Of late, high-throughput microarray and sequencing data have been extensively used to monitor biomarkers and biological processes related to many diseases. Under this circumstance, the support vector ...machine (SVM) has been popularly used and been successful for gene selection in many applications. Despite surpassing benefits of the SVMs, single data analysis using small- and mid-size of data inevitably runs into the problem of low reproducibility and statistical power. To address this problem, we propose a meta-analytic support vector machine (Meta-SVM) that can accommodate multiple omics data, making it possible to detect consensus genes associated with diseases across studies.
Experimental studies show that the Meta-SVM is superior to the existing meta-analysis method in detecting true signal genes. In real data applications, diverse omics data of breast cancer (TCGA) and mRNA expression data of lung disease (idiopathic pulmonary fibrosis; IPF) were applied. As a result, we identified gene sets consistently associated with the diseases across studies. In particular, the ascertained gene set of TCGA omics data was found to be significantly enriched in the ABC transporters pathways well known as critical for the breast cancer mechanism.
The Meta-SVM effectively achieves the purpose of meta-analysis as jointly leveraging multiple omics data, and facilitates identifying potential biomarkers and elucidating the disease process.
In this study, we focus on the estimation of the regression function in the single-index model based on B-splines using penalization techniques. We adopt a spherical coordinates reparameterization of ...an index vector to deal with an identification problem of the single-index model. To provide a spatially adaptive method, two types of penalties are applied to the estimation of the index vector and the regression function. A special penalty called the localized penalty is introduced to handle the sparsity of the index vector using the spherical coordinates, and the total variation penalty is considered to deal with the smoothing function. Using a coordinate descent algorithm with a grid search of the two tuning parameters, the entire solution paths of the index coefficients and the regression functions for tuning parameters can be obtained efficiently. The performance of the proposed estimator is studied through both numerical simulations and real data sets. An R software package pbssim is available.
This study examines a penalized additive regression spline estimator with total variation and non negative garrote-type penalties. The proposed estimator is obtained based on a two-stage procedure. ...In the first stage, an initial estimator is obtained via total variation penalization. The total variation penalty enables data-adaptive knot selection and regularizes the overall smoothness of the estimator. The second stage imposes the non negative garrote penalty on the estimated functional components to attain variable selectivity. Regarding the theoretical aspect, a non asymptotic oracle inequality for the total variation penalized estimator is established under some regularity conditions. Based on the oracle inequality, we prove that the estimator attains the optimal rate of convergence up to a logarithmic factor, which in turn leads to the selection and estimation consistency of the second-stage garrote estimator. Numerical studies are presented to illustrate the usefulness of a combination of these two penalties. The results show that the proposed method outperforms existing methods.
We conducted a study on a regression spline estimator with a few pre-specified auxiliary variables. For the implementation of the proposed estimators, we adapted a coordinate descent algorithm. This ...was implemented by considering a structure of the sum of the residuals squared objective function determined by the B-spline and the auxiliary coeffcients. We also considered an effcient stepwise knot selection algorithm based on the Bayesian information criterion. This was to adaptively select smoothly functioning estimator data. Numerical studies using both simulated and real data sets were conducted to illustrate the proposed method’s performance. An R software package psav is available.
We consider the problem of simultaneously estimating a finite number of quantile functions with B-splines and the total variation penalty. For the implementation of simultaneous quantile function ...estimators, we develop a new coordinate descent algorithm taking into account a special structure of the total variation penalty determined by B-spline coefficients. The entire paths of solution paths for several quantile function estimators and tuning parameters can be efficiently computed using the coordinate descent algorithm. We also consider non-crossing quantile function estimators having additional constraints at the knots of spline functions. Numerical studies using both simulated and real data sets are provided to illustrate the performance of the proposed method. For a theoretical result, we prove that the proposed the quantile regression function estimators achieve the minimax rate under regularity conditions.
We consider a function estimation method with change point detection using truncated power spline basis and elastic-net-type L1-norm penalty. The L1-norm penalty controls the jump detection and ...smoothness depending on the value of the parameter. In terms of the proposed estimators, we introduce two computational algorithms for the Lagrangian dual problem (coordinate descent algorithm) and constrained convex optimization problem (an algorithm based on quadratic programming). Subsequently, we investigate the relationship between the two algorithms and compare them. Using both simulation and real data analysis, numerical studies are conducted to validate the performance of the proposed method.
Celotno besedilo
Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
In this article, we present a penalized log-density estimation method using Legendre polynomials with
penalty to adjust estimate's smoothness. Re-expressing the logarithm of the density estimator via ...a linear combination of Legendre polynomials, we can estimate parameters by maximizing the penalized log-likelihood function. Besides, we proposed an implementation strategy that builds on the coordinate decent algorithm, together with the Bayesian information criterion (BIC). In particular, we derive a numerical solution to the maximum tuning parameter
which leads to all zero coefficients and practically facilitates searching the optimal tuning parameter. Extensive simulation studies clearly show that our proposed estimator is computationally competitive with other existing nonparametric density estimators (e.g., kernel, kernel smooth and logspline estimators) benchmarked by the mean integrated squared errors (MISE) and the mean integrated absolute error (MIAE) under the experiment scenario of separated bimodal models in regard to the true density function. With an application to Old Faithful geyser data, our proposed method is found to effectively perform density estimation.
We propose a penalized regression spline estimator for monotone regression. To construct the estimator, we adopt the I-splines with the total variation penalty. The I-splines lend themselves to the ...monotonicity because of the simpler form of restrictions, and the total variation penalty induces a data-driven knot selection scheme. A coordinate descent algorithm is developed for the estimator. If the number of complexity parameter candidates sufficiently increases, the algorithm considers all possible monotone linear spline fits to the given data. The pruning process of the algorithm not only provides numerical stability, but also implements the data-driven knot selection. We also compute the maximum candidate of the complexity parameter to facilitate complexity parameter selection. Extensive numerical studies show that the proposed estimator captures spatially inhomogeneous behaviors of data, such as sudden jumps.
We study a penalized logspline density estimation method using a total variation penalty. The B-spline basis is adopted to approximate the logarithm of density functions. Total variation of ...derivatives of splines is penalized to impart a data-driven knot selection. The proposed estimator is a bona fide density function in the sense that it is positive and integrates to one. We devise an efficient coordinate descent algorithm for implementation and study its convergence property. An oracle inequality of the proposed estimator is established when the quality of fit is measured by the Kullback–Leibler divergence. Based on the oracle inequality, it is proved that the estimator achieves an optimal rate of convergence in the minimax sense. We also propose a logspline method for the bivariate case by adopting the tensor-product B-spline basis and a two-dimensional total variation type penalty. Numerical studies show that the proposed method captures local features without compromising the global smoothness.
We carry out a study on a penalized regression spline estimator with total variation penalty. In order to provide a spatially adaptive method, we consider total variation penalty for the estimating ...regression function. This paper adopts B-splines for both numerical implementation and asymptotic analysis because they have small supports, so the information matrices are sparse and banded. Once we express the estimator with a linear combination of B-splines, the coefficients are estimated by minimizing a penalized residual sum of squares. A new coordinate descent algorithm is introduced to handle total variation penalty determined by the B-spline coefficients. For large-sample inference, a nonasymptotic oracle inequality for penalized B-spline estimators is obtained. The oracle inequality is then used to show that the estimator is an optimal adaptive for the estimation of the regression function up to a logarithm factor.
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