Subsampling Approach Research Articles

Sketched approximation of regularized canonical correlation analysis

Canonical correlation analysis (CCA) is a popular statistical tool in multivariate analysis. A regularized version is often used to stabilize the estimate. Motivated by recent interests in sketching estimates for linear regression problems which try to address the computational problem associated with massive data sets, here we investigate the sketched estimation for CCA, which includes the random subsampling approach as a special case. Some theoretical results are established based on perturbation theory. The method is also illustrated via some Monte Carlo studies and a real data analysis.

Metabarcoding of canopy arthropods reveals negative impacts of forestry insecticides on community structure across multiple taxa

Abstract Insecticides used to combat outbreaks of forest defoliators can adversely affect non‐target arthropods. Forestry insecticides typically suppress Lepidoptera larvae which are the cornerstone of the canopy community of deciduous oak forests. The abrupt removal of this dominant component of the food web could have far‐reaching implications for forest ecosystems, yet it is rarely investigated in practice owing to several methodological shortcomings. The taxonomic impediment and the biased nature of arthropod sampling techniques particularly impede the assessment of insecticide impacts on diverse communities. To tackle this issue, we propose an experimental approach combining sampling by pyrethrum knockdown and species determination via DNA metabarcoding, using community subsampling to derive estimates of species abundances. We applied this protocol to investigate the short‐term effects of the insecticides diflubenzuron (DFB) and Bacillus thuringiensis var. kurstaki (BTK) on canopy‐dwelling arthropod communities in German oak woodlands. Our approach allowed us to detect most of the diversity and integrate species abundances in our analyses. By classifying arthropod species into assemblages based on their expected sensitivity rather than coarse taxonomic groupings, we could unveil substantial effects of DFB across multiple taxa 5 weeks after application. Although strong effects on single species appear related to direct toxicity, substantial impacts of DFB on parasitoids and xylophagous beetles suggest that anti‐defoliator treatments can have previously unsuspected indirect effects on some components of forest arthropod communities. The impacts of BTK on community structure were consistent with that of DFB though much weaker. Synthesis and applications. Comparing diversity patterns in the arthropod communities of sprayed and unsprayed oak canopies, our results show that selective insecticides can alter species diversity in presumably non‐sensitive taxa. Even though the ecological significance of these impacts has yet to be assessed in an operational setting, their existence calls for increased regulatory scrutiny on indirect effects. As community approaches become more attainable with the rapid development of DNA metabarcoding, we suggest the inclusion of community‐level end points as regulatory requirements for the approval of forest‐use insecticides.

A response to estimating hybridization in the wild using community science data: A path forward.

When working with a citizen science database like eBird, there are many possible ways to filter or subsample observations. Here, we discuss the potential biases and assumptions that surround different subsampling approaches or filtering that can be done to the eBird database. Restricting observations to species that are known to frequently hybridize, a specific time of the year, or a specific location, has the potential to greatly inflate the calculated per-individual rate of hybridization. Such filtering also assumes that researchers know a birds' capacity to hybridize with all other species in its range, which we argue is an unfounded assumption. We ultimately conclude that a limited filtering approach is ideal when using a citizen science database to attempt to address a broad question such as: what is the per individual rate of hybridization across all of the bird species in the United States?

Measurement Invariance of Alabama Parenting Questionnaire Across Age, Gender, Clinical Status, and Informant.

This study aimed to investigate the measurement invariance of the Alabama Parenting Questionnaire (for both long [APQ-lg] and short [APQ-9] forms) across age, gender, clinical status, and informant (i.e., parent vs. child reports). The sample was composed of adolescents (community sample: N = 1,746; clinical sample: N = 166) and parents (N = 149). The analyses were conducted in R. Measurement invariance was assessed via multi-group confirmatory factor analysis, equivalence test, and subsampling approach. The original model of APQ-lg (five factors) showed a significantly better fit than other concurrent models (five concurrent models were specified, based on prior literature). For APQ-lg, we found measurement invariance across gender and partial measurement invariance across age, clinical status, and informant. For APQ-9, we confirmed the measurement invariance across gender and clinical status, while across age and informant partial measurement invariance was attested. Overall, our study indicated that APQ-lg and APQ-9 are two valid tools for measuring parenting practices with some caveats.

Score-matching representative approach for big data analysis with generalized linear models

We propose a fast and efficient strategy, called the representative approach, for big data analysis with generalized linear models, especially for distributed data with localization requirements or limited network bandwidth. With a given partition of massive dataset, this approach constructs a representative data point for each data block and fits the target model using the representative dataset. In terms of time complexity, it is as fast as the subsampling approaches in the literature. As for efficiency, its accuracy in estimating parameters given a homogeneous partition is comparable with the divide-and-conquer method. Supported by comprehensive simulation studies and theoretical justifications, we conclude that mean representatives (MR) work fine for linear models or generalized linear models with a flat inverse link function and moderate coefficients of continuous predictors. For general cases, we recommend the proposed score-matching representatives (SMR), which may improve the accuracy of estimators significantly by matching the score function values. As an illustrative application to the Airline on-time performance data, we show that the MR and SMR estimates are as good as the full data estimate when available.

RFN: A Random-Feature Based Newton Method for Empirical Risk Minimization in Reproducing Kernel Hilbert Spaces

In supervised learning using kernel methods, we often encounter a large-scale finite-sum minimization over a reproducing kernel Hilbert space (RKHS). Large-scale finite-sum problems can be solved using efficient variants of Newton method, where the Hessian is approximated via sub-samples of data. In RKHS, however, the dependence of the penalty function to kernel makes standard sub-sampling approaches inapplicable, since the gram matrix is not readily available in a low-rank form. In this paper, we observe that for this class of problems, one can naturally use kernel approximation to speed up the Newton method. Focusing on randomized features for kernel approximation, we provide a novel second-order algorithm that enjoys local superlinear convergence and global linear convergence (with high probability). We derive the theoretical lower bound for the number of random features required for the approximated Hessian to be close to the true Hessian in the norm sense. Our numerical experiments on real-world data verify the efficiency of our method compared to several benchmarks.

Subsampling to Enhance Efficiency in Input Uncertainty Quantification

Quantifying the impact of input estimation errors in data-driven stochastic simulation often encounters substantial computational challenges due to the entanglement of Monte Carlo and input data noises. In this paper, we propose a subsampling framework to bypass this computational bottleneck, by leveraging the form of the output variance and its estimation error in terms of data size and sampling effort. Compared with standard subsampling in the literature, our motivation is distinctly to reduce the sampling complexity of the two-layer bootstrap required in simulation uncertainty quantification. Compared with standard bootstraps, our subsampling approach provably and experimentally leads to more accurate variance and confidence interval estimations under the same amount of simulation budget.

Bootstrapped Holt Method with Autoregressive Coefficients Based on Harmony Search Algorithm

Exponential smoothing methods are one of the classical time series forecasting methods. It is well known that exponential smoothing methods are powerful forecasting methods. In these methods, exponential smoothing parameters are fixed on time, and they should be estimated with efficient optimization algorithms. According to the time series component, a suitable exponential smoothing method should be preferred. The Holt method can produce successful forecasting results for time series that have a trend. In this study, the Holt method is modified by using time-varying smoothing parameters instead of fixed on time. Smoothing parameters are obtained for each observation from first-order autoregressive models. The parameters of the autoregressive models are estimated by using a harmony search algorithm, and the forecasts are obtained with a subsampling bootstrap approach. The main contribution of the paper is to consider the time-varying smoothing parameters with autoregressive equations and use the bootstrap method in an exponential smoothing method. The real-world time series are used to show the forecasting performance of the proposed method.

Stratification of carotid atheromatous plaque using interpretable deep learning methods on B-mode ultrasound images.

Carotid atherosclerosis is the major cause of ischemic stroke resulting in significant rates of mortality and disability annually. Early diagnosis of such cases is of great importance, since it enables clinicians to apply a more effective treatment strategy. This paper introduces an interpretable classification approach of carotid ultrasound images for the risk assessment and stratification of patients with carotid atheromatous plaque. To address the highly imbalanced distribution of patients between the symptomatic and asymptomatic classes (16 vs 58, respectively), an ensemble learning scheme based on a sub-sampling approach was applied along with a two-phase, cost-sensitive strategy of learning, that uses the original and a resampled data set. Convolutional Neural Networks (CNNs) were utilized for building the primary models of the ensemble. A six-layer deep CNN was used to automatically extract features from the images, followed by a classification stage of two fully connected layers. The obtained results (Area Under the ROC Curve (AUC): 73%, sensitivity: 75%, specificity: 70%) indicate that the proposed approach achieved acceptable discrimination performance. Finally, interpretability methods were applied on the model's predictions in order to reveal insights on the model's decision process as well as to enable the identification of novel image biomarkers for the stratification of patients with carotid atheromatous plaque.Clinical Relevance-The integration of interpretability methods with deep learning strategies can facilitate the identification of novel ultrasound image biomarkers for the stratification of patients with carotid atheromatous plaque.

Adequate sample sizes for improved accuracy of thermal trait estimates

Abstract Thermal traits, such as upper and lower critical thermal limits, are vital indicators of the vulnerability of populations and species to environmental change. Thus, accurate estimates of these traits are needed to explain biological patterns and forecast responses to the changing thermal environment. However, many thermal trait studies measure relatively few individuals to estimate traits for whole populations or species. To ascertain if, and how, sample size affects the accuracy of reported trait means and variances, we applied a subsampling and equivalency testing approach to empirical and simulated trait data to investigate the accuracy of trait estimates relative to sample size and the skew and variance of the trait distribution in the source population. Simulation results indicated that only 7.9% of the 428 critical thermal limit traits documented in a recent synthesis of thermal trait data reported sufficiently large sample sizes, relative to variance, to ensure confidence in the reported mean trait value with negligible (±0.25°C) error. Greater inter‐individual trait variance in the source population requires a larger number of individuals to be measured to accurately estimate the mean and variance of that trait. This pattern is mitigated somewhat by the tendency of thermal traits to exhibit skew‐normal distributions. As measurements of few individuals from a population are unlikely to provide accurate estimates of thermal traits, the propensity towards small sample sizes in thermal trait studies is concerning. Macrophysiological syntheses often use these data to describe, explain and predict broad‐scale ecological patterns. Thus, insufficient sample sizes in the original studies could diminish the robustness of these patterns and predictions. For future studies, we recommend that preliminary data be used to estimate trait variance and calculate minimum sample sizes. If small sample sizes are unavoidable, larger error around the measured trait mean must be assumed and accounted for in subsequent analyses. A free Plain Language Summary can be found within the Supporting Information of this article.

Feature Screening for Massive Data Analysis by Subsampling

Modern statistical analysis often encounters massive datasets with ultrahigh-dimensional features. In this work, we develop a subsampling approach for feature screening with massive datasets. The approach is implemented by repeated subsampling of massive data and can be used for analyzing tasks with memory constraints. To conduct the procedure, we first calculate an R-squared screening measure (and related sample moments) based on subsamples. Second, we consider three methods to combine the local statistics. In addition to the simple average method, we design a jackknife debiased screening measure and an aggregated moment screening measure. Both approaches reduce the bias of the subsampling screening measure and therefore increase the accuracy of the feature screening. Last, we consider a novel sequential sampling method, that is more computationally efficient than the traditional random sampling method. The theoretical properties of the three screening measures under both sampling schemes are rigorously discussed. Finally, we illustrate the usefulness of the proposed method with an airline dataset containing 32.7 million records.

Temporal patterns of the catadromous thinlip grey mullet migration in freshwater

AbstractThe thinlip grey mullet (Chelon ramada Risso, 1827) is a catadromous fish that performs massive migrations to freshwater habitats for feeding purposes that can assume a structuring role on riverine ecology due to the biomass involved in these movements. Seasonal movements of thinlip grey mullet through a vertical slot fish pass located in River Mondego (Portugal) were continuously monitored between 2013 and 2017. The extent of trophic migration, population size structure, biomass and the environmental triggers of bi‐directional species' migratory activity were analysed. Between March and November of 2013/2014, ~2 million and 1 million movements were respectively recorded. From a subsampling approach, the upstream movements between 2015 and 2017 were estimated. Annually, around five hundred thousand upstream movements can occur to provide species access to the upstream freshwater reaches. Movements are exclusively diurnal, and the population composed by young adults in their first year of maturity, yet juveniles and larger fish were present (TL range: 90–540 mm). Upstream movements increased with temperatures above 15°C, reaching a peak at around 20°C coupled with a photoperiod of 15 h. Downstream movements attained the higher rates when temperature dropped from 22°C to 20°C and photoperiod to 13 h. However, under wetter hydrological conditions (as in 2014), discharge flows have a higher influence.These finding provide unique information regarding species migration to freshwater habitats in the Atlantic coast, namely the extended periods spent in such environments, overlapping with the spawning migration period. Additionally, highlights the importance of species' trophic migration both for its life cycle and riverine food‐web.

Application of FLIC model to predict adverse events onset in neuroendocrine tumors treated with PRRT

To develop predictive models of side effect occurrence in GEPNET treated with PRRT. Metastatic GEPNETs patients treated in our centre with PRRT (177Lu-Oxodotreotide) from 2019 to 2020 were considered. Haematological, liver and renal toxicities were collected and graded according to CTCAE v5. Patients were grouped according with ECOG-PS, number of metastatic sites, previous treatment lines and therapies received before PRRT. A FLIC model with backward selection was used to detect the most relevant predictors. A subsampling approach was implemented to assess variable selection stability and model performance. Sixty-seven patients (31 males, 36 females, mean age 63) treated with PRRT were considered and followed up for 30 weeks from the beginning of the therapy. They were treated with PRRT as third or further lines in 34.3% of cases. All the patients showed at least one G1–G2, meanwhile G3–G5 were rare events. No renal G3–G4 were reported. Line of PRRT administration, age, gender and ECOG-PS were the main predictors of haematological, liver and renal CTCAE. The model performance, expressed by AUC, was > 65% for anaemia, creatinine and eGFR. The application of FLIC model can be useful to improve GEPNET decision-making, allowing clinicians to identify the better therapeutic sequence to avoid PRRT-related adverse events, on the basis of patient characteristics and previous treatment lines.

Orthogonal subsampling for big data linear regression

The dramatic growth of big datasets presents a new challenge to data storage and analysis. Data reduction, or subsampling, that extracts useful information from datasets is a crucial step in big-data analysis. We propose an orthogonal subsampling (OSS) approach for big data with a focus on linear regression models. The approach is inspired by the fact that an orthogonal array of two levels provides the best experimental design for linear regression models in the sense that it minimizes the average variance of the estimated parameters and provides the best predictions. The merits of OSS are three-fold: (i) it is easy to implement and fast; (ii) it is suitable for distributed parallel computing and ensures the subsamples selected in different batches have no common data points, and (iii) it outperforms existing methods in minimizing the mean squared errors of the estimated parameters and maximizing the efficiencies of the selected subsamples. Theoretical results and extensive numerical results show that the OSS approach is superior to existing subsampling approaches. It is also more robust to the presence of interactions among covariates, and, when they do exist, OSS provides more precise estimates of the interaction effects than existing methods. The advantages of OSS are also illustrated through analysis of real data.

ASAP – A sub-sampling approach for preserving topological structures modeled with geodesic topographic mapping

Topological data analysis tools enjoy increasing popularity in a wide range of applications, such as Computer graphics, Image analysis, Machine learning, and Astronomy for extracting information. However, due to computational complexity, processing large numbers of samples of higher dimensionality quickly becomes infeasible. This contribution is twofold: We present an efficient novel sub-sampling strategy inspired by Coulomb’s law to decrease the number of data points in d-dimensional point clouds while preserving its homology. The method is not only capable of reducing the memory and computation time needed for the construction of different types of simplicial complexes but also preserves the size of the voids in d-dimensions, which is crucial e.g. for astronomical applications. Furthermore, we propose a technique to construct a probabilistic description of the border of significant cycles and cavities inside the point cloud. We demonstrate and empirically compare the strategy in several synthetic scenarios and an astronomical particle simulation of a dwarf galaxy for the detection of superbubbles (supernova signatures).

The Block-Poisson Estimator for Optimally Tuned Exact Subsampling MCMC

Speeding up Markov chain Monte Carlo (MCMC) for datasets with many observations by data subsampling has recently received considerable attention. A pseudo-marginal MCMC method is proposed that estimates the likelihood by data subsampling using a block-Poisson estimator. The estimator is a product of Poisson estimators, allowing us to update a single block of subsample indicators in each MCMC iteration so that a desired correlation is achieved between the logs of successive likelihood estimates. This is important since pseudo-marginal MCMC with positively correlated likelihood estimates can use substantially smaller subsamples without adversely affecting the sampling efficiency. The block-Poisson estimator is unbiased but not necessarily positive, so the algorithm runs the MCMC on the absolute value of the likelihood estimator and uses an importance sampling correction to obtain consistent estimates of the posterior mean of any function of the parameters. Our article derives guidelines to select the optimal tuning parameters for our method and shows that it compares very favorably to regular MCMC without subsampling, and to two other recently proposed exact subsampling approaches in the literature. Supplementary materials for this article are available online.

Phylogenomic Subsampling and the Search for Phylogenetically Reliable Loci.

Phylogenomic subsampling is a procedure by which small sets of loci are selected from large genome-scale data sets and used for phylogenetic inference. This step is often motivated by either computational limitations associated with the use of complex inference methods or as a means of testing the robustness of phylogenetic results by discarding loci that are deemed potentially misleading. Although many alternative methods of phylogenomic subsampling have been proposed, little effort has gone into comparing their behavior across different data sets. Here, I calculate multiple gene properties for a range of phylogenomic data sets spanning animal, fungal, and plant clades, uncovering a remarkable predictability in their patterns of covariance. I also show how these patterns provide a means for ordering loci by both their rate of evolution and their relative phylogenetic usefulness. This method of retrieving phylogenetically useful loci is found to be among the top performing when compared with alternative subsampling protocols. Relatively common approaches such as minimizing potential sources of systematic bias or increasing the clock-likeness of the data are found to fare worse than selecting loci at random. Likewise, the general utility of rate-based subsampling is found to be limited: loci evolving at both low and high rates are among the least effective, and even those evolving at optimal rates can still widely differ in usefulness. This study shows that many common subsampling approaches introduce unintended effects in off-target gene properties and proposes an alternative multivariate method that simultaneously optimizes phylogenetic signal while controlling for known sources of bias.

Fast Optimal Subsampling Probability Approximation for Generalized Linear Models

For massive data, subsampling techniques are popular to mitigate computational burden by reducing the data size. In a subsampling approach, subsampling probabilities for each data point are specified to obtain an informative sub-data, and then estimates based on the sub-data are obtained to approximate estimates from the full data. Assigning subsampling probabilities based on minimization of the asymptotic mean squared error of the estimator from a general subsample (A-optimality criterion) is a popular approach, however, it is still computationally demanding to calculate the probabilities under this setting. To efficiently approximate the A-optimal subsampling probabilities for generalized linear models, randomized algorithms are proposed. To develop the algorithms, the Johnson-Lindenstrauss Transform and Subsampled Randomized Hadamard Transform are used. Additionally, optimal subsampling probabilities are derived for the Gaussian linear model in the case where both the regression coefficients and dispersion parameter are of interest, and algorithms are developed to approximate the optimal subsampling probabilities. Simulation studies indicate that the estimators based on the developed algorithms have excellent performance for statistical inference and have substantial savings in computing time compared to the direct calculation of the A-optimal subsampling probabilities.

Excess Volatility in Bitcoin: Extreme Value Volatility Estimation

This article investigates the excess volatility in Bitcoin prices using an unbiased extreme value volatility estimator. We capture the time-varying nature of the excess volatility using bootstrap, multi-horizon, sub-sampling and rolling-window approaches. We observe that Bitcoin price changes are almost efficient. Although Bitcoin prices exhibit high volatility and show signs of excess volatility for a few periods, it is decreasing over time. After controlling for the outliers, we also notice that the Bitcoin market shows signs of increasing maturity. Overall, Bitcoin prices show a sign of increasing efficiency with decreasing volatility. Our findings have implications for investors making investment decisions and for regulators making policy choices.

Cramér-Rao Bounds for spectral parametric estimation with compressive multiband architectures

This article tackles the topic of performance analysis for Spectrum Sensing based on Compressive Sampling (CS). More precisely, the lower bound on the variance of any unbiased estimator, the Cramér-Rao Bound (CRB), is investigated in the context of spectral parametric estimation. Compressed samples are obtained from a multiband architecture like the Modulated Wideband Converter, the Quadrature-Analog-to-Information Converter or the Periodic Non Uniform Sampler. An expression of the Fisher information matrix, which allows to compute the CRB, is established for a compressive multiband architecture assuming a disjoint spectral subband model. The relationships between Fisher matrices in a generic framework are exposed: first between compressive multiband and subsampling architectures, then between subsampling and Nyquist sampling architectures. Based on these new considerations, the issue of interferer detection, a canonical case and also a huge thorn in the side of wideband radiofrequency receivers is tackled. A benchmark between Nyquist, Subsampling and Compressive Multiband Sampling approaches is provided for frequency and amplitude estimation of dual-tone signals. This analysis illustrates the way in which interferences between parameters occur in estimation with Compressive Sampling. It is then shown how properties of the sensing matrix for popular compressive architectures enable to control the precision of spectral parametric estimation in specific subbands. This control opportunity opens the door to adaptive methods.