Sufficient Dimension Reduction and Modeling Responses Conditioned on Covariates: An Integrated Approach via Convex Optimization

Given observations of a collection of covariates and responses $(Y, X) \in \mathbb{R}^p \times \mathbb{R}^q$, sufficient dimension reduction (SDR) techniques aim to identify a mapping $f: \mathbb{R}^q \rightarrow \mathbb{R}^k$ with $k \ll q$ such that $Y|f(X)$ is independent of $X$. The image $f(X)$ summarizes the relevant information in a potentially large number of covariates $X$ that influence the responses $Y$. In many contemporary settings, the number of responses $p$ is also quite large, in addition to a large number $q$ of covariates. This leads to the challenge of fitting a succinctly parameterized statistical model to $Y|f(X)$, which is a problem that is usually not addressed in a traditional SDR framework. In this paper, we present a computationally tractable convex relaxation based estimator for simultaneously (a) identifying a linear dimension reduction $f(X)$ of the covariates that is sufficient with respect to the responses, and (b) fitting several types of structured low-dimensional models -- factor models, graphical models, latent-variable graphical models -- to the conditional distribution of $Y|f(X)$. We analyze the consistency properties of our estimator in a high-dimensional scaling regime. We also illustrate the performance of our approach on a newsgroup dataset and on a dataset consisting of financial asset prices.Comment: 34 pages, 1 figur

Multiple Quantitative Trait Analysis Using Bayesian Networks

Models for genome-wide prediction and association studies usually target a single phenotypic trait. However, in animal and plant genetics it is common to record information on multiple phenotypes for each individual that will be genotyped. Modeling traits individually disregards the fact that they are most likely associated due to pleiotropy and shared biological basis, thus providing only a partial, confounded view of genetic effects and phenotypic interactions. In this paper we use data from a Multiparent Advanced Generation Inter-Cross (MAGIC) winter wheat population to explore Bayesian networks as a convenient and interpretable framework for the simultaneous modeling of multiple quantitative traits. We show that they are equivalent to multivariate genetic best linear unbiased prediction (GBLUP), and that they are competitive with single-trait elastic net and single-trait GBLUP in predictive performance. Finally, we discuss their relationship with other additive-effects models and their advantages in inference and interpretation. MAGIC populations provide an ideal setting for this kind of investigation because the very low population structure and large sample size result in predictive models with good power and limited confounding due to relatedness.Comment: 28 pages, 1 figure, code at http://www.bnlearn.com/research/genetics1

Data-driven modelling of biological multi-scale processes

Biological processes involve a variety of spatial and temporal scales. A holistic understanding of many biological processes therefore requires multi-scale models which capture the relevant properties on all these scales. In this manuscript we review mathematical modelling approaches used to describe the individual spatial scales and how they are integrated into holistic models. We discuss the relation between spatial and temporal scales and the implication of that on multi-scale modelling. Based upon this overview over state-of-the-art modelling approaches, we formulate key challenges in mathematical and computational modelling of biological multi-scale and multi-physics processes. In particular, we considered the availability of analysis tools for multi-scale models and model-based multi-scale data integration. We provide a compact review of methods for model-based data integration and model-based hypothesis testing. Furthermore, novel approaches and recent trends are discussed, including computation time reduction using reduced order and surrogate models, which contribute to the solution of inference problems. We conclude the manuscript by providing a few ideas for the development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and Multiscale Dynamics (American Scientific Publishers

Explainable Anatomical Shape Analysis through Deep Hierarchical Generative Models

Quantification of anatomical shape changes currently relies on scalar global indexes which are largely insensitive to regional or asymmetric modifications. Accurate assessment of pathology-driven anatomical remodeling is a crucial step for the diagnosis and treatment of many conditions. Deep learning approaches have recently achieved wide success in the analysis of medical images, but they lack interpretability in the feature extraction and decision processes. In this work, we propose a new interpretable deep learning model for shape analysis. In particular, we exploit deep generative networks to model a population of anatomical segmentations through a hierarchy of conditional latent variables. At the highest level of this hierarchy, a two-dimensional latent space is simultaneously optimised to discriminate distinct clinical conditions, enabling the direct visualisation of the classification space. Moreover, the anatomical variability encoded by this discriminative latent space can be visualised in the segmentation space thanks to the generative properties of the model, making the classification task transparent. This approach yielded high accuracy in the categorisation of healthy and remodelled left ventricles when tested on unseen segmentations from our own multi-centre dataset as well as in an external validation set, and on hippocampi from healthy controls and patients with Alzheimer's disease when tested on ADNI data. More importantly, it enabled the visualisation in three-dimensions of both global and regional anatomical features which better discriminate between the conditions under exam. The proposed approach scales effectively to large populations, facilitating high-throughput analysis of normal anatomy and pathology in large-scale studies of volumetric imaging

SAFS: A Deep Feature Selection Approach for Precision Medicine

In this paper, we propose a new deep feature selection method based on deep architecture. Our method uses stacked auto-encoders for feature representation in higher-level abstraction. We developed and applied a novel feature learning approach to a specific precision medicine problem, which focuses on assessing and prioritizing risk factors for hypertension (HTN) in a vulnerable demographic subgroup (African-American). Our approach is to use deep learning to identify significant risk factors affecting left ventricular mass indexed to body surface area (LVMI) as an indicator of heart damage risk. The results show that our feature learning and representation approach leads to better results in comparison with others

Statistical Methods in Intensive Care Online Monitoring

Intelligent alarm systems are needed for adequate bedside decision support in critical care. Clinical information systems acquire physiological variables online in short time intervals. To identify complications as well as therapeutic effects procedures for rapid classiffication of the current state of the patient have to be developed. Detection of characteristic patterns in the data can be accomplished by statistical time series analysis. In view of the high dimension of the data statistical methods for dimension reduction should be used in advance. We discuss the potential of statistical techniques for online monitoring

Posttraumatic stress disorder and psychophysiological reactivity in female assault survivors: testing the moderating effects of internalizing and externalizing latent dimensions of psychopathology

This study examined individual variability in the strength of association between psychophysiological reactivity to trauma cues and clinician-rated PTSD symptoms in a sample of female survivors of sexual and non-sexual assault. PTSD is a heterogeneous disorder, and individual differences in symptom presentation and accompanying comorbidities may be accounted for by internalizing and externalizing latent temperament-based dimensions of psychopathology. The present study proposed that these dimensions may also account for heterogeneity in the association between psychophysiological reactivity and PTSD. Prior research has demonstrated that most individuals with PTSD display elevated psychophysiological reactivity when exposed to trauma reminders, although some do not. As well, research has shown that externalizing pathologies are typically associated with diminished psychophysiological reactivity to aversive cues whereas internalizing pathologies are associated with elevated psychophysiological reactivity. This study therefore employed structural equation modeling to test hypotheses that externalizing and internalizing pathologies would display mitigating and enhancing moderator effects, respectively, on the prediction of PTSD by psychophysiological reactivity. To that end, confirmatory factor analysis first established a viable internalizing and externalizing model based on an array of clinical measures in one participant subgroup (n = 329) and then affirmed the reliability of the model in a second subgroup (n = 245). Structural equation modeling in the latter subgroup, in which PTSD was regressed on Internalizing, Externalizing, and Psychophysiological Reactivity factors as well as Internalizing by Psychophysiological Reactivity and Externalizing by Psychophysiological Reactivity moderator terms, revealed a significant moderator effect for externalizing but not internalizing pathology. However, the nature of the externalizing moderator effect differed from the hypothesized direction, with higher levels of externalizing pathology strengthening the association between PTSD and psychophysiological reactivity rather than weakening it. It therefore appears that variability in the association between PTSD and psychophysiological reactivity may be partially accounted for by individual differences in the externalizing dimension of psychopathology. As well, the psychophysiology of the externalizing dimension may also be marked by heterogeneity, with externalizing pathology being linked with increased rather than decreased psychophysiological reactivity among women who have experienced sexual or non-sexual assault

Disentangling causal webs in the brain using functional Magnetic Resonance Imaging: A review of current approaches

In the past two decades, functional Magnetic Resonance Imaging has been used to relate neuronal network activity to cognitive processing and behaviour. Recently this approach has been augmented by algorithms that allow us to infer causal links between component populations of neuronal networks. Multiple inference procedures have been proposed to approach this research question but so far, each method has limitations when it comes to establishing whole-brain connectivity patterns. In this work, we discuss eight ways to infer causality in fMRI research: Bayesian Nets, Dynamical Causal Modelling, Granger Causality, Likelihood Ratios, LiNGAM, Patel's Tau, Structural Equation Modelling, and Transfer Entropy. We finish with formulating some recommendations for the future directions in this area