Causality and synchronisation in complex systems with applications to neuroscience

This thesis presents an investigation, of synchronisation and causality, motivated by problems in computational neuroscience. The thesis addresses both theoretical and practical signal processing issues regarding the estimation of interdependence from a set of multivariate data generated by a complex underlying dynamical system. This topic is driven by a series of problems in neuroscience, which represents the principal background motive behind the material in this work. The underlying system is the human brain and the generative process of the data is based on modern electromagnetic neuroimaging methods . In this thesis, the underlying functional of the brain mechanisms are derived from the recent mathematical formalism of dynamical systems in complex networks. This is justified principally on the grounds of the complex hierarchical and multiscale nature of the brain and it offers new methods of analysis to model its emergent phenomena. A fundamental approach to study the neural activity is to investigate the connectivity pattern developed by the brain’s complex network. Three types of connectivity are important to study: 1) anatomical connectivity refering to the physical links forming the topology of the brain network; 2) effective connectivity concerning with the way the neural elements communicate with each other using the brain’s anatomical structure, through phenomena of synchronisation and information transfer; 3) functional connectivity, presenting an epistemic concept which alludes to the interdependence between data measured from the brain network. The main contribution of this thesis is to present, apply and discuss novel algorithms of functional connectivities, which are designed to extract different specific aspects of interaction between the underlying generators of the data. Firstly, a univariate statistic is developed to allow for indirect assessment of synchronisation in the local network from a single time series. This approach is useful in inferring the coupling as in a local cortical area as observed by a single measurement electrode. Secondly, different existing methods of phase synchronisation are considered from the perspective of experimental data analysis and inference of coupling from observed data. These methods are designed to address the estimation of medium to long range connectivity and their differences are particularly relevant in the context of volume conduction, that is known to produce spurious detections of connectivity. Finally, an asymmetric temporal metric is introduced in order to detect the direction of the coupling between different regions of the brain. The method developed in this thesis is based on a machine learning extensions of the well known concept of Granger causality. The thesis discussion is developed alongside examples of synthetic and experimental real data. The synthetic data are simulations of complex dynamical systems with the intention to mimic the behaviour of simple cortical neural assemblies. They are helpful to test the techniques developed in this thesis. The real datasets are provided to illustrate the problem of brain connectivity in the case of important neurological disorders such as Epilepsy and Parkinson’s disease. The methods of functional connectivity in this thesis are applied to intracranial EEG recordings in order to extract features, which characterize underlying spatiotemporal dynamics before during and after an epileptic seizure and predict seizure location and onset prior to conventional electrographic signs. The methodology is also applied to a MEG dataset containing healthy, Parkinson’s and dementia subjects with the scope of distinguishing patterns of pathological from physiological connectivity.

Gaussian process approximations of stochastic differential equations

Stochastic differential equations arise naturally in a range of contexts, from financial to environmental modeling. Current solution methods are limited in their representation of the posterior process in the presence of data. In this work, we present a novel Gaussian process approximation to the posterior measure over paths for a general class of stochastic differential equations in the presence of observations. The method is applied to two simple problems: the Ornstein-Uhlenbeck process, of which the exact solution is known and can be compared to, and the double-well system, for which standard approaches such as the ensemble Kalman smoother fail to provide a satisfactory result. Experiments show that our variational approximation is viable and that the results are very promising as the variational approximate solution outperforms standard Gaussian process regression for non-Gaussian Markov processes.

Short-term electricity demand and gas price forecasts using wavelet transforms and adaptive models

This paper presents some forecasting techniques for energy demand and price prediction, one day ahead. These techniques combine wavelet transform (WT) with fixed and adaptive machine learning/time series models (multi-layer perceptron (MLP), radial basis functions, linear regression, or GARCH). To create an adaptive model, we use an extended Kalman filter or particle filter to update the parameters continuously on the test set. The adaptive GARCH model is a new contribution, broadening the applicability of GARCH methods. We empirically compared two approaches of combining the WT with prediction models: multicomponent forecasts and direct forecasts. These techniques are applied to large sets of real data (both stationary and non-stationary) from the UK energy markets, so as to provide comparative results that are statistically stronger than those previously reported. The results showed that the forecasting accuracy is significantly improved by using the WT and adaptive models. The best models on the electricity demand/gas price forecast are the adaptive MLP/GARCH with the multicomponent forecast; their MSEs are 0.02314 and 0.15384 respectively.

Projected sequential Gaussian processes: flexible interpolation for large data sets

Recently within the machine learning and spatial statistics communities many papers have explored the potential of reduced rank representations of the covariance matrix, often referred to as projected or fixed rank approaches. In such methods the covariance function of the posterior process is represented by a reduced rank approximation which is chosen such that there is minimal information loss. In this paper a sequential framework for inference in such projected processes is presented, where the observations are considered one at a time. We introduce a C++ library for carrying out such projected, sequential estimation which adds several novel features. In particular we have incorporated the ability to use a generic observation operator, or sensor model, to permit data fusion. We can also cope with a range of observation error characteristics, including non-Gaussian observation errors. Inference for the variogram parameters is based on maximum likelihood estimation. We illustrate the projected sequential method in application to synthetic and real data sets. We discuss the software implementation and suggest possible future extensions.

Using secondary knowledge to support decision tree classification of retrospective clinical data

Retrospective clinical data presents many challenges for data mining and machine learning. The transcription of patient records from paper charts and subsequent manipulation of data often results in high volumes of noise as well as a loss of other important information. In addition, such datasets often fail to represent expert medical knowledge and reasoning in any explicit manner. In this research we describe applying data mining methods to retrospective clinical data to build a prediction model for asthma exacerbation severity for pediatric patients in the emergency department. Difficulties in building such a model forced us to investigate alternative strategies for analyzing and processing retrospective data. This paper describes this process together with an approach to mining retrospective clinical data by incorporating formalized external expert knowledge (secondary knowledge sources) into the classification task. This knowledge is used to partition the data into a number of coherent sets, where each set is explicitly described in terms of the secondary knowledge source. Instances from each set are then classified in a manner appropriate for the characteristics of the particular set. We present our methodology and outline a set of experiential results that demonstrate some advantages and some limitations of our approach. © 2008 Springer-Verlag Berlin Heidelberg.

Finding structures in information networks using the affinity network

This thesis proposes a novel graphical model for inference called the Affinity Network,which displays the closeness between pairs of variables and is an alternative to Bayesian Networks and Dependency Networks. The Affinity Network shares some similarities with Bayesian Networks and Dependency Networks but avoids their heuristic and stochastic graph construction algorithms by using a message passing scheme. A comparison with the above two instances of graphical models is given for sparse discrete and continuous medical data and data taken from the UCI machine learning repository. The experimental study reveals that the Affinity Network graphs tend to be more accurate on the basis of an exhaustive search with the small datasets. Moreover, the graph construction algorithm is faster than the other two methods with huge datasets. The Affinity Network is also applied to data produced by a synchronised system. A detailed analysis and numerical investigation into this dynamical system is provided and it is shown that the Affinity Network can be used to characterise its emergent behaviour even in the presence of noise.

Biomedical events extraction using the hidden vector state model

Objective: Biomedical events extraction concerns about events describing changes on the state of bio-molecules from literature. Comparing to the protein-protein interactions (PPIs) extraction task which often only involves the extraction of binary relations between two proteins, biomedical events extraction is much harder since it needs to deal with complex events consisting of embedded or hierarchical relations among proteins, events, and their textual triggers. In this paper, we propose an information extraction system based on the hidden vector state (HVS) model, called HVS-BioEvent, for biomedical events extraction, and investigate its capability in extracting complex events. Methods and material: HVS has been previously employed for extracting PPIs. In HVS-BioEvent, we propose an automated way to generate abstract annotations for HVS training and further propose novel machine learning approaches for event trigger words identification, and for biomedical events extraction from the HVS parse results. Results: Our proposed system achieves an F-score of 49.57% on the corpus used in the BioNLP'09 shared task, which is only 2.38% lower than the best performing system by UTurku in the BioNLP'09 shared task. Nevertheless, HVS-BioEvent outperforms UTurku's system on complex events extraction with 36.57% vs. 30.52% being achieved for extracting regulation events, and 40.61% vs. 38.99% for negative regulation events. Conclusions: The results suggest that the HVS model with the hierarchical hidden state structure is indeed more suitable for complex event extraction since it could naturally model embedded structural context in sentences.

Exploring ant-based algorithms for gene expression data analysis

Objective: Recently, much research has been proposed using nature inspired algorithms to perform complex machine learning tasks. Ant colony optimization (ACO) is one such algorithm based on swarm intelligence and is derived from a model inspired by the collective foraging behavior of ants. Taking advantage of the ACO in traits such as self-organization and robustness, this paper investigates ant-based algorithms for gene expression data clustering and associative classification. Methods and material: An ant-based clustering (Ant-C) and an ant-based association rule mining (Ant-ARM) algorithms are proposed for gene expression data analysis. The proposed algorithms make use of the natural behavior of ants such as cooperation and adaptation to allow for a flexible robust search for a good candidate solution. Results: Ant-C has been tested on the three datasets selected from the Stanford Genomic Resource Database and achieved relatively high accuracy compared to other classical clustering methods. Ant-ARM has been tested on the acute lymphoblastic leukemia (ALL)/acute myeloid leukemia (AML) dataset and generated about 30 classification rules with high accuracy. Conclusions: Ant-C can generate optimal number of clusters without incorporating any other algorithms such as K-means or agglomerative hierarchical clustering. For associative classification, while a few of the well-known algorithms such as Apriori, FP-growth and Magnum Opus are unable to mine any association rules from the ALL/AML dataset within a reasonable period of time, Ant-ARM is able to extract associative classification rules.

Gaussian process quantile regression using expectation propagation

Direct quantile regression involves estimating a given quantile of a response variable as a function of input variables. We present a new framework for direct quantile regression where a Gaussian process model is learned, minimising the expected tilted loss function. The integration required in learning is not analytically tractable so to speed up the learning we employ the Expectation Propagation algorithm. We describe how this work relates to other quantile regression methods and apply the method on both synthetic and real data sets. The method is shown to be competitive with state of the art methods whilst allowing for the leverage of the full Gaussian process probabilistic framework.

Visual data mining using principled projection algorithms and information visualization techniques

We introduce a flexible visual data mining framework which combines advanced projection algorithms from the machine learning domain and visual techniques developed in the information visualization domain. The advantage of such an interface is that the user is directly involved in the data mining process. We integrate principled projection algorithms, such as generative topographic mapping (GTM) and hierarchical GTM (HGTM), with powerful visual techniques, such as magnification factors, directional curvatures, parallel coordinates and billboarding, to provide a visual data mining framework. Results on a real-life chemoinformatics dataset using GTM are promising and have been analytically compared with the results from the traditional projection methods. It is also shown that the HGTM algorithm provides additional value for large datasets. The computational complexity of these algorithms is discussed to demonstrate their suitability for the visual data mining framework. Copyright 2006 ACM.

Proteomic applications of automated GPCR classification

The G-protein coupled receptor (GPCR) superfamily fulfils various metabolic functions and interacts with a diverse range of ligands. There is a lack of sequence similarity between the six classes that comprise the GPCR superfamily. Moreover, most novel GPCRs found have low sequence similarity to other family members which makes it difficult to infer properties from related receptors. Many different approaches have been taken towards developing efficient and accurate methods for GPCR classification, ranging from motif-based systems to machine learning as well as a variety of alignment-free techniques based on the physiochemical properties of their amino acid sequences. This review describes the inherent difficulties in developing a GPCR classification algorithm and includes techniques previously employed in this area.

Guiding local regression using visualisation

Solving many scientific problems requires effective regression and/or classification models for large high-dimensional datasets. Experts from these problem domains (e.g. biologists, chemists, financial analysts) have insights into the domain which can be helpful in developing powerful models but they need a modelling framework that helps them to use these insights. Data visualisation is an effective technique for presenting data and requiring feedback from the experts. A single global regression model can rarely capture the full behavioural variability of a huge multi-dimensional dataset. Instead, local regression models, each focused on a separate area of input space, often work better since the behaviour of different areas may vary. Classical local models such as Mixture of Experts segment the input space automatically, which is not always effective and it also lacks involvement of the domain experts to guide a meaningful segmentation of the input space. In this paper we addresses this issue by allowing domain experts to interactively segment the input space using data visualisation. The segmentation output obtained is then further used to develop effective local regression models.

An artificial neural network stratifies the risks of reintervention and mortality after endovascular aneurysm repair:a retrospective observational study

Background Lifelong surveillance after endovascular repair (EVAR) of abdominal aortic aneurysms (AAA) is considered mandatory to detect potentially life-threatening endograft complications. A minority of patients require reintervention but cannot be predictively identified by existing methods. This study aimed to improve the prediction of endograft complications and mortality, through the application of machine-learning techniques. Methods Patients undergoing EVAR at 2 centres were studied from 2004-2010. Pre-operative aneurysm morphology was quantified and endograft complications were recorded up to 5 years following surgery. An artificial neural networks (ANN) approach was used to predict whether patients would be at low- or high-risk of endograft complications (aortic/limb) or mortality. Centre 1 data were used for training and centre 2 data for validation. ANN performance was assessed by Kaplan-Meier analysis to compare the incidence of aortic complications, limb complications, and mortality; in patients predicted to be low-risk, versus those predicted to be high-risk. Results 761 patients aged 75 +/- 7 years underwent EVAR. Mean follow-up was 36+/- 20 months. An ANN was created from morphological features including angulation/length/areas/diameters/ volume/tortuosity of the aneurysm neck/sac/iliac segments. ANN models predicted endograft complications and mortality with excellent discrimination between a low-risk and high-risk group. In external validation, the 5-year rates of freedom from aortic complications, limb complications and mortality were 95.9% vs 67.9%; 99.3% vs 92.0%; and 87.9% vs 79.3% respectively (p0.001) Conclusion This study presents ANN models that stratify the 5-year risk of endograft complications or mortality using routinely available pre-operative data.

High-accuracy discrimination of Parkinson’s Disease participants from healthy controls using smartphones

Objective: To test the practicality and effectiveness of cheap, ubiquitous, consumer-grade smartphones to discriminate Parkinson’s disease (PD) subjects from healthy controls, using self-administered tests of gait and postural sway. Background: Existing tests for the diagnosis of PD are based on subjective neurological examinations, performed in-clinic. Objective movement symptom severity data, collected using widely-accessible technologies such as smartphones, would enable the remote characterization of PD symptoms based on self-administered, behavioral tests. Smartphones, when backed up by interviews using web-based videoconferencing, could make it feasible for expert neurologists to perform diagnostic testing on large numbers of individuals at low cost. However, to date, the compliance rate of testing using smart-phones has not been assessed. Methods: We conducted a one-month controlled study with twenty participants, comprising 10 PD subjects and 10 controls. All participants were provided identical LG Optimus S smartphones, capable of recording tri-axial acceleration. Using these smartphones, patients conducted self-administered, short (less than 5 minute) controlled gait and postural sway tests. We analyzed a wide range of summary measures of gait and postural sway from the accelerometry data. Using statistical machine learning techniques, we identified discriminating patterns in the summary measures in order to distinguish PD subjects from controls. Results: Compliance was high all 20 participants performed an average of 3.1 tests per day for the duration of the study. Using this test data, we demonstrated cross-validated sensitivity of 98% and specificity of 98% in discriminating PD subjects from healthy controls. Conclusions: Using consumer-grade smartphone accelerometers, it is possible to distinguish PD from healthy controls with high accuracy. Since these smartphones are inexpensive (around $30 each) and easily available, and the tests are highly non-invasive and objective, we envisage that this kind of smartphone-based testing could radically increase the reach and effectiveness of experts in diagnosing PD.

Projected sequential Gaussian processes:a C++ tool for interpolation of large datasets with heterogeneous noise

Heterogeneous datasets arise naturally in most applications due to the use of a variety of sensors and measuring platforms. Such datasets can be heterogeneous in terms of the error characteristics and sensor models. Treating such data is most naturally accomplished using a Bayesian or model-based geostatistical approach; however, such methods generally scale rather badly with the size of dataset, and require computationally expensive Monte Carlo based inference. Recently within the machine learning and spatial statistics communities many papers have explored the potential of reduced rank representations of the covariance matrix, often referred to as projected or fixed rank approaches. In such methods the covariance function of the posterior process is represented by a reduced rank approximation which is chosen such that there is minimal information loss. In this paper a sequential Bayesian framework for inference in such projected processes is presented. The observations are considered one at a time which avoids the need for high dimensional integrals typically required in a Bayesian approach. A C++ library, gptk, which is part of the INTAMAP web service, is introduced which implements projected, sequential estimation and adds several novel features. In particular the library includes the ability to use a generic observation operator, or sensor model, to permit data fusion. It is also possible to cope with a range of observation error characteristics, including non-Gaussian observation errors. Inference for the covariance parameters is explored, including the impact of the projected process approximation on likelihood profiles. We illustrate the projected sequential method in application to synthetic and real datasets. Limitations and extensions are discussed. © 2010 Elsevier Ltd.