Sample Splitting Research Articles

Extending the dynamic range of biomarker quantification through molecular equalization

Precision medicine requires highly scalable methods of multiplexed biomarker quantification that can accurately describe patient physiology. Unfortunately, contemporary molecular detection methods are generally limited to a dynamic range of sensitivity spanning just 3–4 orders of magnitude, whereas the actual physiological dynamic range of the human plasma proteome spans more than 10 orders of magnitude. Current methods rely on sample splitting and differential dilution to compensate for this mismatch, but such measures greatly limit the reproducibility and scalability that can be achieved—in particular, the effects of non-linear dilution can greatly confound the analysis of multiplexed assays. We describe here a two-pronged strategy for equalizing the signal generated by each analyte in a multiplexed panel, thereby enabling simultaneous quantification of targets spanning a wide range of concentrations. We apply our ‘EVROS’ strategy to a proximity ligation assay and demonstrate simultaneous quantification of four analytes present at concentrations spanning from low femtomolar to mid-nanomolar levels. In this initial demonstration, we achieve a dynamic range spanning seven orders of magnitude in a single 5 µl sample of undiluted human serum, highlighting the opportunity to achieve sensitive, accurate detection of diverse analytes in a highly multiplexed fashion.

Testing for the Markov property in time series via deep conditional generative learning.

The Markov property is widely imposed in analysis of time series data. Correspondingly, testing the Markov property, and relatedly, inferring the order of a Markov model, are of paramount importance. In this article, we propose a nonparametric test for the Markov property in high-dimensional time series via deep conditional generative learning. We also apply the test sequentially to determine the order of the Markov model. We show that the test controls the type-I error asymptotically, and has the power approaching one. Our proposal makes novel contributions in several ways. We utilise and extend state-of-the-art deep generative learning to estimate the conditional density functions, and establish a sharp upper bound on the approximation error of the estimators. We derive a doubly robust test statistic, which employs a nonparametric estimation but achieves a parametric convergence rate. We further adopt sample splitting and cross-fitting to minimise the conditions required to ensure the consistency of the test. We demonstrate the efficacy of the test through both simulations and the three data applications.

Early porosity generation in organic-sulfur-rich mudstones

High total organic sulfur (TOS) content (i.e., Type IIS kerogen) is well known to significantly influence kerogen transformation but the effect of TOS content on the evolution of organic porosity has only rarely and indirectly been investigated. This study demonstrates that organic porosity is generated at lower thermal maturity in mudstones containing Type IIS kerogen relative to those with Type II kerogen. To our knowledge this phenomenon has not been previously demonstrated. The implications are relevant for the characterization of organic-rich mudstones as cap rocks, hydrocarbon reservoirs, and disposal reservoirs for CO2 or nuclear waste because pore systems control storage volumes and matrix fluid flow. Five thermally immature core samples were selected from three organic-rich mudstone units with low to high TOS content: the late Devonian Duvernay Formation (Canada), middle late Miocene Onnagawa Formation (Japan), and early Jurassic Gordondale member of the Fernie Formation (Canada). Hydrous pyrolysis was used to artificially mature splits of the immature samples to four maturity stages, upon which petrophysical and organic geochemical properties were measured and compared to baseline immature samples. Most porosity growth in Type IIS samples occurred below 0.70% VRoeqv, but in Type II samples was broader and robust until 1.1% VRoeqv.

Fractal dimension analysis of concrete specimens under different strain rates

To analyze the relationship between the dynamic mechanical performance and fractality of concrete, the specimens of a separate Hopkinson pressure bar (SHPB) from a concrete component using the coring method were obtained. This study designed three common concrete strength grades, C40, C50, and C60 and conducted dynamic splitting tensile tests, together with scanning electron microscopy (SEM) tests on these specimens. Based on the experimental results, the variations in the dynamic splitting strength (DSTS), dynamic increase factor (DIF), and energy absorption (EA) efficiency were analyzed. A semi-empirical formula for a unified DIF value was proposed. A digital image algorithm based on fractal theory was designed to evaluate the fractal dimension (FD) of the impact damage area crack pattern, and regression models were established between strain rate, DIF, and FD. Based on SEM tests, the relationship between dynamic splitting of the core sample and microstructure was analyzed, and a model was established between FD of SEM image and strain rate. The test results demonstrated that the dynamic mechanical performance of concrete has a significant strain-rate effect. The damage characteristics of concrete under impact can be quantitatively evaluated by the FD characteristics under impact loads, and there was a significant correlation between the strain rate, DIF, and crack FD. The internal and interaggregate cracking of the core samples increased and expanded continuously. The change in microstructure was consistent with the changes in the macroscopic failure modes, and FD of the specimen pore area increased with an increase in the strain rate. The research results organically linked FD and dynamic performance, failure mode, SEM images, and other mechanical attributes, providing a reference for using image information to study the dynamic mechanical performance of concrete materials.

A unified diagnostic framework via symmetrized data aggregation

In statistical process control of high-dimensional data streams, in addition to online monitoring of abnormal changes, fault diagnosis of responsible components has become increasingly important. Existing diagnostic procedures have been designed for some typical models with distribution assumptions. Moreover, there is a lack of systematic approaches to provide a theoretical guarantee of significance in estimating shifted components. In this article, we introduce a new procedure to control the False Discovery Rate (FDR) of fault diagnosis. The proposed method formulates the fault diagnosis as a variable selection problem and utilizes the symmetrized data aggregation technique via sample splitting, data screening, and information pooling to control the FDR. Under some mild conditions, we show that the proposed method can achieve FDR control asymptotically. Extensive numerical studies and two real-data examples demonstrate satisfactory FDR control and remarkable diagnostic power in comparison to existing methods.

Neighborhood-based cross fitting approach to treatment effects with high-dimensional data

High-dimensional data are increasingly popular in various physical, biological and social disciplines. A common existing approach of repeatedly splitting data was suggested to address the overfitting problem in high-dimensional statistics, however it is computationally expensive in high dimensions. A computationally efficient data splitting method is proposed and referred to as Neighborhood-Based Cross Fitting (NBCF) double machine learning in causal inference for structural causal models with high-dimensional data. The proposed method deals well with the problem of post-selection bias in causal inference in the presence of high-dimensional confounding. It provides an equivalent basis in unbiased estimation as repeated data splitting, which is suggested to expand the complexity scope of function class by empirical process methods. Numerical simulation studies were conducted to demonstrate that the proposed neighborhood-based approach is not only more computationally efficient than the existing sample splitting methods, but also better in bias reduction compared with other existing methods. Under certain conditions, simulation results further showed that the proposed estimators are asymptotically unbiased and normally distributed, which allows construction of valid confidence intervals. The practical application of NBCF is illustrated with a real dataset.

Reliable Genetic Correlation Estimation via Multiple Sample Splitting and Smoothing

In this paper, we aim to investigate the problem of estimating the genetic correlation between two traits. Instead of making assumptions about the distribution of effect sizes of the genetic factors, we propose the use of a high-dimensional linear model to relate a trait to genetic factors. To estimate the genetic correlation, we develop a generic strategy that combines the use of sparse penalization methods and multiple sample splitting approaches. The final estimate is determined by taking the median of the calculations, resulting in a smoothed and reliable estimate. Through simulations, we demonstrate that our proposed approach is reliable and accurate in comparison to naive plug-in methods. To further illustrate the advantages of our method, we apply it to a real-world example of a bacterial GWAS dataset, specifically to estimate the genetic correlation between antibiotic resistant traits in Streptococus pneumoniae. This application not only validates the effectiveness of our method but also highlights its potential in real-world applications.

A stable and adaptive polygenic signal detection method based on repeated sample splitting

AbstractFocusing on polygenic signal detection in high‐dimensional genetic association studies of complex traits, we develop a stable and adaptive test for generalized linear models to accommodate different alternatives. To facilitate valid post‐selection inference for high‐dimensional data, our study here adheres to the original sample‐splitting principle but does so repeatedly to increase stability of the inference. We show the asymptotic null distribution of the proposed test for both fixed and diverging numbers of variants. We also show the asymptotic properties of the proposed test under local alternatives, providing insights on why power gain attributed to variable selection and weighting can compensate for efficiency loss due to sample splitting. We support our analytical findings through extensive simulation studies and two applications. The proposed procedure is computationally efficient and has been implemented as the R package DoubleCauchy.

Rapid prototyping of polydimethylsiloxane (PDMS) microchips using electrohydrodynamic jet printing: Application to electrokinetic assays.

Polydimethylsiloxane (PDMS) based microfluidic devices have found increasing utility for electrophoretic and electrokinetic assays because of their ease of fabrication using replica molding. However, the fabrication of high-resolution molds for replica molding still requires the resource-intensive and time-consuming photolithography process, which precludes quick design iterations and device optimization. We here demonstrate a low-cost, rapid microfabrication process, based on electrohydrodynamic jet printing (EJP), for fabricating non-sacrificial master molds for replica molding of PDMS microfluidic devices. The method is based on the precise deposition of an electrically stretched polymeric solution of polycaprolactone in acetic acid on a silicon wafer placed on a computer-controlled motion stage. This process offers the high-resolution (order10 m) capability of photolithography and rapid prototyping capability of inkjet printing to print high-resolution templates for elastomeric microfluidic devices within a few minutes. Through proper selection of the operating parameters such as solution flow rate, applied electric field, and stage speed, we demonstrate microfabrication of intricate master molds and corresponding PDMS microfluidic devices for electrokinetic applications. We demonstrate the utility of the fabricated PDMS microchips for nonlinear electrokinetic processes such as electrokinetic instability and controlled sample splitting in ITP. The ability to rapid prototype customized reusable master molds with order 10 m resolution within a few minutes can help in designing and optimizing microfluidic devices for various electrokineticapplications.

Experimental study of dynamic splitting-tensile properties of precast concrete samples under different strain rates

This study investigated the dynamic splitting and tensile properties of the precast concrete core samples under different strain rates using the split-Hopkinson pressure bar (SHPB). The dynamic splitting-tensile strength (DSTS), stress–strain curves, and damage patterns of concrete were analyzed. The modified Weibull statistical model was utilized to analyze the discrete features of DSTS and strain rate effects of the precast concrete samples. Besides, the fractal theory was applied to calculate the fractal dimension of surface cracks on core specimens. The relationships between the fractal dimension, splitting-tensile strength, and strain rate effect were also presented. Consequently, it was found that the stress–strain curves of different strength grades of concrete specimens displayed similar patterns. The DSTS of precast concrete exhibited an apparent impact-strengthening effect. And the modified Weibull model proposed in this paper could accurately predict the distribution of DSTS at different strain rates of precast concrete, which provided a theoretical reference for the strength prediction of precast concrete in practical engineering practices. Furthermore, the fractal dimension could qualitatively characterize the failure evolution trend and extent of splitting-tensile damages, providing a new research direction to investigate crack patterns and dynamic mechanical properties of precast concrete members in future engineering inspection and maintenance.

Sharp global convergence guarantees for iterative nonconvex optimization with random data

We consider a general class of regression models with normally distributed covariates, and the associated nonconvex problem of fitting these models from data. We develop a general recipe for analyzing the convergence of iterative algorithms for this task from a random initialization. In particular, provided each iteration can be written as the solution to a convex optimization problem satisfying some natural conditions, we leverage Gaussian comparison theorems to derive a deterministic sequence that provides sharp upper and lower bounds on the error of the algorithm with sample splitting. Crucially, this deterministic sequence accurately captures both the convergence rate of the algorithm and the eventual error floor in the finite-sample regime, and is distinct from the commonly used “population” sequence that results from taking the infinite-sample limit. We apply our general framework to derive several concrete consequences for parameter estimation in popular statistical models including phase retrieval and mixtures of regressions. Provided the sample size scales near linearly in the dimension, we show sharp global convergence rates for both higher-order algorithms based on alternating updates and first-order algorithms based on subgradient descent. These corollaries, in turn, reveal multiple nonstandard phenomena that are then corroborated by extensive numerical experiments.

Debiased machine learning of set-identified linear models

This paper provides estimation and inference methods for an identified set’s boundary (i.e., support function) where the selection among a very large number of covariates is based on modern regularized tools. I characterize the boundary using a semiparametric moment equation. Combining Neyman-orthogonality and sample splitting ideas, I construct a root-N consistent, uniformly asymptotically Gaussian estimator of the boundary and propose a multiplier bootstrap procedure to conduct inference. I apply this result to the Partially Linear Model, the Partially Linear IV Model and the Average Partial Derivative with an interval-valued outcome.

A Discussion of “A Note on Universal Inference” by Tse and Davison

A Discussion of “A Note on Universal Inference” by Tse and Davison

Inference after latent variable estimation for single-cell RNA sequencing data.

In the analysis of single-cell RNA sequencing data, researchers often characterize the variation between cells by estimating a latent variable, such as cell type or pseudotime, representing some aspect of the cell's state. They then test each gene for association with the estimated latent variable. If the same data are used for both of these steps, then standard methods for computing p-values in the second step will fail to achieve statistical guarantees such as Type 1 error control. Furthermore, approaches such as sample splitting that can be applied to solve similar problems in other settings are not applicable in this context. In this article, we introduce count splitting, a flexible framework that allows us to carry out valid inference in this setting, for virtually any latent variable estimation technique and inference approach, under a Poisson assumption. We demonstrate the Type 1 error control and power of count splitting in a simulation study and apply count splitting to a data set of pluripotent stem cells differentiating to cardiomyocytes.

SEQENS: An ensemble method for relevant gene identification in microarray data

This paper describes an ensemble feature identification algorithm called SEQENS, and measures its capability to identify the relevant variables in a case-control study using a genetic expression microarray dataset. SEQENS uses Sequential Feature Search on multiple sample splitting to select variables showing stronger relation with the target, and a variable relevance ranking is finally produced. Although designed for feature identification, SEQENS could also serve as a basis for feature selection (classifier optimisation). Cliff, a ranking evaluation metric is also presented and used to assess the feature identification algorithms when a groundtruth of relevant variables is available. To test performance, three types of synthetic groundtruths emulating fictitious diseases are generated from ten randomly chosen variables following different target pattern distributions using the E-MTAB-3732 dataset. Several sample-to-dimensionality ratios ranging from 300 to 3,000 observations and 854 to 54,675 variables are explored. SEQENS is compared with other feature selection or identification state-of-the-art methods. On average, the proposed algorithm identifies better the relevant genes and exhibits a stronger stability. The algorithm is available to the community.

Interlaboratory Comparison of 226Ra and 228Ra Activity Concentrations in Groundwater and Surface Water

226Ra and 228Ra are typically monitored for groundwater and surface water compliance at legacy U mining and milling sites. Groundwater monitoring results for combined Ra (226Ra + 228Ra) reported by the existing contract laboratory at a former U mine and mill Site (Converse County, WY, USA) have been highly variable and with increasing trends at the Site compliance and background wells since the method was changed in 2005. Sample reanalysis has indicated poor reproducibility and significant analytical error in 228Ra measurements. An interlaboratory comparison was conducted to evaluate the potential causes of the high variability and analytical error. Two different methods were used for 226Ra (M903.0 and M903.1) and 228Ra (M904.0 and Ra-05). 226Ra results were less variable compared to 228Ra, and 228Ra data from the existing laboratory were qualified as estimated with high bias due to detection of 228Ra in the field blank. Compliance with the 226Ra + 228Ra groundwater standard was either met or not met, depending on which laboratory conducted the analyses. Specific laboratory techniques, rather than the analytical method, are contributing to elevated 228Ra values being reported. It was recommended that samples whose 226Ra + 228Ra results exceed the Site standard in the future be reanalyzed by the existing laboratory with a sample split also being sent to an outside laboratory for confirmatory analysis.

Gaussian universal likelihood ratio testing

Summary The classical likelihood ratio test based on the asymptotic chi-squared distribution of the log-likelihood is one of the fundamental tools of statistical inference. A recent universal likelihood ratio test approach based on sample splitting provides valid hypothesis tests and confidence sets in any setting for which we can compute the split likelihood ratio statistic, or, more generally, an upper bound on the null maximum likelihood. The universal likelihood ratio test is valid in finite samples and without regularity conditions. This test empowers statisticians to construct tests in settings for which no valid hypothesis test previously existed. For the simple, but fundamental, case of testing the population mean of $d$-dimensional Gaussian data with an identity covariance matrix, the classical likelihood ratio test itself applies. Thus, this setting serves as a perfect test bed to compare the classical likelihood ratio test against the universal likelihood ratio test. This work presents the first in-depth exploration of the size, power and relationships between several universal likelihood ratio test variants. We show that a repeated subsampling approach is the best choice in terms of size and power. For large numbers of subsamples, the repeated subsampling set is approximately spherical. We observe reasonable performance even in a high-dimensional setting, where the expected squared radius of the best universal likelihood ratio test’s confidence set is approximately 3/2 times the squared radius of the classical likelihood ratio test’s spherical confidence set. We illustrate the benefits of the universal likelihood ratio test through testing a nonconvex doughnut-shaped null hypothesis, where a universal inference procedure can have higher power than a standard approach.

A robust and adaptive framework for interaction testing in quantitative traits between multiple genetic loci and exposure variables.

The identification and understanding of gene-environment interactions can provide insights into the pathways and mechanisms underlying complex diseases. However, testing for gene-environment interaction remains a challenge since a.) statistical power is often limited and b.) modeling of environmental effects is nontrivial and such model misspecifications can lead to false positive interaction findings. To address the lack of statistical power, recent methods aim to identify interactions on an aggregated level using, for example, polygenic risk scores. While this strategy can increase the power to detect interactions, identifying contributing genes and pathways is difficult based on these relatively global results. Here, we propose RITSS (Robust Interaction Testing using Sample Splitting), a gene-environment interaction testing framework for quantitative traits that is based on sample splitting and robust test statistics. RITSS can incorporate sets of genetic variants and/or multiple environmental factors. Based on the user's choice of statistical/machine learning approaches, a screening step selects and combines potential interactions into scores with improved interpretability. In the testing step, the application of robust statistics minimizes the susceptibility to main effect misspecifications. Using extensive simulation studies, we demonstrate that RITSS controls the type 1 error rate in a wide range of scenarios, and we show how the screening strategy influences statistical power. In an application to lung function phenotypes and human height in the UK Biobank, RITSS identified highly significant interactions based on subcomponents of genetic risk scores. While the contributing single variant interaction signals are weak, our results indicate interaction patterns that result in strong aggregated effects, providing potential insights into underlying gene-environment interaction mechanisms.

Threshold regression with nonparametric sample splitting

This paper develops a threshold regression model where an unknown relationship between two variables nonparametrically determines the threshold. We allow the observations to be cross-sectionally dependent so that the model can be applied to determine an unknown spatial border for sample splitting over a random field. We derive the uniform rate of convergence and the nonstandard limiting distribution of the nonparametric threshold estimator. We also obtain the root-n consistency and the asymptotic normality of the regression coefficient estimator. We illustrate empirical relevance of this new model by estimating the tipping point in social segregation problems as a function of demographic characteristics; and determining metropolitan area boundaries using nighttime light intensity collected from satellite imagery.

How to measure parenting styles?

In this paper, we measure parenting styles through unsupervised machine learning in a panel following children from age 5 to 29 months. The topic model, which is a statistical model originally developed to discover the latent semantic structures in text, classifies parents into two parenting styles: “warm” and “cold”. Parents of the warm type tend to respond to children’s expressions in a supportive manner, while parents of the cold type are less likely to engage with their children in an encouraging manner. Warm parenting is more likely amongst educated and older mothers. Although styles reveal some persistence, the share of parents with a warm style decreases with the age of the child, in particular for boys. Children of warm parents achieve higher cognitive and non-cognitive scores at later ages. We find that the topic model estimated on different sample splits, such as by education or child age, reveal additional information while maintaining robust overall patterns.