Dataset Information

Wavelet-Based Scalar-on-Function Finite Mixture Regression Models.

ABSTRACT: Classical finite mixture regression is useful for modeling the relationship between scalar predictors and scalar responses arising from subpopulations defined by the di ering associations between those predictors and responses. The classical finite mixture regression model is extended to incorporate functional predictors by taking a wavelet-based approach in which both the functional predictors and the component-specific coefficient functions are represented in terms of an appropriate wavelet basis. By using the wavelet representation of the model, the coefficients corresponding to the functional covariates become the predictors. In this setting, there are typically many more predictors than observations. Hence a lasso-type penalization is employed to simultaneously perform feature selection and estimation. Specification of the model is discussed and a fitting algorithm is provided. The wavelet-based approach is evaluated on synthetic data as well as applied to a real data set from a study of the relationship between cognitive ability and di usion tensor imaging measures in subjects with multiple sclerosis.

SUBMITTER: Ciarleglio A

PROVIDER: S-EPMC4620087 | biostudies-literature | 2016 Jan

REPOSITORIES: biostudies-literature

ACCESS DATA

Publications

Wavelet-Based Scalar-on-Function Finite Mixture Regression Models.

Ciarleglio Adam A Ogden R Todd RT

Computational statistics & data analysis 20141217

Classical finite mixture regression is useful for modeling the relationship between scalar predictors and scalar responses arising from subpopulations defined by the di ering associations between those predictors and responses. The classical finite mixture regression model is extended to incorporate functional predictors by taking a wavelet-based approach in which both the functional predictors and the component-specific coefficient functions are represented in terms of an appropriate wavelet ba ...[more]

PMID: 26512156

Similar Datasets

Project description:Radiomics involves the study of tumor images to identify quantitative markers explaining cancer heterogeneity. The predominant approach is to extract hundreds to thousands of image features, including histogram features comprised of summaries of the marginal distribution of pixel intensities, which leads to multiple testing problems and can miss out on insights not contained in the selected features. In this paper, we present methods to model the entire marginal distribution of pixel intensities via the quantile function as functional data, regressed on a set of demographic, clinical, and genetic predictors to investigate their effects of imaging-based cancer heterogeneity. We call this approach quantile functional regression, regressing subject-specific marginal distributions across repeated measurements on a set of covariates, allowing us to assess which covariates are associated with the distribution in a global sense, as well as to identify distributional features characterizing these differences, including mean, variance, skewness, heavy-tailedness, and various upper and lower quantiles. To account for smoothness in the quantile functions, account for intrafunctional correlation, and gain statistical power, we introduce custom basis functions we call quantlets that are sparse, regularized, near-lossless, and empirically defined, adapting to the features of a given data set and containing a Gaussian subspace so non-Gaussianness can be assessed. We fit this model using a Bayesian framework that uses nonlinear shrinkage of quantlet coefficients to regularize the functional regression coefficients and provides fully Bayesian inference after fitting a Markov chain Monte Carlo. We demonstrate the benefit of the basis space modeling through simulation studies, and apply the method to Magnetic resonance imaging (MRI) based radiomic dataset from Glioblastoma Multiforme to relate imaging-based quantile functions to various demographic, clinical, and genetic predictors, finding specific differences in tumor pixel intensity distribution between males and females and between tumors with and without DDIT3 mutations.

Dataset Information

Wavelet-Based Scalar-on-Function Finite Mixture Regression Models.

Publications

Wavelet-Based Scalar-on-Function Finite Mixture Regression Models.

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure

Tweets