Subsampling Method Research Articles

Efficient Parameter Optimisation for Quantum Kernel Alignment: A Sub-sampling Approach in Variational Training

Quantum machine learning with quantum kernels for classification problems is a growing area of research. Recently, quantum kernel alignment techniques that parameterise the kernel have been developed, allowing the kernel to be trained and therefore aligned with a specific dataset. While quantum kernel alignment is a promising technique, it has been hampered by considerable training costs because the full kernel matrix must be constructed at every training iteration. Addressing this challenge, we introduce a novel method that seeks to balance efficiency and performance. We present a sub-sampling training approach that uses a subset of the kernel matrix at each training step, thereby reducing the overall computational cost of the training. In this work, we apply the sub-sampling method to synthetic datasets and a real-world breast cancer dataset and demonstrate considerable reductions in the number of circuits required to train the quantum kernel while maintaining classification accuracy.

A Wasserstein distance-based spectral clustering method for transaction data analysis

With the rapid development of online payment platforms, it is now possible to record massive transaction data. Clustering on transaction data significantly contributes to analyzing merchants’ behavior patterns. This enables payment platforms to provide differentiated services or implement risk management strategies. However, traditional methods exploit transactions by generating low-dimensional features, leading to inevitable information loss. In this study, we use the empirical cumulative distribution of transactions to characterize merchants. We adopt Wasserstein distance to measure the dissimilarity between any two merchants and propose the Wasserstein-distance-based spectral clustering (WSC) approach. Based on the similarities between merchants’ transaction distributions, a graph of merchants is generated. Thus, we treat the clustering of merchants as a graph-cut problem and solve it under the framework of spectral clustering. To ensure feasibility of the proposed method on large-scale datasets with limited computational resources, we propose a subsampling method for WSC (SubWSC). The associated theoretical properties are investigated to verify the efficiency of the proposed approach. The simulations and empirical study demonstrate that the proposed method outperforms feature-based methods in finding behavior patterns of merchants.

A Subsampling Strategy for AIC-based Model Averaging with Generalized Linear Models

Subsampling is an effective approach to address computational challenges associated with massive datasets. However, existing subsampling methods do not consider model uncertainty. In this paper, we investigate the subsampling technique for the Akaike information criterion (AIC) and extend the subsampling method to the smoothed AIC model-averaging framework in the context of generalized linear models. By correcting the asymptotic bias of the maximized subsample objective function used to approximate the Kullback–Leibler divergence, we derive the form of the AIC based on the subsample. We then provide a subsampling strategy for the smoothed AIC model-averaging estimator and study the corresponding asymptotic properties of the loss and the resulting estimator. A practically implementable algorithm is developed, and its performance is evaluated through numerical experiments on both real and simulated datasets.

Spatial-frequency parallel subsampling for distributed compressive sensing in ultrasonic imaging inspection

To address the problem of the high hardware requirements and insufficient data storage capacity in current ultrasonic imaging testing, a novel approach is developed using a programmable device, which combines spatial-frequency parallel subsampling with the distributed compressive sensing simultaneous orthogonal matching pursuit (DCS-SOMP) algorithm to achieve fast and high-quality ultrasonic imaging inspection with a small amount of subsampled data. The spatial sparse measurement method was employed to achieve spatial subsampling and minimize the count of signals. Additionally, frequency subsampling was utilized to significantly reduce the data volume of time-domain signals while ensuring signal quality by truncating the primary testing frequency components. The subsampled data was then reconstructed using distributed compressive sensing (DCS) for multi-channel data reconstruction. The experiment of ultrasonic scanning imaging was conducted on a carbon steel specimen containing six transverse through-holes with a diameter of Ф1.5 mm at different depths. The ultrasonic signals were acquired using the spatial-frequency parallel subsampling method, and subsequently reconstructed using the DCS-SOMP algorithm. The results show that the proposed method achieves comparable image quality to that obtained with complete data, using only 1/8 of the complete data, while accurately locating and quantifying defects.

Optimal subsampling for semi-parametric accelerated failure time models with massive survival data using a rank-based approach.

Subsampling is a practical strategy for analyzing vast survival data, which are progressively encountered across diverse research domains. While the optimal subsampling method has been applied to inferences for Cox models and parametric accelerated failure time (AFT) models, its application to semi-parametric AFT models with rank-based estimation have received limited attention. The challenges arise from the non-smooth estimating function for regression coefficients and the seemingly zero contribution from censored observations in estimating functions in the commonly seen form. To address these challenges, we develop optimal subsampling probabilities for both event and censored observations by expressing the estimating functions through a well-defined stochastic process. Meanwhile, we apply an induced smoothing procedure to the non-smooth estimating functions. As the optimal subsampling probabilities depend on the unknown regression coefficients, we employ a two-step procedure to obtain a feasible estimation method. An additional benefit of the method is its ability to resolve the issue of underestimation of the variance when the subsample size approaches the full sample size. We validate the performance of our estimators through a simulation study and apply the methods to analyze the survival time of lymphoma patients in the surveillance, epidemiology, and end results program.

An efficient subsampling method for estimating corn root characteristics with scanner‐based image analysis

AbstractQuantifying root length, surface area, average diameter, and volume of fully‐matured corn (Zea mays L.) is labor intensive, time consuming, and costly. Accurate and efficient subsampling techniques are needed to overcome these limitations. In this study, eight corn root systems were grown to maturity in a sand‐culture hydroponics system to develop and test root system subsampling techniques for accuracy (uncertainty assessment) and efficiency (time). Each entire root system was separated into coarse and fine roots, which were then composited into 65 subsamples, either visually or by mass, followed by subsample scanning to quantify root characteristics. A bootstrap non‐parametric procedure was used to determine the sample size needed to represent the total root system and quantify uncertainty based on the number of subsamples analyzed. When subsamples were composited visually, as many as 60 subsamples (92% of the total root system) were necessary to represent the characteristics of the root system within ±5% of the true mean at a 95% confidence level. In contrast, when subsamples were composited by equal mass, a maximum of 15 subsamples (23% of the total root system) were needed to be representative, requiring 2 h and 15 min per root system. The findings show that separating the entire root system by coarse and fine roots and then weighing into equal mass subsamples before scanning decreased the number of subsamples and time required to accurately estimate corn root characteristics. Thus, this subsampling approach considerably reduced the effort and cost of processing corn root systems.

Evaluation of the microbial wet-vacuum system (M-Vac®) for DNA sampling from rough, porous substrates, and its compatibility with fully automated platforms

DNA retrieval methods traditionally used during forensic evidence recovery including swabbing and tape lifting, can have limited effectiveness when used on porous, rough substrates such as bricks and carpet. This is possibly due to the DNA material being dispersed and unreachable for surface sampling techniques. In this evaluation we investigated the effectiveness of the Microbial Wet-Vacuum System (M-Vac®; M-Vac® Systems, Inc., Sandy, UT), as it has been reported to retrieve greater amounts of DNA material from challenging exhibits. A four-stage evaluation was conducted, starting with seeding carpet and brick substrates with a known donor’s saliva in two dilutions and comparing the DNA recovery of tape lifting, swabbing, and the M-Vac®. A victim struggle scenario on carpet was then mimicked to compare trace DNA recovery by each method. Two mock scenarios were also conducted; a shirt was submerged in a creek bed for a period of five days to sample for the wearer’s DNA, and a car boot was sampled to assess the possibility of recovering a victim’s DNA amongst background DNA from the usual car occupants. Finally, the compatibility of the M-Vac® sampling process was optimised for the fully automated DNA lysis and extraction platforms used in the NSW (Australia) jurisdiction by comparing filter subsampling methods. The results from the study were mixed. For bricks, none of the collection methods were effective in retrieving DNA. On carpet, the M-Vac® retrieved the greatest quantities of DNA from the saliva-seeded samples, however, tape lifts outperformed all methods for ‘touch’ DNA recovery. The M-Vac® retrieved the greatest amount of DNA from the t-shirt recovered from a creek bed as it was able to retrieve the embedded DNA. The final mock case car boot scenario resulted in greater victim DNA recovery from tape lifts, with the M-Vac® more likely to recover mixtures too weak and/or complex to be interpreted. Finally, operational considerations regarding the compatibility of the M-Vac® system with fully automated DNA lysis and extraction are discussed. Considering the substantial time and cost to deploy the M-Vac®, it is recommended to be utilised in casework only after swabbing and tape lifting methods have failed to yield sufficient DNA material, where the substrate properties would likely benefit from the M-Vac’s® niche capabilities for retrieving embedded DNA, and low levels of background DNA may be anticipated.

Distinguishing subsampled power laws from other heavy-tailed distributions.

Distinguishing power-law distributions from other heavy-tailed distributions is challenging, and this task is often further complicated by subsampling effects. In this work, we evaluate the performance of two commonly used methods for detecting power-law distributions-the maximum likelihood method of Clauset etal. and the extreme value method of Voitalov etal.-in distinguishing subsampled power laws from two other heavy-tailed distributions, the lognormal and the stretched exponential distributions. We focus on a random subsampling method commonly applied in network science and biological sciences. In this subsampling scheme, we are ultimately interested in the frequency distribution of elements with a certain number of constituent parts-for example, species with k individuals or nodes with k connections-and each part is selected to the subsample with an equal probability. We investigate how well the results obtained from low-subsampling-depth subsamples generalize to the original distribution. Our results show that the power-law exponent of the original distribution can be estimated fairly accurately from subsamples, but classifying the distribution correctly is more challenging. The maximum likelihood method falsely rejects the power-law hypothesis for a large fraction of subsamples from power-law distributions. While the extreme value method correctly recognizes subsampled power-law distributions with all tested subsampling depths, its capacity to distinguish power laws from the heavy-tailed alternatives is limited. However, these false positives tend to result not from the subsampling itself but from the estimators' inability to classify the original sample correctly. In fact, we show that the extreme value method can sometimes be expected to perform better on subsamples than on the original samples from the lognormal and the stretched exponential distributions, while the contrary is true for the main tests included in the maximum likelihood method.

Distributed optimal subsampling for quantile regression with massive data

Methods for reducing distributed subsample sizes have increasingly become popular statistical problems in the big data era. Existing works of optimal subsample selection on the massive linear and generalized linear models with distributed data sources have been solidly investigated and widely applied. Nevertheless, few studies have developed distributed optimal subsample selection procedures for quantile regression in massive data. In such settings, the distributed optimal subsampling probabilities and subset sizes selection criteria need to be established simultaneously. In this work, we propose a distributed subsampling technique for the quantile regression models. The estimation approach is based on a two-step algorithm for the distributed subsampling procedures. Furthermore, the theoretical results, such as consistency and asymptotic normality of resultant estimators, are rigorously established under some regularity conditions. The empirical evaluation and performance of the proposed subsampling method are conducted in simulation experiments and real data applications.

Entropy-Based Subsampling Methods for Big Data

Entropy-Based Subsampling Methods for Big Data

Topological detection of phenomenological bifurcations with unreliable kernel density estimates

Phenomenological (P-type) bifurcations are qualitative changes in stochastic dynamical systems whereby the stationary probability density function (PDF) changes its topology. The current state of the art for detecting these bifurcations requires reliable kernel density estimates computed from an ensemble of system realizations. However, in several real world signals such as Big Data, only a single system realization is available—making it impossible to estimate a reliable kernel density. This study presents an approach for detecting P-type bifurcations using unreliable density estimates. The approach creates an ensemble of objects from Topological Data Analysis (TDA) called persistence diagrams from the system’s sole realization and statistically analyzes the resulting set. We compare several methods for replicating the original persistence diagram including Gibbs point process modelling, Pairwise Interaction Point Modelling, and subsampling. We show that for the purpose of predicting a bifurcation, the simple method of subsampling exceeds the other two methods of point process modelling in performance.

Overlapping Batch Confidence Intervals on Statistical Functionals Constructed from Time Series: Application to Quantiles, Optimization, and Estimation

We propose a general purpose confidence interval procedure (CIP) for statistical functionals constructed using data from a stationary time series. The procedures we propose are based on derived distribution-free analogues of the χ 2 and Student’s t random variables for the statistical functional context, and hence apply in a wide variety of settings including quantile estimation, gradient estimation, M-estimation, CVAR-estimation, and arrival process rate estimation, apart from more traditional statistical settings. Like the method of subsampling, we use overlapping batches of time series data to estimate the underlying variance parameter; unlike subsampling and the bootstrap, however, we assume that the implied point estimator of the statistical functional obeys a central limit theorem (CLT) to help identify the weak asymptotics (called OB-x limits, x=I,II,III) of batched Studentized statistics. The OB-x limits, certain functionals of the Wiener process parameterized by the size of the batches and the extent of their overlap, form the essential machinery for characterizing dependence, and consequently the correctness of the proposed CIPs. The message from extensive numerical experimentation is that in settings where a functional CLT on the point estimator is in effect, using large overlapping batches alongside OB-x critical values yields confidence intervals that are often of significantly higher quality than those obtained from more generic methods like subsampling or the bootstrap. We illustrate using examples from CVaR estimation, ARMA parameter estimation, and NHPP rate estimation; R and MATLAB code for OB-x critical values is available at web.ics.purdue.edu/ ∼ pasupath .

Board gender diversity and debt utilization: Evidence from the global microfinance industry

To support the continued expansion of their operations, microfinance institutions (MFIs) worldwide rely heavily on debt, which exposes them to bankruptcy risk. This underscores the need for prudent selection of debt instruments by MFIs. Therefore, this study aims to investigate the possible influence of board gender diversity on the choice of debt instruments utilized by MFIs. Data from unique 1670 MFIs in 93 countries, spanning the period of 2010–2018, were collected from the World Bank and analyzed using various econometric methods, including Random Effects Model (REM), Fixed Effects Model (FEM), Pooled Ordinary Least Squares (POLS), Generalized Least Squares (GLS), and endogeneity-corrected techniques such as the Generalized Method of Moments (GMM). The study revealed that gender-diverse boards tend to utilize fewer debt instruments, reflecting the risk-averse nature of the female board members, as observed in the existing literature. However, the statistical significance of these outcomes varies depending on the specific debt, proxies, sub-sample, and econometric methods considered in the analysis.

Model-Free Subsampling Method Based on Uniform Designs

Model-Free Subsampling Method Based on Uniform Designs

Impact of truncating diffusion MRI scans on diffusional kurtosis imaging

ObjectiveDiffusional kurtosis imaging (DKI) extends diffusion tensor imaging (DTI), characterizing non-Gaussian diffusion effects but requires longer acquisition times. To ensure the robustness of DKI parameters, data acquisition ordering should be optimized allowing for scan interruptions or shortening. Three methodologies were used to examine how reduced diffusion MRI scans impact DKI histogram-metrics: 1) the electrostatic repulsion model (OptEEM); 2) spherical codes (OptSC); 3) random (RandomTRUNC).Materials and methodsPre-acquired diffusion multi-shell data from 14 female healthy volunteers (29±5 years) were used to generate reordered data. For each strategy, subsets containing different amounts of the full dataset were generated. The subsampling effects were assessed on histogram-based DKI metrics from tract-based spatial statistics (TBSS) skeletonized maps. To evaluate each subsampling method on simulated data at different SNRs and the influence of subsampling on in vivo data, we used a 3-way and 2-way repeated measures ANOVA, respectively.ResultsSimulations showed that subsampling had different effects depending on DKI parameter, with fractional anisotropy the most stable (up to 5% error) and radial kurtosis the least stable (up to 26% error). RandomTRUNC performed the worst while the others showed comparable results. Furthermore, the impact of subsampling varied across distinct histogram characteristics, the peak value the least affected (OptEEM: up to 5% error; OptSC: up to 7% error) and peak height (OptEEM: up to 8% error; OptSC: up to 11% error) the most affected.ConclusionThe impact of truncation depends on specific histogram-based DKI metrics. The use of a strategy for optimizing the acquisition order is advisable to improve DKI robustness to exam interruptions.

Fast subsampling strategy for point cloud based on novel octree coding

Owing to the continuous expansion in data scale, the calculation, storage, and transmission of 3D data have been plagued by numerous issues. The point cloud data, in particular, often contain duplicated and anomalous points, which can hinder tasks such as measurement. To address this issue, it is crucial to utilize point cloud pre-processing methods that combine subsampling and denoising. These methods help obtain clean, evenly distributed, and compact points to enhance the accuracy of the data. In this study, an efficient point cloud subsampling method is proposed that combines point cloud denoising capabilities. This method can effectively preserve salient features while improving the quality of point cloud data. By constructing the octree structure of the point cloud, the corresponding node code is obtained according to the spatial coordinates of the point cloud, and the feature vector of the node is calculated based on the analysis of covariance. Node feature similarity is introduced to distinguish the node into feature and non-feature nodes, forming the node feature code, and the layer threshold is introduced to filter outliers. Experimental results demonstrate that our proposed algorithm has a time ratio of over four compared to the curvature-based algorithm. Additionally, it exhibits an average grey entropy that is 1.6×e−3 lower than that of the random sampling method. And considering both time cost and subsampling effectiveness, proposed algorithm outperforms the state-of-the-art subsampling strategies, such as Approximate Intrinsic Voxel Structure and SampleNet. This approach is effective in removing noise while preserving important features, thereby reducing overall size of the point cloud. The high computational efficiency of our algorithm makes it a valuable reference for fast and precise measurements that require timeliness. It successfully addresses the challenges posed by the continuous expansion of data scale and offers significant advantages over existing subsampling methods. By improving the quality of point cloud data, our algorithm contributes to reducing complexity, enables efficient and accurate measurements.

Group-Orthogonal Subsampling for Hierarchical Data Based on Linear Mixed Models

Hierarchical data analysis is crucial in various fields for making discoveries. The linear mixed model is often used for training hierarchical data, but its parameter estimation is computationally expensive, especially with big data. Subsampling techniques have been developed to address this challenge. However, most existing subsampling methods assume homogeneous data and do not consider the possible heterogeneity in hierarchical data. To address this limitation, we develop a new approach called group-orthogonal subsampling (GOSS) for selecting informative subsets of hierarchical data that may exhibit heterogeneity. GOSS selects subdata with balanced data size among groups and combinatorial orthogonality within each group, resulting in subdata that are D- and A-optimal for building linear mixed models. Estimators of parameters trained on GOSS subdata are consistent and asymptotically normal. GOSS is shown to be numerically appealing via simulations and a real data application. Theoretical proofs, R codes, and supplementary numerical results are accessible online as supplementary materials.

Identifying changes in the distribution of income from higher‐order moments with an application to Australia

SummaryChanges in the distribution of income over time are identified based on an adjusted two‐sample version of the Neyman smooth test by using subsampling methods to approximate the sampling distribution of the test statistic when samples are not independent of each other. A range of Monte Carlo experiments show that the approach corrects for size distortions arising from dependent samples as well as generating monotonic power functions. Applying the approach to studying the distribution of income in Australia over the business cycle and the Global Financial Crisis, the empirical results highlight the importance of higher‐order moments and demonstrate that business cycles are not all alike as the relative strengths of higher‐order moments vary over phases of the cycle.

A distance metric-based space-filling subsampling method for nonparametric models

A distance metric-based space-filling subsampling method for nonparametric models

Properties of Test Statistics for Nonparametric Cointegrating Regression Functions Based on Subsamples

Nonparametric cointegrating regression models have been extensively used in financial markets, stock prices, heavy traffic, climate datasets, and energy markets. Models with parametric regression functions can be more appealing in practice compared to nonparametric forms, but do result in potential functional misspecification. Thus, there exists a vast literature on developing a model specification test for parametric forms of regression functions. In this article, we develop two test statistics which are applicable for the endogenous regressors driven by long memory and semi-long memory input shocks in the regression model. The limit distributions of the test statistics under these two scenarios are complicated and cannot be effectively used in practice. To overcome this difficulty, we use the subsampling method and compute the test statistics on smaller blocks of the data to construct their empirical distributions. Throughout, Monte Carlo simulation studies are used to illustrate the properties of test statistics. We also provide an empirical example of relating gross domestic product to total output of carbon dioxide in two European countries. Supplementary materials for this article are available online.