Cluster weighted models for functional data

ABSTRACTThe aim of this article is to develop a novel class of functional structural equation models (FSEMs) for dissecting functional genetic and environmental effects on twin functional data, while characterizing the varying association between functional data and covariates of interest. We propose a three-stage estimation procedure to estimate varying coefficient functions for various covariates (e.g., gender) as well as three covariance operators for the genetic and environmental effects. We develop an inference procedure based on weighted likelihood ratio statistics to test the genetic/environmental effect at either a fixed location or a compact region. We also systematically carry out the theoretical analysis of the estimated varying functions, the weighted likelihood ratio statistics, and the estimated covariance operators. We conduct extensive Monte Carlo simulations to examine the finite-sample performance of the estimation and inference procedures. We apply the proposed FSEM to quantify the degree of genetic and environmental effects on twin white matter tracts obtained from the UNC early brain development study. Supplementary materials for this article are available online.

The aim of this paper is to extend the ideas of generalized additive models for multivariate data (with known or unknown link function) to functional data covariates. The proposed algorithmis a modified version of the local scoring and backfitting algorithms that allows for the non-parametric estimation of the link function. This algorithm would be applied to predict a binary response example.

BackgroundThe RDF triple provides a simple linguistic means of describing limitless types of information. Triples can be flexibly combined into a unified data source we call a semantic model. Semantic models open new possibilities for the integration of variegated biological data. We use Semantic Web technology to explicate high throughput clinical data in the context of fundamental biological knowledge. We have extended Corvus, a data warehouse which provides a uniform interface to various forms of Omics data, by providing a SPARQL endpoint. With the querying and reasoning tools made possible by the Semantic Web, we were able to explore quantitative semantic models retrieved from Corvus in the light of systematic biological knowledge.ResultsFor this paper, we merged semantic models containing genomic, transcriptomic and epigenomic data from melanoma samples with two semantic models of functional data - one containing Gene Ontology (GO) data, the other, regulatory networks constructed from transcription factor binding information. These two semantic models were created in an ad hoc manner but support a common interface for integration with the quantitative semantic models. Such combined semantic models allow us to pose significant translational medicine questions. Here, we study the interplay between a cell's molecular state and its response to anti-cancer therapy by exploring the resistance of cancer cells to Decitabine, a demethylating agent.ConclusionsWe were able to generate a testable hypothesis to explain how Decitabine fights cancer - namely, that it targets apoptosis-related gene promoters predominantly in Decitabine-sensitive cell lines, thus conveying its cytotoxic effect by activating the apoptosis pathway. Our research provides a framework whereby similar hypotheses can be developed easily.

Surface functional models

We consider modeling and analysis of functional data arising in method comparison studies. The observed data consist of repeated measurements of a continuous variable obtained using multiple methods of measurement on a sample of subjects. The data are treated as multivariate functional data that are observed with noise at a common set of discrete time points which may vary from subject to subject. The proposed methodology uses functional principal components analysis within the framework of a mixed-effects model to represent the observations in terms of a small number of method-specific principal components. Two approaches for estimating the unknowns in the model, both adaptations of general techniques developed for multivariate functional principal components analysis, are presented. Bootstrapping is employed to get estimates of bias and covariance matrix of model parameter estimates. These in turn are used to compute confidence intervals for parameters and functions thereof, such as the measures of similarity and agreement between the measurement methods, that are necessary for data analysis. The estimation approaches are evaluated using simulation. The methodology is illustrated by analyzing two datasets.

An important goal in medical research is to identify groups of subjects characterized with a particular trait or quality and to distinguish them from other subjects in a clinically relevant way. Measures of biological phenomena, in general, and of psychiatric conditions, in particular, often exhibit symmetric shapes resembling a normal distribution; yet, the statistical approaches predominantly applied have been based on an assumption of underlying categories, whether observed or latent. It is well known that members of homogeneous populations with symmetric (multivariate) unimodal distributions can exhibit very distinct characteristics. Tarpey (2007a) and For example, guidelines for treatment for depression would require the identification of a cut off on a given depression measure, whether or not the measure exhibits evidence for distinct clusters or mixtures.

Functional data capture a wide range of processes, including growth curves and spectral absorption patterns. In this study, we analyse air pollution data from the In-service Aircraft for a Global Observing System, focusing on the spatial interactions among atmospheric chemicals and their dependence on meteorological conditions. This analysis necessitates functional regression, where both response and covariates are functional objects evolving throughout the troposphere. Quantifying both the functional dependencies between the response and covariates and the interdependencies among multivariate response functions poses significant challenges. To address these challenges, we introduce a functional Gaussian graphical regression model, which extends conditional Gaussian graphical models to partially separable functional data. We propose a doubly penalized estimator for model inference and develop a novel adaptation of Kullback–Leibler cross-validation, specifically tailored for graphical estimators. This criterion, named joint Kullback–Leibler cross-validation, simultaneously accounts for both precision and regression matrices, particularly in scenarios where the population comprises multiple sub-groups. Model performance is evaluated in terms of Kullback–Leibler divergence and graph recovery power.

ABSTRACTSparsity-inducing penalties are useful tools for variable selection and are also effective for regression problems where the data are functions. We consider the problem of selecting not only variables but also decision boundaries in multiclass logistic regression models for functional data, using sparse regularization. The parameters of the functional logistic regression model are estimated in the framework of the penalized likelihood method with the sparse group lasso-type penalty, and then tuning parameters for the model are selected using the model selection criterion. The effectiveness of the proposed method is investigated through simulation studies and the analysis of a gene expression data set.

Regression models for functional data by reproducing kernel Hilbert spaces methods

We are developing a multi-database architecture to provide integrated access to heterogeneous, distributed databases. The work described here is motivated by the desire to have RDF/RDFS collections as component data resources in this system, along with relational and other databases. To achieve this, the RDF/RDFS collection, like all other component resources in the system, is mapped to the functional data model, and a query translator is implemented that can translate queries originally expressed in Daplex (the query language associated with the functional data model) into SPARQL. SPARQL is the prominent query language for RDF and it is used here to bridge between the functional data model and the Semantic Web.KeywordsResource Description FrameworkQuery LanguageResource Description Framework DataResource Description Framework GraphQuery TranslationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Improving diagnostic accuracy of obsessive-compulsive disorder (OCD) using models of brain imaging data is a key goal of the field, but this objective is challenging due to the limited size and phenotypic depth of clinical datasets. Leveraging the phenotypic diversity in large non-clinical datasets such as the UK Biobank (UKBB), offers a potential solution to this problem. Nevertheless, it remains unclear whether classification models trained on non-clinical populations will generalise to individuals with clinical OCD. This question is also relevant for the conceptualisation of OCD; specifically, whether the symptomology of OCD exists on a continuum from normal to pathological. Here, we examined a recently published "meta-matching" model trained on functional connectivity data from five large normative datasets (N = 45,507) to predict cognitive, health and demographic variables. Specifically, we tested whether this model could classify OCD status in three independent datasets (N = 345). We found that the model could identify out-of-sample OCD individuals. Notably, the most predictive functional connectivity features mapped onto known cortico-striatal abnormalities in OCD and correlated with genetic brain expression maps previously implicated in the disorder. Further, the meta-matching model relied upon estimates of cognitive functions, such as cognitive flexibility and inhibition, to successfully predict OCD. These findings suggest that variability in non-clinical brain and behavioural features can discriminate clinical OCD status. These results support a dimensional and transdiagnostic conceptualisation of the brain and behavioural basis of OCD, with implications for research approaches and treatment targets.

In order to analyze intensive longitudinal data collected across multiple individuals, researchers frequently have to decide between aggregating all individuals or analyzing each individual separately. This paper presents an R package, gimme, which allows for the automatic specification of individual-level structural equation models that combine group-, subgroup-, and individual-level information. This R package is a complement of the GIMME program currently available via a combination of MATLAB and LISREL. By capitalizing on the flexibility of R and the capabilities of the existing structural equation modeling package lavaan, gimme allows for the automated specification and estimation of group-, subgroup-, and individual-level relations in time series data from within a structural equation modeling framework. Applications include daily diary data as well as functional magnetic resonance imaging data.

Functional magnetic resonance imaging (fMRI), a noninvasive neuroimaging method that provides an indirect measure of neuronal activity by detecting blood flow changes, has experienced an explosive growth in the past years. Statistical methods play a crucial role in understanding and analyzing fMRI data. Bayesian approaches, in particular, have shown great promise in applications. A remarkable feature of fully Bayesian approaches is that they allow a flexible modeling of spatial and temporal correlations in the data. This paper provides a review of the most relevant models developed in recent years. We divide methods according to the objective of the analysis. We start from spatio-temporal models for fMRI data that detect task-related activation patterns. We then address the very important problem of estimating brain connectivity. We also touch upon methods that focus on making predictions of an individual's brain activity or a clinical or behavioral response. We conclude with a discussion of recent integrative models that aim at combining fMRI data with other imaging modalities, such as EEG/MEG and DTI data, measured on the same subjects. We also briefly discuss the emerging field of imaging genetics.

Multinomial choice models are fundamental for empirical modeling of economic choices among discrete alternatives. We analyze identification of binary and multinomial choice models when the choice utilities are nonseparable in observed attributes and multidimensional unobserved heterogeneity with cross-section and panel data. We show that derivatives of choice probabilities with respect to continuous attributes are weighted averages of utility derivatives in cross-section models with exogenous heterogeneity. In the special case of random coefficient models with an independent additive effect, we further characterize that the probability derivative at zero is proportional to the population mean of the coefficients. We extend the identification results to models with endogenous heterogeneity using either a control function or panel data. In time stationary panel models with two periods, we find that differences over time of derivatives of choice probabilities identify utility derivatives "on the diagonal," i.e. when the observed attributes take the same values in the two periods. We also show that time stationarity does not identify structural derivatives "off the diagonal" both in continuous and multinomial choice panel models.

We are at the crossroads of human history where data are becoming the new currency. Artificial intelligence, big data and cloud technologies are powering insightful realizations about almost every aspect of our lives, allowing us to get a richer and more informed sense of ourselves. Virtually everything we do generates data, and disease is not an exception. Electronic health records capture a detailed and unique description of a cancer, useful properties such as response to therapy or risk of relapse are the currency of molecular tumor boards. Cancer patients are systematically screened at the clinic for a myriad of molecular information from which decisions are taken regarding the best therapeutic options available. Integrating these molecular profiles with other clinical data requires computational predictive models developed from EHRs which integrated with AI models of gene function and big data from multi-omics analysis are paving the way to new exciting opportunities in precision oncology.