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An increasing array of biomedical and computer vision applications requires the predictive modeling of complex data, for example images and shapes. The main challenge when predicting such objects lies in the fact that they do not comply to the assumptions of Euclidean geometry. Rather, they occupy non-linear spaces, a.k.a. manifolds, where it is difficult to define concepts such as coordinates, vectors and expected values. In this work, we construct a non-parametric predictive methodology for manifold-valued objects, based on a distance modification of the Random Forest algorithm. Our method is versatile and can be applied both in cases where the response space is a well-defined manifold, but also when such knowledge is not available. Model fitting and prediction phases only require the definition of a suitable distance function for the observed responses. We validate our methodology using simulations and apply it on a series of illustrative image completion applications, showcasing superior predictive performance, compared to various established regression methods., Comment: 10 pages, 4 figures

X-rays are commonly performed imaging tests that use small amounts of radiation to produce pictures of the organs, tissues, and bones of the body. X-rays of the chest are used to detect abnormalities or diseases of the airways, blood vessels, bones, heart, and lungs. In this work we present a stochastic attention-based model that is capable of learning what regions within a chest X-ray scan should be visually explored in order to conclude that the scan contains a specific radiological abnormality. The proposed model is a recurrent neural network (RNN) that learns to sequentially sample the entire X-ray and focus only on informative areas that are likely to contain the relevant information. We report on experiments carried out with more than $100,000$ X-rays containing enlarged hearts or medical devices. The model has been trained using reinforcement learning methods to learn task-specific policies., Comment: NIPS 2016 Workshop on Machine Learning for Health

Machine learning analysis of neuroimaging data can accurately predict chronological age in healthy people and deviations from healthy brain ageing have been associated with cognitive impairment and disease. Here we sought to further establish the credentials of "brain-predicted age" as a biomarker of individual differences in the brain ageing process, using a predictive modelling approach based on deep learning, and specifically convolutional neural networks (CNN), and applied to both pre-processed and raw T1-weighted MRI data. Firstly, we aimed to demonstrate the accuracy of CNN brain-predicted age using a large dataset of healthy adults (N = 2001). Next, we sought to establish the heritability of brain-predicted age using a sample of monozygotic and dizygotic female twins (N = 62). Thirdly, we examined the test-retest and multi-centre reliability of brain-predicted age using two samples (within-scanner N = 20; between-scanner N = 11). CNN brain-predicted ages were generated and compared to a Gaussian Process Regression (GPR) approach, on all datasets. Input data were grey matter (GM) or white matter (WM) volumetric maps generated by Statistical Parametric Mapping (SPM) or raw data. Brain-predicted age represents an accurate, highly reliable and genetically-valid phenotype, that has potential to be used as a biomarker of brain ageing. Moreover, age predictions can be accurately generated on raw T1-MRI data, substantially reducing computation time for novel data, bringing the process closer to giving real-time information on brain health in clinical settings.

Large scale, streaming datasets are ubiquitous in modern machine learning. Streaming algorithms must be scalable, amenable to incremental training and robust to the presence of non-stationarity. In this work consider the problem of learning $\ell_1$ regularized linear models in the context of streaming data. In particular, the focus of this work revolves around how to select the regularization parameter when data arrives sequentially and the underlying distribution is non-stationary (implying the choice of optimal regularization parameter is itself time-varying). We propose a framework through which to infer an adaptive regularization parameter. Our approach employs an $\ell_1$ penalty constraint where the corresponding sparsity parameter is iteratively updated via stochastic gradient descent. This serves to reformulate the choice of regularization parameter in a principled framework for online learning. The proposed method is derived for linear regression and subsequently extended to generalized linear models. We validate our approach using simulated and real datasets and present an application to a neuroimaging dataset., Comment: 20 pages, 3 figures. arXiv admin note: text overlap with arXiv:1511.02187

Characterizing the transcriptome architecture of the human brain is fundamental in gaining an understanding of brain function and disease. A number of recent studies have investigated patterns of brain gene expression obtained from an extensive anatomical coverage across the entire human brain using experimental data generated by the Allen Human Brain Atlas (AHBA) project. In this paper, we propose a new representation of a gene's transcription activity that explicitly captures the pattern of spatial co-expression across different anatomical brain regions. For each gene, we define a Spatial Expression Network (SEN), a network quantifying co-expression patterns amongst several anatomical locations. Network similarity measures are then employed to quantify the topological resemblance between pairs of SENs and identify naturally occurring clusters. Using network-theoretical measures, three large clusters have been detected featuring distinct topological properties. We then evaluate whether topological diversity of the SENs reflects significant differences in biological function through a gene ontology analysis. We report on evidence suggesting that one of the three SEN clusters consists of genes specifically involved in the nervous system, including genes related to brain disorders, while the remaining two clusters are representative of immunity, transcription and translation. These findings are consistent with previous studies showing that brain gene clusters are generally associated with one of these three major biological processes., Comment: 8 pages, 4 figures, 2 tables, conference

Computed tomography (CT) generates a stack of cross-sectional images covering a region of the body. The visual assessment of these images for the identification of potential abnormalities is a challenging and time consuming task due to the large amount of information that needs to be processed. In this article we propose a deep artificial neural network architecture, ReCTnet, for the fully-automated detection of pulmonary nodules in CT scans. The architecture learns to distinguish nodules and normal structures at the pixel level and generates three-dimensional probability maps highlighting areas that are likely to harbour the objects of interest. Convolutional and recurrent layers are combined to learn expressive image representations exploiting the spatial dependencies across axial slices. We demonstrate that leveraging intra-slice dependencies substantially increases the sensitivity to detect pulmonary nodules without inflating the false positive rate. On the publicly available LIDC/IDRI dataset consisting of 1,018 annotated CT scans, ReCTnet reaches a detection sensitivity of 90.5% with an average of 4.5 false positives per scan. Comparisons with a competing multi-channel convolutional neural network for multi-slice segmentation and other published methodologies using the same dataset provide evidence that ReCTnet offers significant performance gains.

Motivated by the need to automate medical information extraction from free-text radiological reports, we present a bi-directional long short-term memory (BiLSTM) neural network architecture for modelling radiological language. The model has been used to address two NLP tasks: medical named-entity recognition (NER) and negation detection. We investigate whether learning several types of word embeddings improves BiLSTM's performance on those tasks. Using a large dataset of chest x-ray reports, we compare the proposed model to a baseline dictionary-based NER system and a negation detection system that leverages the hand-crafted rules of the NegEx algorithm and the grammatical relations obtained from the Stanford Dependency Parser. Compared to these more traditional rule-based systems, we argue that BiLSTM offers a strong alternative for both our tasks., Comment: LOUHI 2016 conference proceedings

The human face is a complex trait under strong genetic control, as evidenced by the striking visual similarity between twins. Nevertheless, heritability estimates of facial traits have often been surprisingly low or difficult to replicate. Furthermore, the construction of facial phenotypes that correspond to naturally perceived facial features remains largely a mystery. We present here a large-scale heritability study of face geometry that aims to address these issues. High-resolution, three-dimensional facial models have been acquired on a cohort of $952$ twins recruited from the TwinsUK registry, and processed through a novel landmarking workflow, GESSA (Geodesic Ensemble Surface Sampling Algorithm). The algorithm places thousands of landmarks throughout the facial surface and automatically establishes point-wise correspondence across faces. These landmarks enabled us to intuitively characterize facial geometry at a fine level of detail through curvature measurements, yielding accurate heritability maps of the human face (www.heritabilitymaps.info)., Comment: 21 pages, 5 figures Updated content

In cardiac magnetic resonance imaging, fully-automatic segmentation of the heart enables precise structural and functional measurements to be taken, e.g. from short-axis MR images of the left-ventricle. In this work we propose a recurrent fully-convolutional network (RFCN) that learns image representations from the full stack of 2D slices and has the ability to leverage inter-slice spatial dependences through internal memory units. RFCN combines anatomical detection and segmentation into a single architecture that is trained end-to-end thus significantly reducing computational time, simplifying the segmentation pipeline, and potentially enabling real-time applications. We report on an investigation of RFCN using two datasets, including the publicly available MICCAI 2009 Challenge dataset. Comparisons have been carried out between fully convolutional networks and deep restricted Boltzmann machines, including a recurrent version that leverages inter-slice spatial correlation. Our studies suggest that RFCN produces state-of-the-art results and can substantially improve the delineation of contours near the apex of the heart., Comment: MICCAI Workshop RAMBO 2016

Men and women differ in specific cognitive abilities and in the expression of several neuropsychiatric conditions. Such findings could be attributed to sex hormones, brain differences, as well as a number of environmental variables. Existing research on identifying sex-related differences in brain structure have predominantly used cross-sectional studies to investigate, for instance, differences in average gray matter volumes (GMVs). In this article we explore the potential of a recently proposed multi-view matrix factorisation (MVMF) methodology to study structural brain changes in men and women that occur from adolescence to adulthood. MVMF is a multivariate variance decomposition technique that extends principal component analysis to "multi-view" datasets, i.e. where multiple and related groups of observations are available. In this application, each view represents a different age group. MVMF identifies latent factors explaining shared and age-specific contributions to the observed overall variability in GMVs over time. These latent factors can be used to produce low-dimensional visualisations of the data that emphasise age-specific effects once the shared effects have been accounted for. The analysis of two datasets consisting of individuals born prematurely as well as healthy controls provides evidence to suggest that the separation between males and females becomes increasingly larger as the brain transitions from adolescence to adulthood. We report on specific brain regions associated to these variance effects., Comment: Submitted to the 6th International Workshop on Pattern Recognition in Neuroimaging (PRNI)

Non-invasive brain stimulation, such as transcranial alternating current stimulation (tACS) provides a powerful tool to directly modulate brain oscillations that mediate complex cognitive processes. While the body of evidence about the effect of tACS on behavioral and cognitive performance is constantly growing, those studies fail to address the importance of subject- specific stimulation protocols. With this study here, we set the foundation to combine tACS with a recently presented framework that utilizes real-time fRMI and Bayesian optimization in order to identify the most optimal tACS protocol for a given individual. While Bayesian optimization is particularly relevant to such a scenario, its success depends on two fundamental choices: the choice of covariance kernel for the Gaussian process prior as well as the choice of acquisition function that guides the search. Using empirical (functional neuroimaging) as well as simulation data, we identified the squared exponential kernel and the upper confidence bound acquisition function to work best for our problem. These results will be used to inform our upcoming real- time experiments., Comment: accepted for oral presentation at PRNI 2016 - 6th International Workshop on Pattern Recognition in Neuroimaging

Large-scale automated meta-analysis of neuroimaging data has recently established itself as an important tool in advancing our understanding of human brain function. This research has been pioneered by NeuroSynth, a database collecting both brain activation coordinates and associated text across a large cohort of neuroimaging research papers. One of the fundamental aspects of such meta-analysis is text-mining. To date, word counts and more sophisticated methods such as Latent Dirichlet Allocation have been proposed. In this work we present an unsupervised study of the NeuroSynth text corpus using Deep Boltzmann Machines (DBMs). The use of DBMs yields several advantages over the aforementioned methods, principal among which is the fact that it yields both word and document embeddings in a high-dimensional vector space. Such embeddings serve to facilitate the use of traditional machine learning techniques on the text corpus. The proposed DBM model is shown to learn embeddings with a clear semantic structure., Comment: 4 pages, 1 figure

Network theory provides a principled abstraction of the human brain: reducing a complex system into a simpler representation from which to investigate brain organisation. Recent advancement in the neuroimaging field are towards representing brain connectivity as a dynamic process in order to gain a deeper understanding of the interplay between functional modules for efficient information transport. In this work, we employ heat kernels to model the process of energy diffusion in functional networks. We extract node-based, multi-scale features which describe the propagation of heat over 'time' which not only inform the importance of a node in the graph, but also incorporate local and global information of the underlying geometry of the network. As a proof-of-concept, we test the efficacy of two heat kernel features for discriminating between motor and working memory functional networks from the Human Connectome Project. For comparison, we also classified task networks using traditional network metrics which similarly provide rankings of node importance. In addition, a variant of the Smooth Incremental Graphical Lasso Estimation algorithm was used to estimate non-sparse, precision matrices to account for non-stationarity in the time series. We illustrate differences in heat kernel features between tasks, and also between regions of the brain. Using a random forest classifier, we showed heat kernel metrics to capture intrinsic properties of functional networks that serve well as features for task classification., Comment: Pattern Recognition in Neuroimaging, 2016

In neuroimaging data analysis, Gaussian graphical models are often used to model statistical dependencies across spatially remote brain regions known as functional connectivity. Typically, data is collected across a cohort of subjects and the scientific objectives consist of estimating population and subject-specific graphical models. A third objective that is often overlooked involves quantifying inter-subject variability and thus identifying regions or sub-networks that demonstrate heterogeneity across subjects. Such information is fundamental in order to thoroughly understand the human connectome. We propose Mixed Neighborhood Selection in order to simultaneously address the three aforementioned objectives. By recasting covariance selection as a neighborhood selection problem we are able to efficiently learn the topology of each node. We introduce an additional mixed effect component to neighborhood selection in order to simultaneously estimate a graphical model for the population of subjects as well as for each individual subject. The proposed method is validated empirically through a series of simulations and applied to resting state data for healthy subjects taken from the ABIDE consortium., Comment: 32 pages, 6 figures

Bayesian optimization has been proposed as a practical and efficient tool through which to tune parameters in many difficult settings. Recently, such techniques have been combined with real-time fMRI to propose a novel framework which turns on its head the conventional functional neuroimaging approach. This closed-loop method automatically designs the optimal experiment to evoke a desired target brain pattern. One of the challenges associated with extending such methods to real-time brain imaging is the need for adequate stopping criteria, an aspect of Bayesian optimization which has received limited attention. In light of high scanning costs and limited attentional capacities of subjects an accurate and reliable stopping criteria is essential. In order to address this issue we propose and empirically study the performance of two stopping criteria., Comment: Oral presentation at MLINI 2015 - 5th NIPS Workshop on Machine Learning and Interpretation in Neuroimaging: Beyond the Scanner

We propose a framework to perform streaming covariance selection. Our approach employs regularization constraints where a time-varying sparsity parameter is iteratively estimated via stochastic gradient descent. This allows for the regularization parameter to be efficiently learnt in an online manner. The proposed framework is developed for linear regression models and extended to graphical models via neighbourhood selection. Under mild assumptions, we are able to obtain convergence results in a non-stochastic setting. The capabilities of such an approach are demonstrated using both synthetic data as well as neuroimaging data., Comment: Paper withdrawn as it is no longer up to date

Multiplex networks, a special type of multilayer networks, are increasingly applied in many domains ranging from social media analytics to biology. A common task in these applications concerns the detection of community structures. Many existing algorithms for community detection in multiplexes attempt to detect communities which are shared by all layers. In this article we propose a community detection algorithm, LART (Locally Adaptive Random Transitions), for the detection of communities that are shared by either some or all the layers in the multiplex. The algorithm is based on a random walk on the multiplex, and the transition probabilities defining the random walk are allowed to depend on the local topological similarity between layers at any given node so as to facilitate the exploration of communities across layers. Based on this random walk, a node dissimilarity measure is derived and nodes are clustered based on this distance in a hierarchical fashion. We present experimental results using networks simulated under various scenarios to showcase the performance of LART in comparison to related community detection algorithms.

There is increasing evidence to suggest functional connectivity networks are non-stationary. This has lead to the development of novel methodologies with which to accurately estimate time-varying functional connectivity networks. Many of these methods provide unprecedented temporal granularity by estimating a functional connectivity network at each point in time; resulting in high-dimensional output which can be studied in a variety of ways. One possible method is to employ graph embedding algorithms. Such algorithms effectively map estimated networks from high-dimensional spaces down to a low dimensional vector space; thus facilitating visualization, interpretation and classification. In this work, the dynamic properties of functional connectivity are studied using working memory task data from the Human Connectome Project. A recently proposed method is employed to estimate dynamic functional connectivity networks. The results are subsequently analyzed using two graph embedding methods based on linear projections. These methods are shown to provide informative embeddings that can be directly interpreted as functional connectivity networks., Comment: 4 pages, 1 figure, 5th International Workshop on Pattern Recognition in Neuroimaging, Stanford University, 2015

In cancer research, the comparison of gene expression or DNA methylation networks inferred from healthy controls and patients can lead to the discovery of biological pathways associated to the disease. As a cancer progresses, its signalling and control networks are subject to some degree of localised re-wiring. Being able to detect disrupted interaction patterns induced by the presence or progression of the disease can lead to the discovery of novel molecular diagnostic and prognostic signatures. Currently there is a lack of scalable statistical procedures for two-network comparisons aimed at detecting localised topological differences. We propose the dGHD algorithm, a methodology for detecting differential interaction patterns in two-network comparisons. The algorithm relies on a statistic, the Generalised Hamming Distance (GHD), for assessing the degree of topological difference between networks and evaluating its statistical significance. dGHD builds on a non-parametric permutation testing framework but achieves computationally efficiency through an asymptotic normal approximation. We show that the GHD is able to detect more subtle topological differences compared to a standard Hamming distance between networks. This results in the dGHD algorithm achieving high performance in simulation studies as measured by sensitivity and specificity. An application to the problem of detecting differential DNA co-methylation subnetworks associated to ovarian cancer demonstrates the potential benefits of the proposed methodology for discovering network-derived biomarkers associated with a trait of interest.

A standard approach in functional neuroimaging explores how a particular cognitive task activates a set of brain regions (one task-to-many regions mapping). Importantly though, the same neural system can be activated by inherently different tasks. To date, there is no approach available that systematically explores whether and how distinct tasks probe the same neural system (many tasks-to-region mapping). In our work, presented here we propose an alternative framework, the Automatic Neuroscientist, which turns the typical fMRI approach on its head. We use real-time fMRI in combination with state-of-the-art optimisation techniques to automatically design the optimal experiment to evoke a desired target brain state. Here, we present two proof-of-principle studies involving visual and auditory stimuli. The data demonstrate this closed-loop approach to be very powerful, hugely speeding up fMRI and providing an accurate estimation of the underlying relationship between stimuli and neural responses across an extensive experimental parameter space. Finally, we detail four scenarios where our approach can be applied, suggesting how it provides a novel description of how cognition and the brain interrelate., Comment: 22 pages, 7 figures, work presented at OHBM 2015

Gene expression levels in a population vary extensively across tissues. Such heterogeneity is caused by genetic variability and environmental factors, and is expected to be linked to disease development. The abundance of experimental data now enables the identification of features of gene expression profiles that are shared across tissues, and those that are tissue-specific. While most current research is concerned with characterising differential expression by comparing mean expression profiles across tissues, it is also believed that a significant difference in a gene expression's variance across tissues may also be associated to molecular mechanisms that are important for tissue development and function. We propose a sparse multi-view matrix factorisation (sMVMF) algorithm to jointly analyse gene expression measurements in multiple tissues, where each tissue provides a different "view" of the underlying organism. The proposed methodology can be interpreted as an extension of principal component analysis in that it provides the means to decompose the total sample variance in each tissue into the sum of two components: one capturing the variance that is shared across tissues, and one isolating the tissue-specific variances. sMVMF has been used to jointly model mRNA expression profiles in three tissues - adipose, skin and LCL - which are available for a large and well-phenotyped twins cohort, TwinsUK. Using sMVMF, we are able to prioritise genes based on whether their variation patterns are specific to each tissue. Furthermore, using DNA methylation profiles available, we provide supporting evidence that adipose-specific gene expression patterns may be driven by epigenetic effects., Comment: in Bioinformatics 2015

Pattern recognition methods using neuroimaging data for the diagnosis of Alzheimer's disease have been the subject of extensive research in recent years. In this paper, we use deep learning methods, and in particular sparse autoencoders and 3D convolutional neural networks, to build an algorithm that can predict the disease status of a patient, based on an MRI scan of the brain. We report on experiments using the ADNI data set involving 2,265 historical scans. We demonstrate that 3D convolutional neural networks outperform several other classifiers reported in the literature and produce state-of-art results.

We present a novel approach to automatically segment magnetic resonance (MR) images of the human brain into anatomical regions. Our methodology is based on a deep artificial neural network that assigns each voxel in an MR image of the brain to its corresponding anatomical region. The inputs of the network capture information at different scales around the voxel of interest: 3D and orthogonal 2D intensity patches capture the local spatial context while large, compressed 2D orthogonal patches and distances to the regional centroids enforce global spatial consistency. Contrary to commonly used segmentation methods, our technique does not require any non-linear registration of the MR images. To benchmark our model, we used the dataset provided for the MICCAI 2012 challenge on multi-atlas labelling, which consists of 35 manually segmented MR images of the brain. We obtained competitive results (mean dice coefficient 0.725, error rate 0.163) showing the potential of our approach. To our knowledge, our technique is the first to tackle the anatomical segmentation of the whole brain using deep neural networks.

There has been an explosion of interest in functional Magnetic Resonance Imaging (MRI) during the past two decades. Naturally, this has been accompanied by many major advances in the understanding of the human connectome. These advances have served to pose novel challenges as well as open new avenues for research. One of the most promising and exciting of such avenues is the study of functional MRI in real-time. Such studies have recently gained momentum and have been applied in a wide variety of settings; ranging from training of healthy subjects to self-regulate neuronal activity to being suggested as potential treatments for clinical populations. To date, the vast majority of these studies have focused on a single region at a time. This is due in part to the many challenges faced when estimating dynamic functional connectivity networks in real-time. In this work we propose a novel methodology with which to accurately track changes in functional connectivity networks in real-time. We adapt the recently proposed SINGLE algorithm for estimating sparse and temporally homo- geneous dynamic networks to be applicable in real-time. The proposed method is applied to motor task data from the Human Connectome Project as well as to real-time data ob- tained while exploring a virtual environment. We show that the algorithm is able to estimate significant task-related changes in network structure quickly enough to be useful in future brain-computer interface applications., Comment: 37 pages

Understanding the functional architecture of the brain in terms of networks is becoming increasingly common. In most fMRI applications functional networks are assumed to be stationary, resulting in a single network estimated for the entire time course. However recent results suggest that the connectivity between brain regions is highly non-stationary even at rest. As a result, there is a need for new brain imaging methodologies that comprehensively account for the dynamic (i.e., non-stationary) nature of the fMRI data. In this work we propose the Smooth Incremental Graphical Lasso Estimation (SINGLE) algorithm which estimates dynamic brain networks from fMRI data. We apply the SINGLE algorithm to functional MRI data from 24 healthy patients performing a choice-response task to demonstrate the dynamic changes in network structure that accompany a simple but attentionally demanding cognitive task. Using graph theoretic measures we show that the Right Inferior Frontal Gyrus, frequently reported as playing an important role in cognitive control, dynamically changes with the task. Our results suggest that the Right Inferior Frontal Gyrus plays a fundamental role in the attention and executive function during cognitively demanding tasks and may play a key role in regulating the balance between other brain regions.

We propose a non-parametric regression methodology, Random Forests on Distance Matrices (RFDM), for detecting genetic variants associated to quantitative phenotypes representing the human brain's structure or function, and obtained using neuroimaging techniques. RFDM, which is an extension of decision forests, requires a distance matrix as response that encodes all pair-wise phenotypic distances in the random sample. We discuss ways to learn such distances directly from the data using manifold learning techniques, and how to define such distances when the phenotypes are non-vectorial objects such as brain connectivity networks. We also describe an extension of RFDM to detect espistatic effects while keeping the computational complexity low. Extensive simulation results and an application to an imaging genetics study of Alzheimer's Disease are presented and discussed.

Due to rapid technological advances, a wide range of different measurements can be obtained from a given biological sample including single nucleotide polymorphisms, copy number variation, gene expression levels, DNA methylation and proteomic profiles. Each of these distinct measurements provides the means to characterize a certain aspect of biological diversity, and a fundamental problem of broad interest concerns the discovery of shared patterns of variation across different data types. Such data types are heterogeneous in the sense that they represent measurements taken at very different scales or described by very different data structures. We propose a distance-based statistical test, the generalized RV (GRV) test, to assess whether there is a common and non-random pattern of variability between paired biological measurements obtained from the same random sample. The measurements enter the test through distance measures which can be chosen to capture particular aspects of the data. An approximate null distribution is proposed to compute p-values in closed-form and without the need to perform costly Monte Carlo permutation procedures. Compared to the classical Mantel test for association between distance matrices, the GRV test has been found to be more powerful in a number of simulation settings. We also report on an application of the GRV test to detect biological pathways in which genetic variability is associated to variation in gene expression levels in ovarian cancer samples, and present results obtained from two independent cohorts.

Predictive modelling of multivariate data where both the covariates and responses are high-dimensional is becoming an increasingly popular task in many data mining applications. Partial Least Squares (PLS) regression often turns out to be a useful model in these situations since it performs dimensionality reduction by assuming the existence of a small number of latent factors that may explain the linear dependence between input and output. In practice, the number of latent factors to be retained, which controls the complexity of the model and its predictive ability, has to be carefully selected. Typically this is done by cross validating a performance measure, such as the predictive error. Although cross validation works well in many practical settings, it can be computationally expensive. Various extensions to PLS have also been proposed for regularising the PLS solution and performing simultaneous dimensionality reduction and variable selection, but these come at the expense of additional complexity parameters that also need to be tuned by cross-validation. In this paper we derive a computationally efficient alternative to leave-one-out cross validation (LOOCV), a predicted sum of squares (PRESS) statistic for two-block PLS. We show that the PRESS is nearly identical to LOOCV but has the computational expense of only a single PLS model fit. Examples of the PRESS for selecting the number of latent factors and regularisation parameters are provided.

In many longitudinal microarray studies, the gene expression levels in a random sample are observed repeatedly over time under two or more conditions. The resulting time courses are generally very short, high-dimensional, and may have missing values. Moreover, for every gene, a certain amount of variability in the temporal profiles, among biological replicates, is generally observed. We propose a functional mixed-effects model for estimating the temporal pattern of each gene, which is assumed to be a smooth function. A statistical test based on the distance between the fitted curves is then carried out to detect differential expression. A simulation procedure for assessing the statistical power of our model is also suggested. We evaluate the model performance using both simulations and a real data set investigating the human host response to BCG exposure.

Motivated by a challenging problem in financial trading we are presented with a mixture of regressions with variable selection problem. In this regard, one is faced with data which possess outliers, skewness and, simultaneously, due to the nature of financial trading, one would like to be able to construct clusters with specific predictors that are fairly sparse. We develop a Bayesian mixture of lasso regressions with $t-$errors to reflect these specific demands. The resulting model is necessarily complex and to fit the model to real data, we develop a state-of-the-art Particle Markov chain Monte Carlo (PMCMC) algorithm based upon sequential Monte Carlo (SMC) methods. The model and algorithm are investigated on both simulated and real data.

In several modern applications, ranging from genetics to genomics and neuroimaging, there is a need to compare observations across different populations, such as groups of healthy and diseased individuals. The interest is in detecting a group effect. When the observations are vectorial, real-valued and follow a multivariate Normal distribution, multivariate analysis of variance (MANOVA) tests are routinely applied. However, such traditional procedures are not suitable when dealing with more complex data structures such as functional (e.g. curves) or graph-structured (e.g. trees and networks) objects, where the required distributional assumptions may be violated. In this paper we discuss a distance-based MANOVA-like approach, the DBF test, for detecting differences between groups for a wider range of data types. The test statistic, analogously to other distance-based statistics, only relies on a suitably chosen distance measure that captures the pairwise dissimilarity among all available samples. An approximate null probability distribution of the DBF statistic is proposed thus allowing inferences to be drawn without the need for costly permutation procedures. Through extensive simulations we provide evidence that the proposed methodology works well for a range of data types and distances, and generalizes the traditional MANOVA tests. We also report on an application of the proposed methodology for the analysis of a multi-locus genome-wide association study of Alzheimer's disease, which has been carried out using several genetic distance measures.

We present a new method for the detection of gene pathways associated with a multivariate quantitative trait, and use it to identify causal pathways associated with an imaging endophenotype characteristic of longitudinal structural change in the brains of patients with Alzheimer's disease (AD). Our method, known as pathways sparse reduced-rank regression (PsRRR), uses group lasso penalised regression to jointly model the effects of genome-wide single nucleotide polymorphisms (SNPs), grouped into functional pathways using prior knowledge of gene-gene interactions. Pathways are ranked in order of importance using a resampling strategy that exploits finite sample variability. Our application study uses whole genome scans and MR images from 464 subjects in the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. 66,182 SNPs are mapped to 185 gene pathways from the KEGG pathways database. Voxel-wise imaging signatures characteristic of AD are obtained by analysing 3D patterns of structural change at 6, 12 and 24 months relative to baseline. High-ranking, AD endophenotype-associated pathways in our study include those describing chemokine, Jak-stat and insulin signalling pathways, and tight junction interactions. All of these have been previously implicated in AD biology. In a secondary analysis, we investigate SNPs and genes that may be driving pathway selection, and identify a number of previously validated AD genes including CR1, APOE and TOMM40.

In several application domains, high-dimensional observations are collected and then analysed in search for naturally occurring data clusters which might provide further insights about the nature of the problem. In this paper we describe a new approach for partitioning such high-dimensional data. Our assumption is that, within each cluster, the data can be approximated well by a linear subspace estimated by means of a principal component analysis (PCA). The proposed algorithm, Predictive Subspace Clustering (PSC) partitions the data into clusters while simultaneously estimating cluster-wise PCA parameters. The algorithm minimises an objective function that depends upon a new measure of influence for PCA models. A penalised version of the algorithm is also described for carrying our simultaneous subspace clustering and variable selection. The convergence of PSC is discussed in detail, and extensive simulation results and comparisons to competing methods are presented. The comparative performance of PSC has been assessed on six real gene expression data sets for which PSC often provides state-of-art results.

Many modern data mining applications are concerned with the analysis of datasets in which the observations are described by paired high-dimensional vectorial representations or "views". Some typical examples can be found in web mining and genomics applications. In this article we present an algorithm for data clustering with multiple views, Multi-View Predictive Partitioning (MVPP), which relies on a novel criterion of predictive similarity between data points. We assume that, within each cluster, the dependence between multivariate views can be modelled by using a two-block partial least squares (TB-PLS) regression model, which performs dimensionality reduction and is particularly suitable for high-dimensional settings. The proposed MVPP algorithm partitions the data such that the within-cluster predictive ability between views is maximised. The proposed objective function depends on a measure of predictive influence of points under the TB-PLS model which has been derived as an extension of the PRESS statistic commonly used in ordinary least squares regression. Using simulated data, we compare the performance of MVPP to that of competing multi-view clustering methods which rely upon geometric structures of points, but ignore the predictive relationship between the two views. State-of-art results are obtained on benchmark web mining datasets., Comment: 31 pages, 12 figures

Where causal SNPs (single nucleotide polymorphisms) tend to accumulate within biological pathways, the incorporation of prior pathways information into a statistical model is expected to increase the power to detect true associations in a genetic association study. Most existing pathways-based methods rely on marginal SNP statistics and do not fully exploit the dependence patterns among SNPs within pathways. We use a sparse regression model, with SNPs grouped into pathways, to identify causal pathways associated with a quantitative trait. Notable features of our "pathways group lasso with adaptive weights" (P-GLAW) algorithm include the incorporation of all pathways in a single regression model, an adaptive pathway weighting procedure that accounts for factors biasing pathway selection, and the use of a bootstrap sampling procedure for the ranking of important pathways. P-GLAW takes account of the presence of overlapping pathways and uses a novel combination of techniques to optimise model estimation, making it fast to run, even on whole genome datasets. In a comparison study with an alternative pathways method based on univariate SNP statistics, our method demonstrates high sensitivity and specificity for the detection of important pathways, showing the greatest relative gains in performance where marginal SNP effect sizes are small., Comment: 29 pages

Cluster analysis of biological samples using gene expression measurements is a common task which aids the discovery of heterogeneous biological sub-populations having distinct mRNA profiles. Several model-based clustering algorithms have been proposed in which the distribution of gene expression values within each sub-group is assumed to be Gaussian. In the presence of noise and extreme observations, a mixture of Gaussian densities may over-fit and overestimate the true number of clusters. Moreover, commonly used model-based clustering algorithms do not generally provide a mechanism to quantify the relative contribution of each gene to the final partitioning of the data. We propose a penalised mixture of Student's t distributions for model-based clustering and gene ranking. Together with a bootstrap procedure, the proposed approach provides a means for ranking genes according to their contributions to the clustering process. Experimental results show that the algorithm performs well comparably to traditional Gaussian mixtures in the presence of outliers and longer tailed distributions. The algorithm also identifies the true informative genes with high sensitivity, and achieves improved model selection. An illustrative application to breast cancer data is also presented which confirms established tumor subclasses., Comment: 18 pages, 4 figures

In this paper we have demonstrated a complete framework for the analysis of microarray time series data. The unique characteristics of microarry data lend themselves well to a functional data analysis approach and we have shown how this naturally extends to the inclusion of covariates such as age and sex. Our model presented here is a specialisation of the more general functional mixed-effects model and, to the best of our knowledge, we are the first to show how to derive the maximum-likelihood estimators, EM-algorithm, confidence intervals and smoother matrix with more than one fixed-effects function. We were motivated by a real data set characterising healthy human gene expression levels over time and we have aimed to improve upon the existing results with a more flexible model. By taking a roughness penalty approach, this is achieved while avoiding overfitting, allowing for a departure from the original linear mixed-effects model when the data permits it. A deeper biological interpretation is required to fully assess our success here, but the results we have highlighted in this paper suggest that we can easily attach meaning to our findings.

A powerful study design in the fields of genomics and metabolomics is the 'replicated time course experiment' where individual time series are observed for a sample of biological units, such as human patients, termed replicates. Standard practice for analysing these data sets is to fit each variable (e.g. gene transcript) independently with a functional mixed-effects model to account for between-replicate variance. However, such an independence assumption is biologically implausible given that the variables are known to be highly correlated. In this article we present a skew-t-normal multi-level reduced-rank functional principal components analysis (FPCA) model for simultaneously modelling the between-variable and between-replicate variance. The reduced-rank FPCA model is computationally efficient and, analogously with a standard PCA for vectorial data, provides a low dimensional representation that can be used to identify the major patterns of temporal variation. Using an example case study exploring the genetic response to BCG infection we demonstrate that these low dimensional representations are eminently biologically interpretable. We also show using a simulation study that modelling all variables simultaneously greatly reduces the estimation error compared to the independence assumption.

In this paper we propose a computationally efficient algorithm for on-line variable selection in multivariate regression problems involving high dimensional data streams. The algorithm recursively extracts all the latent factors of a partial least squares solution and selects the most important variables for each factor. This is achieved by means of only one sparse singular value decomposition which can be efficiently updated on-line and in an adaptive fashion. Simulation results based on artificial data streams demonstrate that the algorithm is able to select important variables in dynamic settings where the correlation structure among the observed streams is governed by a few hidden components and the importance of each variable changes over time. We also report on an application of our algorithm to a multivariate version of the "enhanced index tracking" problem using financial data streams. The application consists of performing on-line asset allocation with the objective of overperforming two benchmark indices simultaneously., Comment: 26 pages, 6 figures, submitted

Statistical arbitrage strategies, such as pairs trading and its generalizations, rely on the construction of mean-reverting spreads enjoying a certain degree of predictability. Gaussian linear state-space processes have recently been proposed as a model for such spreads under the assumption that the observed process is a noisy realization of some hidden states. Real-time estimation of the unobserved spread process can reveal temporary market inefficiencies which can then be exploited to generate excess returns. Building on previous work, we embrace the state-space framework for modeling spread processes and extend this methodology along three different directions. First, we introduce time-dependency in the model parameters, which allows for quick adaptation to changes in the data generating process. Second, we provide an on-line estimation algorithm that can be constantly run in real-time. Being computationally fast, the algorithm is particularly suitable for building aggressive trading strategies based on high-frequency data and may be used as a monitoring device for mean-reversion. Finally, our framework naturally provides informative uncertainty measures of all the estimated parameters. Experimental results based on Monte Carlo simulations and historical equity data are discussed, including a co-integration relationship involving two exchange-traded funds., Comment: 34 pages, 6 figures. Submitted

A number of recent emerging applications call for studying data streams, potentially infinite flows of information updated in real-time. When multiple co-evolving data streams are observed, an important task is to determine how these streams depend on each other, accounting for dynamic dependence patterns without imposing any restrictive probabilistic law governing this dependence. In this paper we argue that flexible least squares (FLS), a penalized version of ordinary least squares that accommodates for time-varying regression coefficients, can be deployed successfully in this context. Our motivating application is statistical arbitrage, an investment strategy that exploits patterns detected in financial data streams. We demonstrate that FLS is algebraically equivalent to the well-known Kalman filter equations, and take advantage of this equivalence to gain a better understanding of FLS and suggest a more efficient algorithm. Promising experimental results obtained from a FLS-based algorithmic trading system for the S&P 500 Futures Index are reported., Comment: 28 pages, 6 figures, submitted to journal

In this paper we develop a Bayesian procedure for estimating multivariate stochastic volatility (MSV) using state space models. A multiplicative model based on inverted Wishart and multivariate singular beta distributions is proposed for the evolution of the volatility, and a flexible sequential volatility updating is employed. Being computationally fast, the resulting estimation procedure is particularly suitable for on-line forecasting. Three performance measures are discussed in the context of model selection: the log-likelihood criterion, the mean of standardized one-step forecast errors, and sequential Bayes factors. Finally, the proposed methods are applied to a data set comprising eight exchange rates vis-a-vis the US dollar., Comment: 15 pages, 4 figures