scholarly journals AdaReg: data adaptive robust estimation in linear regression with application in GTEx gene expressions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Meng Wang ◽  
Lihua Jiang ◽  
Michael P. Snyder
Keyword(s):  
Linear Regression ◽  
Robust Estimation ◽  
Population Distribution ◽  
Selection Criterion ◽  
Simulation Studies ◽  
Gene Expressions ◽  
Regression Problem ◽  
Data Adaptive ◽  
Robust Likelihood ◽  
Tissue Effect

Abstract The Genotype-Tissue Expression (GTEx) project provides a valuable resource of large-scale gene expressions across multiple tissue types. Under various technical noise and unknown or unmeasured factors, how to robustly estimate the major tissue effect becomes challenging. Moreover, different genes exhibit heterogeneous expressions across different tissue types. Therefore, we need a robust method which adapts to the heterogeneities of gene expressions to improve the estimation for the tissue effect. We followed the approach of the robust estimation based on γ-density-power-weight in the works of Fujisawa, H. and Eguchi, S. (2008). Robust parameter estimation with a small bias against heavy contamination. J. Multivariate Anal. 99: 2053–2081 and Windham, M.P. (1995). Robustifying model fitting. J. Roy. Stat. Soc. B: 599–609, where γ is the exponent of density weight which controls the balance between bias and variance. As far as we know, our work is the first to propose a procedure to tune the parameter γ to balance the bias-variance trade-off under the mixture models. We constructed a robust likelihood criterion based on weighted densities in the mixture model of Gaussian population distribution mixed with unknown outlier distribution, and developed a data-adaptive γ-selection procedure embedded into the robust estimation. We provided a heuristic analysis on the selection criterion and found that our practical selection trend under various γ’s in average performance has similar capability to capture minimizer γ as the inestimable mean squared error (MSE) trend from our simulation studies under a series of settings. Our data-adaptive robustifying procedure in the linear regression problem (AdaReg) showed a significant advantage in both simulation studies and real data application in estimating tissue effect of heart samples from the GTEx project, compared to the fixed γ procedure and other robust methods. At the end, the paper discussed some limitations on this method and future work.

scholarly journals AdaReg: Data Adaptive Robust Estimation in Linear Regression with Application in GTEx Gene Expressions

2019 ◽  
Author(s):  
Meng Wang ◽  
Lihua Jiang ◽  
Michael P. Snyder
Keyword(s):  
Linear Regression ◽  
Robust Estimation ◽  
Population Distribution ◽  
Estimation Method ◽  
Selection Criterion ◽  
Simulation Studies ◽  
Regression Problem ◽  
Data Set ◽  
Data Adaptive ◽  
Robust Likelihood

AbstractWith the development of high-throughput RNA sequencing (RNA-seq) technology, the Genotype Tissue-Expression (GTEx) project (Consortium et al., 2015) generated a valuable resource of gene expression data from more than 11,000 samples. The large-scale data set is a powerful resource for understanding the human transcriptome. However, the technical variation, sequencing background noise and unknown factors make the statistical analysis challenging. To eliminate the possibility that outliers might affect the estimation of population distribution, we need a more robust estimation method, a method that will adapt to heterogeneous genes and further optimize the estimate for each gene. We followed the approach of the robust estimation based on γ-density-power-weight (Fujisawa and Eguchi, 2008; Windham, 1995), where γ is the exponent of density weight which controls the balance between bias and variance. As far as we know, our work is the first to propose a procedure to tune the parameter γ to balance the bias-variance trade-off under the mixture distributions. We constructed a robust likelihood criterion based on weighted densities in the mixture model of Gaussian population distribution mixed with unknown outlier distribution, and developed a data-adaptive γ-selection procedure embedded into the robust estimation. We provided a heuristic analysis on the selection criterion and found that our practical selection trend under various γ’s in average performance has similar capability to capture minimizer γ as the inestimable Mean Squared Error (MSE) trend from our simulation studies under a series of settings. Our data-adaptive robustifying procedure in the linear regression problem (AdaReg) shows a significant advantage in both simulation studies and real data application of heart samples from the GTEx project compared to the fixed γ procedure and other robust methods. This paper discusses some limitations of this method, and future work.

scholarly journals AdaTiSS: A Novel Data-Adaptive Robust Method for Quantifying Tissue Specificity Scores

2019 ◽  
Author(s):  
Meng Wang ◽  
Lihua Jiang ◽  
Michael P. Snyder
Keyword(s):  
Large Scale ◽  
Tissue Specificity ◽  
Population Distribution ◽  
Specific Gene ◽  
Robust Method ◽  
Gene Expressions ◽  
Regression Problem ◽  
Tissue Specific ◽  
Tissue Specific Gene ◽  
Data Adaptive

AbstractMotivationAccurately detecting tissue specificity (TS) in genes helps researchers understand tissue functions at the molecular level, and further identify disease mechanisms and discover tissue-specific therapeutic targets. The Genotype-Tissue Expression (GTEx) project (Consortium, 2015), and the Human Protein Atlas (HPA) project (Uhlén, et al., 2015) are two publicly available data resources, providing large-scale gene expressions across multiple tissue types. Multiple tissue comparisons, technical background noise and unknown variation factors make it challenging to accurately identify tissue specific gene expressions. Several methods worked on measuring the overall TS in gene expressions and classifying genes into tissue-enrichment categories. There still lacks a robust method to provide quantitative TS scores for each tissue.MethodsWe recognized that the key to quantify tissue specific gene expressions is to properly define a concept of expression population. We considered that inside the population, the sample expressions from various tissues are more or less balanced, and the outlier expressions outside the population may indicate tissue specificity. We then formulated the question to robustly estimate the population distribution. In a linear regression problem, we developed a novel data-adaptive robust estimation based on density-power-weight under unknown outlier distribution and non-vanishing outlier proportion (Wang, et al., 2019). In the question of quantifying TS, we focused on the Gaussian-population mixture model. We took into account gene heterogeneities and applied the robust data-adaptive procedure to estimate the population. With the robustly estimated population parameters, we constructed the AdaTiSS algorithm to obtain data-adaptive quantitative TS scores.ResultsOur TS scores from the AdaTiSS algorithm achieve the goal that the TS scores are comparable across tissues and also across genes, which standardize gene expressions in terms of TS. Compared to the categorical TS method such as the HPA criterion, our method provides more information on the population fitting, and shows advantages in quantitatively analyzing tissue specific functions, making the biology functional analysis more precise. We also discuss some limitations and possible future [email protected]

scholarly journals An Alternative Promotion Time Cure Model with Overdispersed Number of Competing Causes: An Application to Melanoma Data

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1815
Author(s):  
Diego I. Gallardo ◽  
Mário de Castro ◽  
Héctor W. Gómez
Keyword(s):  
Estimation Method ◽  
Selection Criterion ◽  
Likelihood Method ◽  
Simulation Studies ◽  
Cure Rate ◽  
Nested Models ◽  
Proposed Model ◽  
The Em Algorithm ◽  
Competing Causes ◽  
The One

A cure rate model under the competing risks setup is proposed. For the number of competing causes related to the occurrence of the event of interest, we posit the one-parameter Bell distribution, which accommodates overdispersed counts. The model is parameterized in the cure rate, which is linked to covariates. Parameter estimation is based on the maximum likelihood method. Estimates are computed via the EM algorithm. In order to compare different models, a selection criterion for non-nested models is implemented. Results from simulation studies indicate that the estimation method and the model selection criterion have a good performance. A dataset on melanoma is analyzed using the proposed model as well as some models from the literature.

scholarly journals Discussion of Identification, Estimation and Approximation of Risk under Interventions that Depend on the Natural Value of Treatment Using Observational Data, by Jessica Young, Miguel Hernán, and James Robins

2014 ◽  
Vol 3 (1) ◽  
Author(s):  
Mark J. van der Laan ◽  
Alexander R. Luedtke ◽  
Iván Díaz
Keyword(s):  
Statistical Model ◽  
Observational Data ◽  
Robust Estimation ◽  
Statistical Estimation ◽  
Estimation Problem ◽  
Target Parameter ◽  
Adaptive Parameters ◽  
The Mean ◽  
Data Adaptive ◽  
Statistical Estimation Problem

AbstractYoung, Hernán, and Robins consider the mean outcome under a dynamic intervention that may rely on the natural value of treatment. They first identify this value with a statistical target parameter, and then show that this statistical target parameter can also be identified with a causal parameter which gives the mean outcome under a stochastic intervention. The authors then describe estimation strategies for these quantities. Here we augment the authors’ insightful discussion by sharing our experiences in situations where two causal questions lead to the same statistical estimand, or the newer problem that arises in the study of data adaptive parameters, where two statistical estimands can lead to the same estimation problem. Given a statistical estimation problem, we encourage others to always use a robust estimation framework where the data generating distribution truly belongs to the statistical model. We close with a discussion of a framework which has these properties.

scholarly journals Robust Bayesian Regression with Synthetic Posterior Distributions

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 661 ◽  
Author(s):  
Shintaro Hashimoto ◽  
Shonosuke Sugasawa
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Bayesian Variable Selection ◽  
Bayesian Regression ◽  
Simulation Studies ◽  
Posterior Distributions ◽  
Linear Regression Models ◽  
Computation Algorithm ◽  
Shrinkage Priors ◽  
Variable Selection And Estimation

Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not necessarily straightforward. We here propose a Bayesian approach to robust inference on linear regression models using synthetic posterior distributions based on γ-divergence, which enables us to naturally assess the uncertainty of the estimation through the posterior distribution. We also consider the use of shrinkage priors for the regression coefficients to carry out robust Bayesian variable selection and estimation simultaneously. We develop an efficient posterior computation algorithm by adopting the Bayesian bootstrap within Gibbs sampling. The performance of the proposed method is illustrated through simulation studies and applications to famous datasets.

scholarly journals Approximating Sets of Symmetric and Positive-Definite Matrices by Geodesics

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
L. Machado ◽  
F. Silva Leite
Keyword(s):  
Linear Regression ◽  
Riemannian Manifolds ◽  
General Linear Group ◽  
Positive Definite ◽  
Positive Definite Matrices ◽  
Regression Problem ◽  
Natural Action ◽  
Normal Equations ◽  
Linear Regression Problem ◽  
Classical Linear Regression

We formulate a generalized version of the classical linear regression problem on Riemannian manifolds and derive the counterpart to the normal equations for the manifold of symmetric and positive definite matrices, equipped with the only metric that is invariant under the natural action of the general linear group.

scholarly journals Urban Population Distribution Mapping with Multisource Geospatial Data Based on Zonal Strategy

2020 ◽  
Vol 9 (11) ◽  
pp. 654
Author(s):  
Guanwei Zhao ◽  
Muzhuang Yang
Keyword(s):  
Random Forest ◽  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Population Distribution ◽  
Random Forest Model ◽  
Geospatial Data ◽  
Forest Model ◽  
Distribution Mapping ◽  
Better Than

Mapping population distribution at fine resolutions with high accuracy is crucial to urban planning and management. This paper takes Guangzhou city as the study area, illustrates the gridded population distribution map by using machine learning methods based on zoning strategy with multisource geospatial data such as night light remote sensing data, point of interest data, land use data, and so on. The street-level accuracy evaluation results show that the proposed approach achieved good overall accuracy, with determinant coefficient (R2) being 0.713 and root mean square error (RMSE) being 5512.9. Meanwhile, the goodness of fit for single linear regression (LR) model and random forest (RF) regression model are 0.0039 and 0.605, respectively. For dense area, the accuracy of the random forest model is better than the linear regression model, while for sparse area, the accuracy of the linear regression model is better than the random forest model. The results indicated that the proposed method has great potential in fine-scale population mapping. Therefore, it is advised that the zonal modeling strategy should be the primary choice for solving regional differences in the population distribution mapping research.

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