Divide and Recombine Approaches for Fitting Smoothing Spline Models with Large Datasets

Xu, Danqing; Wang, Yuedong

doi:10.1080/10618600.2017.1402775

Cited by 13 publications

(9 citation statements)

References 11 publications

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“…The resulting 25 bp CDTS scores have 13.46% missing rate. In our analyses, we apply a Sequential Divide and Recombine approach 20 and impute the missing data by cubic smoothing spline estimates whenever possible, as follows. (1) Divide the range of positions into disjoint intervals so that the CDTS values are either available or missing in each interval.…”

Section: Cdts Imputation By Cubic Smoothing Splinesmentioning

confidence: 99%

Co-localization between Sequence Constraint and Epigenomic Information Improves Interpretation of Whole-Genome Sequencing Data

Wang

Kiryluk

et al. 2020

The American Journal of Human Genetics

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The identification of functional regions in the noncoding human genome is difficult but critical in order to gain understanding of the role noncoding variation plays in gene regulation in human health and disease. We describe here a co-localization approach that aims to identify constrained sequences that co-localize with tissue-or cell-type-specific regulatory regions, and we show that the resulting score is particularly well suited for the identification of rare regulatory variants. For 127 tissues and cell types in the ENCODE/Roadmap Epigenomics Project, we provide catalogs of putative tissue-or cell-type-specific regulatory regions under sequence constraint. We use the newly developed co-localization score for brain tissues to score de novo mutations in whole genomes from 1,902 individuals affected with autism spectrum disorder (ASD) and their unaffected siblings in the Simons Simplex Collection. We show that noncoding de novo mutations near genes co-expressed in midfetal brain with high confidence ASD risk genes, and near FMRP gene targets are more likely to be in co-localized regions if they occur in ASD probands versus in their unaffected siblings. We also observed a similar enrichment for mutations near lincRNAs, previously shown to co-express with ASD risk genes. Additionally, we provide strong evidence that prioritized de novo mutations in autism probands point to a small set of well-known ASD genes, the disruption of which produces relevant mouse phenotypes such as abnormal social investigation and abnormal discrimination/associative learning, unlike the de novo mutations in unaffected siblings. The genome-wide co-localization results are available online.

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Section: Cdts Imputation By Cubic Smoothing Splinesmentioning

confidence: 99%

Co-localization between Sequence Constraint and Epigenomic Information Improves Interpretation of Whole-Genome Sequencing Data

Wang

Kiryluk

et al. 2020

The American Journal of Human Genetics

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“…Shang and Cheng (2017) studied the divide-and-conquer method for periodic smoothing splines and argued from a theoretical perspective that sample splitting may be viewed as an alternative form of regularization, playing a role similar to a smoothing parameter. Xu and Wang (2018) proposed two pairs of D&C approaches to fitting a cubic smoothing splines model on a large data set. One pair of approaches divide data in a simple random way, and the other in a sequential way by partitioning the domain into subintervals.…”

Section: A3 Proof Of Theorem 222mentioning

confidence: 99%

“…One pair of approaches divide data in a simple random way, and the other in a sequential way by partitioning the domain into subintervals. We note that both Shang and Cheng (2017) and Xu and Wang (2018) only considered smoothing splines on a univariate domain. And the extension of D&C to modeling of our temperature monitoring experiment may have some other issues.…”

Section: A3 Proof Of Theorem 222mentioning

confidence: 99%

“…On one hand, a simple random partition of the data does not take full advantage of the dense and regular sampling feature of our data. On the other hand, a sequential partition similar to Xu and Wang (2018) is much harder to implement for a 2D or 3D space. In addition, no matter how the data are partitioned, the ensuing recombining step can be cumbersome since we need to estimate a 3D mean function and two 2D variance functions as well as test on the existence of a variance 60 function change point.…”

Section: A3 Proof Of Theorem 222mentioning

confidence: 99%

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Variance Change Point Detection Under a Smoothly-Changing Mean Trend with Application to Liver Procurement

Gao

Shang

et al. 2018

Journal of the American Statistical Association

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Literature on change point analysis mostly requires a sudden change in the data distribution, either in a few parameters or the distribution as a whole. We are interested in the scenario that the variance of data may make a significant jump while the mean of data changes in a smooth fashion. It is motivated by a liver procurement experiment with organ surface temperature monitoring. Blindly applying the existing change point analysis methods to the example can yield erratic change point estimates since the smoothly-changing mean violates the sudden-change assumption. In my dissertation, we propose a penalized weighted least squares approach with an iterative estimation procedure that naturally integrates variance change point detection and smooth mean function estimation. Given the variance components, the mean function is estimated by smoothing splines as the minimizer of the penalized weighted least squares. Given the mean function, we propose a likelihood ratio test statistic for identifying the variance change point. The null distribution of the test statistic is derived together with the rates of convergence of all the parameter estimates. Simulations show excellent performance of the proposed method. Application analysis offers numerical support to the non-invasive organ viability assessment by surface temperature monitoring.The method above can only yield the variance change point of temperature at a single point on the surface of the organ at a time. In practice, an organ is often transplanted as a whole or in part. Therefore, it is generally of more interest to study the variance change point for a chunk of organ. With this motivation, we extend our method to study variance change point for a chunk of the organ surface. Now the variances become functions on a 2D space of locations (longitude and latitude) and the mean is a function on a 3D space of location and time. We model the variance functions by thin-plate splines and the mean function by the tensor product of thin-plate splines and cubic splines. However, the additional dimensions in these functions incur serious computational problems since the sample size, as a product of the number of locations and the number of sampling time points, becomes too large to run the standard multi-dimensional spline models. To overcome the computational hurdle, we introduce a multi-stages subsampling strategy into our modified iterative algorithm.The strategy involves several down-sampling or subsampling steps educated by preliminary statistical measures. We carry out extensive simulations to show that the new method can efficiently cut down the computational cost and make a practically unsolvable problem solvable with reasonable time and satisfactory parameter estimates. Application of the new method to the liver surface temperature monitoring data shows its effectiveness in providing accurate status change information for a portion of or the whole organ.The viability evaluation is the key issue in the organ transplant operation. The donated organ must be viable a...

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“…Ma et al (2015) developed an adaptive sampling scheme to select subsets of representers according to the magnitude of the response variable. When the roughness and magnitude of the underlying function do not coincide, the method in Ma et al (2015) is not spatially adaptive (Xu & Wang, 2018). Wood (2003) used the Lanczos algorithm (Lanczos, 1950) to obtain the truncated eigendecomposition for thin‐plate splines in O ( Kn 2 ) operations with K being the rank of the low‐rank approximation.…”

Section: Introductionmentioning

confidence: 99%

Low‐rank approximation for smoothing spline via eigensystem truncation

Wang

2021

Stat

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Smoothing splines provide a powerful and flexible means for nonparametric estimation and inference. With a cubic time complexity, fitting smoothing spline models to large data is computationally prohibitive. In this paper, we use the theoretical optimal eigenspace to derive a low‐rank approximation of the smoothing spline estimates. We develop a method to approximate the eigensystem when it is unknown and derive error bounds for the approximate estimates. The proposed methods are easy to implement with existing software. Extensive simulations show that the new methods are accurate, fast and compare favourably against existing methods.

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Divide and Recombine Approaches for Fitting Smoothing Spline Models with Large Datasets

Cited by 13 publications

References 11 publications

Co-localization between Sequence Constraint and Epigenomic Information Improves Interpretation of Whole-Genome Sequencing Data

Co-localization between Sequence Constraint and Epigenomic Information Improves Interpretation of Whole-Genome Sequencing Data

Variance Change Point Detection Under a Smoothly-Changing Mean Trend with Application to Liver Procurement

Low‐rank approximation for smoothing spline via eigensystem truncation

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