Subsample Size Research Articles

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.

Towards optimal model evaluation: enhancing active testing with actively improved estimators

With rapid advancements in machine learning and statistical models, ensuring the reliability of these models through accurate evaluation has become imperative. Traditional evaluation methods often rely on fully labeled test data, a requirement that is becoming increasingly impractical due to the growing size of datasets. In this work, we address this issue by extending existing work on active testing (AT) methods which are designed to sequentially sample and label data for evaluating pre-trained models. We propose two novel estimators: the Actively Improved Levelled Unbiased Risk (AILUR) and the Actively Improved Inverse Probability Weighting (AIIPW) estimators which are derived from nonparametric smoothing estimation. In addition, a model recalibration process is designed for the AIIPW estimator to optimize the sampling probability within the AT framework. We evaluate the proposed estimators on four real-world datasets and demonstrate that they consistently outperform existing AT methods. Our study also shows that the proposed methods are robust to changes in subsample sizes, and effective at reducing labeling costs.

Lite RGB-based measurement method for ballast fouling index prediction through subsampling

Ballasted track is the major form of freight railroads. Despite various requirements for material selection, ballast will degrade due to wear and the infiltration of fine materials. These fine particles will cause ballast fouling and degraded track performance. The fouling condition is directly related to both ballast performance and track maintenance planning. It can be quantitatively assessed using the Fouling Index (FI), calculated as the sum of the percentages of materials passing through No. 4 (4.75 mm) and No. 200 (75 µm) sieves. Traditional fouling assessment methods rely on labor-intensive sieve analysis. While non-destructive techniques such as Ground Penetration Radar, Impulse Response, Surface Wave, and SmartRock offer alternatives, they require specialized equipment and skilled technicians for accurate interpretation. Deep learning models have also been employed, trying to assess ballast fouling conditions by segmenting particles. However, these models struggle to account for fine materials. Recently, the FI was found to be linearly correlated with the variance of RGB (Red, Green, Blue) intensities in fouled ballast images, and this correlation could be used to assess ballast fouling conditions. Improving upon the previously developed FI prediction model and making it more practical, this study proposes an enhanced and lite RGB-based model that predicts the FI through a simple random subsampling approach. The optimal subsample size is determined both experimentally and analytically. Based on the results obtained from this study, the correlation between FI and the variance of RGB intensities in fouled ballast images is further confirmed. The proposed lite model can achieve the same accuracy in FI prediction but requires fewer than 1 % of the data points needed by previous methods, which demonstrates its promising potential for ballast fouling condition assessment practice.

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.

How many microplastics do you need to (sub)sample?

Analysis of microplastics in the environment requires polymer characterization as a confirmation step for suspected microplastic particles found in a sample. Material characterization is costly and can take a long time per particle. When microplastic particle counts are high, many researchers cannot characterize every particle in their sample due to time or monetary constraints. Moreover, characterizing every particle in samples with high plastic particle counts is unnecessary for describing the sample properties. We propose an a priori approach to determine the number of suspected microplastic particles in a sample that should be randomly subsampled for characterization to accurately assess the polymer distribution in the environmental sample. The proposed equation is well-founded in statistics literature and was validated using published microplastic data and simulations for typical microplastic subsampling routines. We report values from the whole equation but also derive a simple way to calculate the necessary particle count for samples or subsamples by taking the error to the power of negative two. Assuming an error of 0.05 (5 %) with a confidence interval of 95 %, an unknown expected proportion, and a sample with many particles (> 100k), the minimum number of particles in a subsample should be 386 particles to accurately characterize the polymer distribution of the sample, given the particles are randomly characterized from the full population of suspected particles. Extending this equation to simultaneously estimate polymer, color, size, and morphology distributions reveals more particles (620) would be needed in the subsample to achieve the same high absolute error threshold for all properties. The above proposal for minimum subsample size also applies to the minimum count that should be present in samples to accurately characterize particle type presence and diversity in a given environmental compartment.

A Joint Equivalence and Difference (JED) Test for Practical Use in Controlled Trials

A joint equivalence and difference (JED) test is needed because difference tests and equivalence (more exactly, similarity) tests each provide only a one-sided answer. The concept and underlying theory have appeared numerous times, noted and discussed here, but never in a form usable in workaday statistical applications. This work provides such a form as a straightforward simple test with a step-by-step guide and possible interpretations and formulas. For initial treatment, it restricts attention to a t test of two means. The guide is illustrated by a numerical example from the field of orthopedics. To assess the quality of the JED test, its sensitivity and specificity are examined for test outcomes depending on error risk α, total sample size, sub-sample size ratio, and variability ratio. These results are shown in tables. Interpretations are discussed. It is concluded that the test exhibits high power and effect size and that only quite small samples show any effect on the power or effect size of the JED test by commonly seen values of any of the parameters. Data for the example and computer codes for using the JED test are accessible through links to supplementary material. We recommend that this work be extended to other test forms and multivariate forms.

Homogenisation method based on energy conservation and independent of boundary conditions

The foundation of homogenisation methods rests on the postulate of Hill–Mandel, describing energy consistency throughout the transition of scales. The consideration of this principle is therefore crucial in the discipline of Digital Rock Physics which focuses on the upscaling of rock properties. For this reason, numerous studies have developed numerical schemes for porous media to enforce the Hill–Mandel condition to be respected. The most common method is to impose specific boundary conditions, such as periodic ones. However, these boundary conditions influence both the effective property and the size of the REV. The recent study of Thovert and Mourzenko (2020) has shown that most boundary conditions still result in the same intrinsic effective physical property if the averaging is applied outside the range of the boundary layer. From this discovery, it becomes logical to question the status of Hill–Mandel postulate in porous media when homogenising away from the boundary. In this contribution, we simulate Stokes flow through random packings of spheres and a range of rock microstructures. For each, we plot the evolution of the ratio micro- vs macro-scale of the energy of the fluid transport outside the boundary layer, for a growing subsample size of porous media. Here, we prove that we naturally find energy consistency across scales when reaching the size of the Representative Elementary Volume (REV), which is a known condition for rigorous upscaling. Furthermore, we show that this index for the energy consistency is a more accurate indicator of REV convergence since the mean value is already known to be unitary.

“Using 26,000 diary entries to show ovulatory changes in sexual desire and behavior”: Correction to Arslan et al. (2018).

Reports an error in "Using 26,000 diary entries to show ovulatory changes in sexual desire and behavior" by Ruben C. Arslan, Katharina M. Schilling, Tanja M. Gerlach and Lars Penke (Journal of Personality and Social Psychology, Advanced Online Publication, Aug 27, 2018, np). In the original article the number of participants available for robustness checks should have been 1,054, not 1,043; this applies to the third sentence in the abstract, the first sentence of the second paragraph in the Participants section, the first sentence of the second paragraph in the Robustness Checks section, and the subsample size of women in Table 3. The correct number of naturally cycling usable data should have been 429, not 421. The correct number of diary days should have been 26,680, not 25,948. The correct percentage of diary days in the fourth sentence in the Exclusion Criteria section should have been 5%. Figure 1 should have included guessing hypotheses (n 40) and long diary interruptions (n 41) as further reasons for exclusion, and an error in the effsize R package led to the reporting of inflated effect sizes for the differences between hormonal contraceptive users and non-users in Table 1. Figure 1, Table 1, and Table 3 have been corrected. All versions of this article have been corrected. (The following abstract of the original article appeared in record 2018-41799-001.) Previous research reported ovulatory changes in women's appearance, mate preferences, extra- and in-pair sexual desire, and behavior, but has been criticized for small sample sizes, inappropriate designs, and undisclosed flexibility in analyses. In the present study, we sought to address these criticisms by preregistering our hypotheses and analysis plan and by collecting a large diary sample. We gathered more than 26,000 usable online self-reports in a diary format from 1,054 women, of which 429 were naturally cycling. We inferred the fertile period from menstrual onset reports. We used hormonal contraceptive users as a quasi-control group, as they experience menstruation, but not ovulation. We probed our results for robustness to different approaches (including different fertility estimates, different exclusion criteria, adjusting for potential confounds, moderation by methodological factors). We found robust evidence supporting previously reported ovulatory increases in extra-pair desire and behavior, in-pair desire, and self-perceived desirability, as well as no unexpected associations. Yet, we did not find predicted effects on partner mate retention behavior, clothing choices, or narcissism. Contrary to some of the earlier literature, partners' sexual attractiveness did not moderate the cycle shifts. Taken together, the replicability of the existing literature on ovulatory changes was mixed. We conclude with simulation-based recommendations for reading the past literature and for designing future large-scale preregistered within-subject studies to understand ovulatory cycle changes and the effects of hormonal contraception. Interindividual differences in the size of ovulatory changes emerge as an important area for further study. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Extrapolated Cross-Validation for Randomized Ensembles

Ensemble methods such as bagging and random forests are ubiquitous in various fields, from finance to genomics. Despite their prevalence, the question of the efficient tuning of ensemble parameters has received relatively little attention. This article introduces a cross-validation method, Extrapolated Cross-Validation (ECV), for tuning the ensemble and subsample sizes in randomized ensembles. Our method builds on two primary ingredients: initial estimators for small ensemble sizes using out-of-bag errors and a novel risk extrapolation technique that leverages the structure of prediction risk decomposition. By establishing uniform consistency of our risk extrapolation technique over ensemble and subsample sizes, we show that ECV yields δ-optimal (with respect to the oracle-tuned risk) ensembles for squared prediction risk. Our theory accommodates general predictors, only requires mild moment assumptions, and allows for high-dimensional regimes where the feature dimension grows with the sample size. As a practical case study, we employ ECV to predict surface protein abundances from gene expressions in single-cell multiomics using random forests under a computational constraint on the maximum ensemble size. Compared to sample-split and K-fold cross-validation, ECV achieves higher accuracy by avoiding sample splitting. Meanwhile, its computational cost is considerably lower owing to the use of the risk extrapolation technique. Supplementary materials for this article are available online.

Efficient Model-Free Subsampling Method for Massive Data

Subsampling plays a crucial role in tackling problems associated with the storage and statistical learning of massive datasets. However, most existing subsampling methods are model-based, which means their performances can drop significantly when the underlying model is misspecified. Such an issue calls for model-free subsampling methods that are robust under diverse model specifications. Recently, several model-free subsampling methods have been developed. However, the computing time of these methods grows explosively with the sample size, making them impractical for handling massive data. In this article, an efficient model-free subsampling method is proposed, which segments the original data into some regular data blocks and obtains subsamples from each data block by the data-driven subsampling method. Compared with existing model-free subsampling methods, the proposed method has a significant speed advantage and performs more robustly for datasets with complex underlying distributions. As demonstrated in simulation experiments, the proposed method is an order of magnitude faster than other commonly used model-free subsampling methods when the sample size of the original dataset reaches the order of 107. Moreover, simulation experiments and case studies show that the proposed method is more robust than other model-free subsampling methods under diverse model specifications and subsample sizes.

Police burnout and organizational stress: job and rank associations

PurposeBurnout is an issue affecting not only individual officers, but also the agencies they work for and the communities they serve. Despite its prevalence, there is limited evidence for effective interventions that address officer burnout. This study aims to advance this area of study by identifying organizational factors associated with police burnout. By identifying these factors, stakeholders interested in officer wellness will have more clearly defined targets for intervention.Design/methodology/approachSelf-report data were gathered from US police officers partitioned into command staff (n = 125), detective (n = 41), and patrol officer (n = 191) samples. Bootstrapped correlations were calculated between 20 organizational stressors and officer burnout.FindingsFindings revealed several shared organizational stressors associated with burnout regardless of role (command staff, detective, patrol officer), as well as several role-specific organizational stressors strongly associated with burnout. Together, these findings suggest utility in considering broad-based organizational interventions and role-specific interventions to affect burnout amidst varying job duties.Research limitations/implicationsPrimary limitations to consider when interpreting these results include sample homogeneity, unequal subsample sizes, cross-sectional data limitations, and the need for implementation of interventions to test the experimental effects of reducing identified organizational stressors.Practical implicationsThis study may provide command staff and consulting parties with targets to improve departmental conditions and officer burnout.Originality/valueThis represents the first study to evaluate organizational stressors by their strength of association with burnout across a stratified police sample.

Subselection of seasonal ensemble precipitation predictions for East Africa

AbstractThe Greater Horn of Africa (GHA) is highly vulnerable to climate and weather hazards such as drought, heat waves, and floods. There is a need for accurate seasonal forecasts to prepare for risks (such as crop failure and reduced grazing opportunities) and take advantage of favorable conditions (rains arrive on time and where they are needed) when they arise. As such, information at finer spatial scales than current state‐of‐the‐art global prediction models can provide is needed. Dynamical downscaling is one method employed to obtain information at finer scales. However, providers of seasonal forecasts over the GHA are hampered by limited computational resources and time constraints that restrict the number of global model ensemble members that can be downscaled. Some ensemble subselection criteria must be employed. Currently, providers take an uninformed (or random) approach. Specifically, forecasters simply take the first ensemble member of the global model seasonal forecast ensemble. However, recent work, focused on decadal prediction, has shown that subselecting global model ensemble members in an informed way, that is, according to their ability to reproduce key features of the climate system, results in improved predictions. This emerges from the fact that the climate system is likely more predictable than our models would have us believe. Seeing an opportunity for improvement, we apply the same thinking to the seasonal context and assess several procedures for subselecting ensemble members from seasonal predictions with exchangeable members. Such informed subselections have the potential to take advantage of information in an ensemble of global simulations that might be missed by random selection. Three subselection methods are investigated, with a focus on seasonal predictions for rainfall over GHA. We demonstrate that informed subselection leads to systematically higher skill than random subselection. We find that (1) for small subsample sizes, such as would be chosen for dynamical downscaling and/or downstream impact modeling, informed subselection nearly always outperforms random subselection, (2) subselecting based on well‐known teleconnections benefits those seasons in which such pathways are active, such as OND and JJAS, and (3) ‐means subselection outperforms random selection for small ensemble sizes throughout all seasons, including the notoriously difficult to predict MAM season. These techniques require only input that is available at the time of the forecast release and are easy to apply operationally.

A rarefaction approach for measuring population differences in rare and common variation.

In studying allele-frequency variation across populations, it is often convenient to classify an allelic type as "rare," with nonzero frequency less than or equal to a specified threshold, "common," with a frequency above the threshold, or entirely unobserved in a population. When sample sizes differ across populations, however, especially if the threshold separating "rare" and "common" corresponds to a small number of observed copies of an allelic type, discreteness effects can lead a sample from one population to possess substantially more rare allelic types than a sample from another population, even if the two populations have extremely similar underlying allele-frequency distributions across loci. We introduce a rarefaction-based sample-size correction for use in comparing rare and common variation across multiple populations whose sample sizes potentially differ. We use our approach to examine rare and common variation in worldwide human populations, finding that the sample-size correction introduces subtle differences relative to analyses that use the full available sample sizes. We introduce several ways in which the rarefaction approach can be applied: we explore the dependence of allele classifications on subsample sizes, we permit more than two classes of allelic types of nonzero frequency, and we analyze rare and common variation in sliding windows along the genome. The results can assist in clarifying similarities and differences in allele-frequency patterns across populations.

Comprehensive Analysis of Compressible Perceptual Encryption Methods-Compression and Encryption Perspectives.

Perceptual encryption (PE) hides the identifiable information of an image in such a way that its intrinsic characteristics remain intact. This recognizable perceptual quality can be used to enable computation in the encryption domain. A class of PE algorithms based on block-level processing has recently gained popularity for their ability to generate JPEG-compressible cipher images. A tradeoff in these methods, however, is between the security efficiency and compression savings due to the chosen block size. Several methods (such as the processing of each color component independently, image representation, and sub-block-level processing) have been proposed to effectively manage this tradeoff. The current study adapts these assorted practices into a uniform framework to provide a fair comparison of their results. Specifically, their compression quality is investigated under various design parameters, such as the choice of colorspace, image representation, chroma subsampling, quantization tables, and block size. Our analyses have shown that at best the PE methods introduce a decrease of 6% and 3% in the JPEG compression performance with and without chroma subsampling, respectively. Additionally, their encryption quality is quantified in terms of several statistical analyses. The simulation results show that block-based PE methods exhibit several favorable properties for the encryption-then-compression schemes. Nonetheless, to avoid any pitfalls, their principal design should be carefully considered in the context of the applications for which we outlined possible future research directions.

AutoML with Bayesian Optimizations for Big Data Management

The field of automated machine learning (AutoML) has gained significant attention in recent years due to its ability to automate the process of building and optimizing machine learning models. However, the increasing amount of big data being generated has presented new challenges for AutoML systems in terms of big data management. In this paper, we introduce Fabolas and learning curve extrapolation as two methods for accelerating hyperparameter optimization. Four methods for quickening training were presented including Bag of Little Bootstraps, k-means clustering for Support Vector Machines, subsample size selection for gradient descent, and subsampling for logistic regression. Additionally, we also discuss the use of Markov Chain Monte Carlo (MCMC) methods and other stochastic optimization techniques to improve the efficiency of AutoML systems in managing big data. These methods enhance various facets of the training process, making it feasible to combine them in diverse ways to gain further speedups. We review several combinations that have potential and provide a comprehensive understanding of the current state of AutoML and its potential for managing big data in various industries. Furthermore, we also mention the importance of parallel computing and distributed systems to improve the scalability of the AutoML systems while working with big data.

Optimal subsampling design for polynomial regression in one covariate

Improvements in technology lead to increasing availability of large data sets which makes the need for data reduction and informative subsamples ever more important. In this paper we construct D-optimal subsampling designs for polynomial regression in one covariate for invariant distributions of the covariate. We study quadratic regression more closely for specific distributions. In particular we make statements on the shape of the resulting optimal subsampling designs and the effect of the subsample size on the design. To illustrate the advantage of the optimal subsampling designs we examine the efficiency of uniform random subsampling.

Cannabis vaping among high school seniors in adult-use, medical, and prohibited legal contexts

BackgroundVaping cannabis among adolescents has been increasing. Monitoring the Future (MTF) indicated in 2019 that past-month cannabis vaping among 12th graders underwent the second-highest single-year jump ever tracked by MTF for any substance in its 45-year history. These increases in adolescents who vape cannabis do not parallel declining general adolescent cannabis use trends. Nevertheless, research on cannabis consumption via vaping, especially among adolescents, has been substantially limited. MethodWe examined associations between legal contexts (prohibited, medical, and adult use) and vaping cannabis in the past year among high school seniors. In addition, associations between vaping cannabis and factors such as availability and acceptability were examined using secondary data from MTF (2020), with a sub-sample size of 556 participants (overall sample size: n = 3,770), using multivariate logistic regression models. ResultsWe found that high school seniors in medical states had higher odds of past-year vaping cannabis, but 12th graders in adult-use states were not significantly more likely to vape cannabis than those in prohibited states. Increased availability of vaping products and decreased risk perceptions in medical states may explain this relationship. Adolescents who perceived high risks associated with regular cannabis use had decreased odds of vaping cannabis. High school seniors reporting very easy access to cannabis cartridges had increased odds of vaping cannabis, regardless of legal context. ConclusionThese results contribute knowledge about contextual factors related to adolescent cannabis vaping, a relatively new technique of cannabis consumption for which there is growing societal concern.

Model constraints independent optimal subsampling probabilities for softmax regression

A prevailing method to alleviate the computational cost is to perform analysis on a subsample of the full data. Optimal subsampling algorithm utilizes non-uniform subsampling probabilities, derived through minimizing the asymptotic mean squared error of the subsample estimator, to acquire a higher estimation efficiency for a given subsample size. The optimal subsampling probabilities for softmax regression have been studied under the baseline constraint which treats one dimension of the multivariate response differently from other dimensions. In this paper, we show that different model constraints lead to different optimal subsampling probabilities, and the summation constraint corresponds to a better subsampling strategy than the baseline constraint in terms of balancing the responses among all categories. Furthermore, we derive the asymptotic distribution of the mean squared prediction error, and minimize its asymptotic expectation to define the optimal subsampling probabilities that are invariant to model constraints. Simulations and a real data example are provided to show the effectiveness of the proposed optimal subsampling probabilities.

On the asymptotic properties of a bagging estimator with a massive dataset

Bagging is a useful method for large‐scale statistical analysis, especially when the computing resources are very limited. We study here the asymptotic properties of bagging estimators for ‐estimation problems but with massive datasets. We theoretically prove that the resulting estimator is consistent and asymptotically normal under appropriate conditions. The results show that the bagging estimator can achieve the optimal statistical efficiency, provided that the bagging subsample size and the number of subsamples are sufficiently large. Moreover, we derive a variance estimator for valid asymptotic inference. All theoretical findings are further verified by extensive simulation studies. Finally, we apply the bagging method to the US Airline Dataset to demonstrate its practical usefulness.

On the Sampling Size for Inverse Sampling

In the Big Data era, sampling remains a central theme. This paper investigates the characteristics of inverse sampling on two different datasets (real and simulated) to determine when big data become too small for inverse sampling to be used and to examine the impact of the sampling rate of the subsamples. We find that the method, using the appropriate subsample size for both the mean and proportion parameters, performs well with a smaller dataset than big data through the simulation study and real-data application. Different settings related to the selection bias severity are considered during the simulation study and real application.