罗数值模拟结果和实证分析充分说明了Subsampling抽样方法的可行性和有效性。因此,基于Subsampling的残量平方累积和检验对于稳定分布的ARCH模型均值变点检验仍不失为一种有效的方法。

ultiscale full-waveform inversion based on shot subsampling

Conventional full-waveform inversion is computationally intensive because it considers all shots in each iteration. To tackle this, we establish the number of shots needed and propose multiscale inversion in the frequency domain while using only the shots that are positively correlated with frequency. When using low-frequency data, the method considers only a small number of shots and raw data. More shots are used with increasing frequency. The random-in-group subsampling method is used to rotate the shots between iterations and avoid the loss of shot information. By reducing the number of shots in the inversion, we decrease the computational cost. There is no crosstalk between shots, no noise addition, and no observational limits. Numerical modeling suggests that the proposed method reduces the computing time, is more robust to noise, and produces better velocity models when using data with noise.

Subsampling Method for Robust Estimation of Regression Models

We propose a subsampling method for robust estimation of regression models which is built on classical methods such as the least squares method. It makes use of the non-robust nature of the underlying classical method to find a good sample from regression data contaminated with outliers, and then applies the classical method to the good sample to produce robust estimates of the regression model parameters. The subsampling method is a computational method rooted in the bootstrap methodology which trades analytical treatment for intensive computation;it finds the good sample through repeated fitting of the regression model to many random subsamples of the contaminated data instead of through an analytical treatment of the outliers. The subsampling method can be applied to all regression models for which non-robust classical methods are available. In the present paper, we focus on the basic formulation and robustness property of the subsampling method that are valid for all regression models. We also discuss variations of the method and apply it to three examples involving three different regression models.

Responses of diff erent biodiversity indices to subsampling efforts in lotic macroinvertebrate assemblages

As a less time-consuming procedure, subsampling technology has been widely used in biological monitoring and assessment programs. It is clear that subsampling counts af fect the value of traditional biodiversity indices, but its ef fect on taxonomic distinctness(TD) indices is less well studied. Here, we examined the responses of traditional(species richness, Shannon-Wiener diversity) and TD(average taxonomic distinctness: Δ +, and variation in taxonomic distinctness: Λ +) indices to subsample counts using a random subsampling procedure from 50 to 400 individuals, based on macroinvertebrate datasets from three dif ferent river systems in China. At regional scale, taxa richness asymptotically increased with ?xed-count size; ≥250–300 individuals to express 95% information of the raw data. In contrast, TD indices were less sensitive to the subsampling procedure. At local scale, TD indices were more stable and had less deviation than species richness and Shannon-Wiener index, even at low subsample counts, with ≥100 individuals needed to estimate 95% of the information of the actual Δ + and Λ + in the three river basins. We also found that abundance had a certain ef fect on diversity indices during the subsampling procedure, with dif ferent subsampling counts for species richness and TD indices varying by regions. Therefore, we suggest that TD indices are suitable for biodiversity assessment and environment monitoring. Meanwhile, pilot analyses are necessary when to determine the appropriate subsample counts for bioassessment in a new region or habitat type.

Novel block-matching algorithms by subsampling both search candidates and pixels

A new faster block-matching algorithm （BMA） by using both search candidate and pixd sulzsamplings is proposed. Firstly a pixd-subsampling approach used in adjustable partial distortion search （APDS） is adjusted to visit about half points of all search candidates by subsampling them, using a spiral-scanning path with one skip. Two sdected candidates that have minimal and second minimal block distortion measures are obtained. Then a fine-tune step is taken around them to find the best one. Some analyses are given to approve the rationality of the approach of this paper. Experimental results show that, as compared to APDS, the proposed algorithm can enhance the block-matching speed by about 30% while maintaining its MSE performance very close to that of it. And it performs much better than many other BMAs such as TSS, NTSS, UCDBS and NPDS.

Optimal decorrelated score subsampling for generalized linear models with massive data

In this paper, we consider the unified optimal subsampling estimation and inference on the lowdimensional parameter of main interest in the presence of the nuisance parameter for low/high-dimensionalgeneralized linear models (GLMs) with massive data. We first present a general subsampling decorrelated scorefunction to reduce the influence of the less accurate nuisance parameter estimation with the slow convergencerate. The consistency and asymptotic normality of the resultant subsample estimator from a general decorrelatedscore subsampling algorithm are established, and two optimal subsampling probabilities are derived under theA- and L-optimality criteria to downsize the data volume and reduce the computational burden. The proposedoptimal subsampling probabilities provably improve the asymptotic efficiency of the subsampling schemes in thelow-dimensional GLMs and perform better than the uniform subsampling scheme in the high-dimensional GLMs.A two-step algorithm is further proposed to implement, and the asymptotic properties of the correspondingestimators are also given. Simulations show satisfactory performance of the proposed estimators, and twoapplications to census income and Fashion-MNIST datasets also demonstrate its practical applicability.

Analyzing the Dissemination of News by Model Averaging and Subsampling

The dissemination of news is a vital topic in management science,social science and data science.With the development of technology,the sample sizes and dimensions of digital news data increase remarkably.To alleviate the computational burden in big data,this paper proposes a method to deal with massive and moderate-dimensional data for linear regression models via combing model averaging and subsampling methodologies.The author first samples a subsample from the full data according to some special probabilities and split covariates into several groups to construct candidate models.Then,the author solves each candidate model and calculates the model-averaging weights to combine these estimators based on this subsample.Additionally,the asymptotic optimality in subsampling form is proved and the way to calculate optimal subsampling probabilities is provided.The author also illustrates the proposed method via simulations,which shows it takes less running time than that of the full data and generates more accurate estimations than uniform subsampling.Finally,the author applies the proposed method to analyze and predict the sharing number of news,and finds the topic,vocabulary and dissemination time are the determinants.

Optimal Poisson Subsampling for Softmax Regression

Softmax regression,which is also called multinomial logistic regression,is widely used in various fields for modeling the relationship between covariates and categorical responses with multiple levels.The increasing volumes of data bring new challenges for parameter estimation in softmax regression,and the optimal subsampling method is an effective way to solve them.However,optimal subsampling with replacement requires to access all the sampling probabilities simultaneously to draw a subsample,and the resultant subsample could contain duplicate observations.In this paper,the authors consider Poisson subsampling for its higher estimation accuracy and applicability in the scenario that the data exceed the memory limit.The authors derive the asymptotic properties of the general Poisson subsampling estimator and obtain optimal subsampling probabilities by minimizing the asymptotic variance-covariance matrix under both A-and L-optimality criteria.The optimal subsampling probabilities contain unknown quantities from the full dataset,so the authors suggest an approximately optimal Poisson subsampling algorithm which contains two sampling steps,with the first step as a pilot phase.The authors demonstrate the performance of our optimal Poisson subsampling algorithm through numerical simulations and real data examples.

Closed-Form Models of Accuracy Loss due to Subsampling in SVD Collaborative Filtering

We postulate and analyze a nonlinear subsampling accuracy loss(SSAL)model based on the root mean square error(RMSE)and two SSAL models based on the mean square error(MSE),suggested by extensive preliminary simulations.The SSAL models predict accuracy loss in terms of subsampling parameters like the fraction of users dropped(FUD)and the fraction of items dropped(FID).We seek to investigate whether the models depend on the characteristics of the dataset in a constant way across datasets when using the SVD collaborative filtering(CF)algorithm.The dataset characteristics considered include various densities of the rating matrix and the numbers of users and items.Extensive simulations and rigorous regression analysis led to empirical symmetrical SSAL models in terms of FID and FUD whose coefficients depend only on the data characteristics.The SSAL models came out to be multi-linear in terms of odds ratios of dropping a user(or an item)vs.not dropping it.Moreover,one MSE deterioration model turned out to be linear in the FID and FUD odds where their interaction term has a zero coefficient.Most importantly,the models are constant in the sense that they are written in closed-form using the considered data characteristics(densities and numbers of users and items).The models are validated through extensive simulations based on 850 synthetically generated primary(pre-subsampling)matrices derived from the 25M MovieLens dataset.Nearly 460000 subsampled rating matrices were then simulated and subjected to the singular value decomposition(SVD)CF algorithm.Further validation was conducted using the 1M MovieLens and the Yahoo!Music Rating datasets.The models were constant and significant across all 3 datasets.

Subsampling bias and the best-discrepancy systematic cross validation

Statistical machine learning models should be evaluated and validated before putting to work.Conventional k-fold Monte Carlo cross-validation(MCCV)procedure uses a pseudo-random sequence to partition instances into k subsets,which usually causes subsampling bias,inflates generalization errors and jeopardizes the reliability and effectiveness of cross-validation.Based on ordered systematic sampling theory in statistics and low-discrepancy sequence theory in number theory,we propose a new k-fold cross-validation procedure by replacing a pseudo-random sequence with a best-discrepancy sequence,which ensures low subsampling bias and leads to more precise expected-prediction-error(EPE)estimates.Experiments with 156 benchmark datasets and three classifiers(logistic regression,decision tree and na?ve bayes)show that in general,our cross-validation procedure can extrude subsampling bias in the MCCV by lowering the EPE around 7.18%and the variances around 26.73%.In comparison,the stratified MCCV can reduce the EPE and variances of the MCCV around 1.58%and 11.85%,respectively.The leave-one-out(LOO)can lower the EPE around 2.50%but its variances are much higher than the any other cross-validation(CV)procedure.The computational time of our cross-validation procedure is just 8.64%of the MCCV,8.67%of the stratified MCCV and 16.72%of the LOO.Experiments also show that our approach is more beneficial for datasets characterized by relatively small size and large aspect ratio.This makes our approach particularly pertinent when solving bioscience classification problems.Our proposed systematic subsampling technique could be generalized to other machine learning algorithms that involve random subsampling mechanism.

Combined subsampling and analytical integration for efficient large-scale GW calculations for 2D systems

Accurate and efficient predictions of the quasiparticle properties of complex materials remain a major challenge due to the convergence issue and the unfavorable scaling of the computational cost with respect to the system size.Quasiparticle GW calculations for two-dimensional(2D)materials are especially difficult.The unusual analytical behaviors of the dielectric screening and the electron self-energy of 2D materials make the conventional Brillouin zone(BZ)integration approach rather inefficient and require an extremely dense k-grid to properly converge the calculated quasiparticle energies.In this work,we present a combined nonuniform subsampling and analytical integration method that can drastically improve the efficiency of the BZ integration in 2D GW calculations.

Optimal Dependence of Performance and Efficiency of Collaborative Filtering on Random Stratified Subsampling

Dropping fractions of users or items judiciously can reduce the computational cost of Collaborative Filtering(CF)algorithms.The effect of this subsampling on the computing time and accuracy of CF is not fully understood,and clear guidelines for selecting optimal or even appropriate subsampling levels are not available.In this paper,we present a Density-based Random Stratified Subsampling using Clustering(DRSC)algorithm in which the desired Fraction of Users Dropped(FUD)and Fraction of Items Dropped(FID)are specified,and the overall density during subsampling is maintained.Subsequently,we develop simple models of the Training Time Improvement(TTI)and the Accuracy Loss(AL)as functions of FUD and FID,based on extensive simulations of seven standard CF algorithms as applied to various primary matrices from MovieLens,Yahoo Music Rating,and Amazon Automotive data.Simulations show that both TTI and a scaled AL are bi-linear in FID and FUD for all seven methods.The TTI linear regression of a CF method appears to be same for all datasets.Extensive simulations illustrate that TTI can be estimated reliably with FUD and FID only,but AL requires considering additional dataset characteristics.The derived models are then used to optimize the levels of subsampling addressing the tradeoff between TTI and AL.A simple sub-optimal approximation was found,in which the optimal AL is proportional to the optimal Training Time Reduction Factor(TTRF)for higher values of TTRF,and the optimal subsampling levels,like optimal FID/(1-FID),are proportional to the square root of TTRF.

Spatially Adaptive Subsampling for Motion Detection

Many video surveillance applications rely on efficient motion detection. However, the algorithms are usually costly since they compute a background model at every pixel of the frame. This paper shows that, in the case of a planar scene with a fixed calibrated camera, a set of pixels can be selected to compute the background model while ignoring the other pixels for accurate but less costly motion detection. The cali- bration is used to first define a volume of interest in the real world and to project the volume of interest onto the image, and to define a spatial adaptive subsampling of this region of interest with a subsampling density that depends on the camera distance. Indeed, farther objects need to be analyzed with more precision than closer objects. Tests on many video sequences have integrated this adaptive subsampling to various motion detection techniques.

Deep learning for predictive mechanical properties of hot-rolled strip in complex manufacturing systems

Higher requirements for the accuracy of relevant models are put throughout the transformation and upgrade of the iron and steel sector to intelligent production.It has been difficult to meet the needs of the field with the usual prediction model of mechanical properties of hotrolled strip.Insufficient data and difficult parameter adjustment limit deep learning models based on multi-layer networks in practical applications;besides,the limited discrete process parameters used make it impossible to effectively depict the actual strip processing process.In order to solve these problems,this research proposed a new sampling approach for mechanical characteristics input data of hot-rolled strip based on the multi-grained cascade forest(gcForest)framework.According to the characteristics of complex process flow and abnormal sensitivity of process path and parameters to product quality in the hot-rolled strip production,a three-dimensional continuous time series process data sampling method based on time-temperature-deformation was designed.The basic information of strip steel(chemical composition and typical process parameters)is fused with the local process information collected by multi-grained scanning,so that the next link’s input has both local and global features.Furthermore,in the multi-grained scanning structure,a sub sampling scheme with a variable window was designed,so that input data with different dimensions can get output characteristics of the same dimension after passing through the multi-grained scanning structure,allowing the cascade forest structure to be trained normally.Finally,actual production data of three steel grades was used to conduct the experimental evaluation.The results revealed that the gcForest-based mechanical property prediction model outperforms the competition in terms of comprehensive performance,ease of parameter adjustment,and ability to sustain high prediction accuracy with fewer samples.

CMOS analog and mixed-signal phase-locked loops: An overview

CMOS analog and mixed-signal phase-locked loops(PLL)are widely used in varies of the system-on-chips(SoC)as the clock generator or frequency synthesizer.This paper presents an overview of the AMS-PLL,including:1)a brief introduction of the basics of the charge-pump based PLL,which is the most widely used AMS-PLL architecture due to its simplicity and robustness;2)a summary of the design issues of the basic CPPLL architecture;3)a systematic introduction of the techniques for the performance enhancement of the CPPLL;4)a brief overview of ultra-low-jitter AMS-PLL architectures which can achieve lower jitter(<100 fs)with lower power consumption compared with the CPPLL,including the injection-locked PLL(ILPLL),subsampling(SSPLL)and sampling PLL(SPLL);5)a discussion about the consideration of the AMS-PLL architecture selection,which could help designers meet their performance requirements.

Fast color transfer from multiple images

Color transfer between images uses the statistics information of image effectively. We present a novel approach of local color transfer between images based on the simple statistics and locally linear embedding. A sketching interface is proposed for quickly and easily specifying the color correspondences between target and source image. The user can specify the corre- spondences of local region using scribes, which more accurately transfers the target color to the source image while smoothly preserving the boundaries, and exhibits more natural output results. Our algorithm is not restricted to one-to-one image color transfer and can make use of more than one target images to transfer the color in different regions in the source image. Moreover, our algorithm does not require to choose the same color style and image size between source and target images. We propose the sub-sampling to reduce the computational load. Comparing with other approaches, our algorithm is much better in color blending in the input data. Our approach preserves the other color details in the source image. Various experimental results show that our approach specifies the correspondences of local color region in source and target images. And it expresses the intention of users and generates more actual and natural results of visual effect.

Conversion of adverse data corpus to shrewd output using sampling metrics

An imbalanced dataset is commonly found in at least one class,which are typically exceeded by the other ones.A machine learning algorithm(classifier)trained with an imbalanced dataset predicts the majority class(frequently occurring)more than the other minority classes(rarely occurring).Training with an imbalanced dataset poses challenges for classifiers;however,applying suitable techniques for reducing class imbalance issues can enhance classifiers’performance.In this study,we consider an imbalanced dataset from an educational context.Initially,we examine all shortcomings regarding the classification of an imbalanced dataset.Then,we apply data-level algorithms for class balancing and compare the performance of classifiers.The performance of the classifiers is measured using the underlying information in their confusion matrices,such as accuracy,precision,recall,and F measure.The results show that classification with an imbalanced dataset may produce high accuracy but low precision and recall for the minority class.The analysis confirms that undersampling and oversampling are effective for balancing datasets,but the latter dominates.