Statistical learning theory for geospatial data. Case study: Aral sea

In recent years there has been an explosive growth in the development of adaptive and data driven methods. One of the efficient and data-driven approaches is based on statistical learning theory (Vapnik 1998). The theory is based on Structural Risk Minimisation (SRM) principle and has a solid statistical background. When applying SRM we are trying not only to reduce training error ? to fit the available data with a model, but also to reduce the complexity of the model and to reduce generalisation error. Many nonlinear learning procedures recently developed in neural networks and statistics can be understood and interpreted in terms of the structural risk minimisation inductive principle. A recent methodology based on SRM is called Support Vector Machines (SVM). At present SLT is still under intensive development and SVM find new areas of application (www.kernel-machines.org). SVM develop robust and non linear data models with excellent generalisation abilities that is very important both for monitoring and forecasting. SVM are extremely good when input space is high dimensional and training data set i not big enough to develop corresponding nonlinear model. Moreover, SVM use only support vectors to derive decision boundaries. It opens a way to sampling optimization, estimation of noise in data, quantification of data redundancy etc. Presentation of SVM for spatially distributed data is given in (Kanevski and Maignan 2004).

Mapping of Environmental Data Using Kernel-Based Methods

Recently, kernel-based Machine Learning methods have gained great popularity in many data analysis and data mining fields: pattern recognition, biocomputing, speech and vision, engineering, remote sensing etc. The paper describes the use of kernel methods to approach the processing of large datasets from environmental monitoring networks. Several typical problems of the environmental sciences and their solutions provided by kernel-based methods are considered: classification of categorical data (soil type classification), mapping of environmental and pollution continuous information (pollution of soil by radionuclides), mapping with auxiliary information (climatic data from Aral Sea region). The promising developments, such as automatic emergency hot spot detection and monitoring network optimization are discussed as well.

Automatic classification of MR scans in Alzheimer's disease.

To be diagnostically useful, structural MRI must reliably distinguish Alzheimer's disease (AD) from normal aging in individual scans. Recent advances in statistical learning theory have led to the application of support vector machines to MRI for detection of a variety of disease states. The aims of this study were to assess how successfully support vector machines assigned individual diagnoses and to determine whether data-sets combined from multiple scanners and different centres could be used to obtain effective classification of scans. We used linear support vector machines to classify the grey matter segment of T1-weighted MR scans from pathologically proven AD patients and cognitively normal elderly individuals obtained from two centres with different scanning equipment. Because the clinical diagnosis of mild AD is difficult we also tested the ability of support vector machines to differentiate control scans from patients without post-mortem confirmation. Finally we sought to use these methods to differentiate scans between patients suffering from AD from those with frontotemporal lobar degeneration. Up to 96% of pathologically verified AD patients were correctly classified using whole brain images. Data from different centres were successfully combined achieving comparable results from the separate analyses. Importantly, data from one centre could be used to train a support vector machine to accurately differentiate AD and normal ageing scans obtained from another centre with different subjects and different scanner equipment. Patients with mild, clinically probable AD and age/sex matched controls were correctly separated in 89% of cases which is compatible with published diagnosis rates in the best clinical centres. This method correctly assigned 89% of patients with post-mortem confirmed diagnosis of either AD or frontotemporal lobar degeneration to their respective group. Our study leads to three conclusions: Firstly, support vector machines successfully separate patients with AD from healthy aging subjects. Secondly, they perform well in the differential diagnosis of two different forms of dementia. Thirdly, the method is robust and can be generalized across different centres. This suggests an important role for computer based diagnostic image analysis for clinical practice.

Analysis, modelling and classification of geospatial data using machine learning

The research considers the problem of spatial data classification using machine learning algorithms: probabilistic neural networks (PNN) and support vector machines (SVM). As a benchmark model simple k-nearest neighbor algorithm is considered. PNN is a neural network reformulation of well known nonparametric principles of probability density modeling using kernel density estimator and Bayesian optimal or maximum a posteriori decision rules. PNN is well suited to problems where not only predictions but also quantification of accuracy and integration of prior information are necessary. An important property of PNN is that they can be easily used in decision support systems dealing with problems of automatic classification. Support vector machine is an implementation of the principles of statistical learning theory for the classification tasks. Recently they were successfully applied for different environmental topics: classification of soil types and hydro-geological units, optimization of monitoring networks, susceptibility mapping of natural hazards. In the present paper both simulated and real data case studies (low and high dimensional) are considered. The main attention is paid to the detection and learning of spatial patterns by the algorithms applied.

Estimation of the noisy component of anatomical backgrounds.

The knowledge of the relationship that links radiation dose and image quality is a prerequisite to any optimization of medical diagnostic radiology. Image quality depends, on the one hand, on the physical parameters such as contrast, resolution, and noise, and on the other hand, on characteristics of the observer that assesses the image. While the role of contrast and resolution is precisely defined and recognized, the influence of image noise is not yet fully understood. Its measurement is often based on imaging uniform test objects, even though real images contain anatomical backgrounds whose statistical nature is much different from test objects used to assess system noise. The goal of this study was to demonstrate the importance of variations in background anatomy by quantifying its effect on a series of detection tasks. Several types of mammographic backgrounds and signals were examined by psychophysical experiments in a two-alternative forced-choice detection task. According to hypotheses concerning the strategy used by the human observers, their signal to noise ratio was determined. This variable was also computed for a mathematical model based on the statistical decision theory. By comparing theoretical model and experimental results, the way that anatomical structure is perceived has been analyzed. Experiments showed that the observer's behavior was highly dependent upon both system noise and the anatomical background. The anatomy partly acts as a signal recognizable as such and partly as a pure noise that disturbs the detection process. This dual nature of the anatomy is quantified. It is shown that its effect varies according to its amplitude and the profile of the object being detected. The importance of the noisy part of the anatomy is, in some situations, much greater than the system noise. Hence, reducing the system noise by increasing the dose will not improve task performance. This observation indicates that the tradeoff between dose and image quality might be optimized by accepting a higher system noise. This could lead to a better resolution, more contrast, or less dose.

Kernel-based Mapping of Meteorological Fields in Complex Orography

Due to the advances in sensor networks and remote sensing technologies, the acquisition and storage rates of meteorological and climatological data increases every day and ask for novel and efficient processing algorithms. A fundamental problem of data analysis and modeling is the spatial prediction of meteorological variables in complex orography, which serves among others to extended climatological analyses, for the assimilation of data into numerical weather prediction models, for preparing inputs to hydrological models and for real time monitoring and short-term forecasting of weather.In this thesis, a new framework for spatial estimation is proposed by taking advantage of a class of algorithms emerging from the statistical learning theory. Nonparametric kernel-based methods for nonlinear data classification, regression and target detection, known as support vector machines (SVM), are adapted for mapping of meteorological variables in complex orography.With the advent of high resolution digital elevation models, the field of spatial prediction met new horizons. In fact, by exploiting image processing tools along with physical heuristics, an incredible number of terrain features which account for the topographic conditions at multiple spatial scales can be extracted. Such features are highly relevant for the mapping of meteorological variables because they control a considerable part of the spatial variability of meteorological fields in the complex Alpine orography. For instance, patterns of orographic rainfall, wind speed and cold air pools are known to be correlated with particular terrain forms, e.g. convex/concave surfaces and upwind sides of mountain slopes.Kernel-based methods are employed to learn the nonlinear statistical dependence which links the multidimensional space of geographical and topographic explanatory variables to the variable of interest, that is the wind speed as measured at the weather stations or the occurrence of orographic rainfall patterns as extracted from sequences of radar images. Compared to low dimensional models integrating only the geographical coordinates, the proposed framework opens a way to regionalize meteorological variables which are multidimensional in nature and rarely show spatial auto-correlation in the original space making the use of classical geostatistics tangled.The challenges which are explored during the thesis are manifolds. First, the complexity of models is optimized to impose appropriate smoothness properties and reduce the impact of noisy measurements. Secondly, a multiple kernel extension of SVM is considered to select the multiscale features which explain most of the spatial variability of wind speed. Then, SVM target detection methods are implemented to describe the orographic conditions which cause persistent and stationary rainfall patterns. Finally, the optimal splitting of the data is studied to estimate realistic performances and confidence intervals characterizing the uncertainty of predictions.The resulting maps of average wind speeds find applications within renewable resources assessment and opens a route to decrease the temporal scale of analysis to meet hydrological requirements. Furthermore, the maps depicting the susceptibility to orographic rainfall enhancement can be used to improve current radar-based quantitative precipitation estimation and forecasting systems and to generate stochastic ensembles of precipitation fields conditioned upon the orography.

Robust Nonlinear Mapping of Soil Contamination Using Support Regression

Spatial data analysis mapping and visualization is of great importance in various fields: environment, pollution, natural hazards and risks, epidemiology, spatial econometrics, etc. A basic task of spatial mapping is to make predictions based on some empirical data (measurements). A number of state-of-the-art methods can be used for the task: deterministic interpolations, methods of geostatistics: the family of kriging estimators (Deutsch and Journel, 1997), machine learning algorithms such as artificial neural networks (ANN) of different architectures, hybrid ANN-geostatistics models (Kanevski and Maignan, 2004; Kanevski et al., 1996), etc. All the methods mentioned above can be used for solving the problem of spatial data mapping. Environmental empirical data are always contaminated/corrupted by noise, and often with noise of unknown nature. That's one of the reasons why deterministic models can be inconsistent, since they treat the measurements as values of some unknown function that should be interpolated. Kriging estimators treat the measurements as the realization of some spatial randomn process. To obtain the estimation with kriging one has to model the spatial structure of the data: spatial correlation function or (semi-)variogram. This task can be complicated if there is not sufficient number of measurements and variogram is sensitive to outliers and extremes. ANN is a powerful tool, but it also suffers from the number of reasons. of a special type ? multiplayer perceptrons ? are often used as a detrending tool in hybrid (ANN+geostatistics) models (Kanevski and Maignank, 2004). Therefore, development and adaptation of the method that would be nonlinear and robust to noise in measurements, would deal with the small empirical datasets and which has solid mathematical background is of great importance. The present paper deals with such model, based on Statistical Learning Theory (SLT) - Support Vector Regression. SLT is a general mathematical framework devoted to the problem of estimation of the dependencies from empirical data (Hastie et al, 2004; Vapnik, 1998). SLT models for classification - Support Vector Machines - have shown good results on different machine learning tasks. The results of SVM classification of spatial data are also promising (Kanevski et al, 2002). The properties of SVM for regression - Support Vector Regression (SVR) are less studied. First results of the application of SVR for spatial mapping of physical quantities were obtained by the authorsin for mapping of medium porosity (Kanevski et al, 1999), and for mapping of radioactively contaminated territories (Kanevski and Canu, 2000). The present paper is devoted to further understanding of the properties of SVR model for spatial data analysis and mapping. Detailed description of the SVR theory can be found in (Cristianini and Shawe-Taylor, 2000; Smola, 1996) and basic equations for the nonlinear modeling are given in section 2. Section 3 discusses the application of SVR for spatial data mapping on the real case study - soil pollution by Cs137 radionuclide. Section 4 discusses the properties of the modelapplied to noised data or data with outliers.

Advances in Sequence Analysis: Theory, Methods, Applications

This book gives a general view of sequence analysis, the statistical study of successions of states or events. It includes innovative contributions on life course studies, transitions into and out of employment, contemporaneous and historical careers, and political trajectories. The approach presented in this book is now central to the life-course perspective and the study of social processes more generally. This volume promotes the dialogue between approaches to sequence analysis that developed separately, within traditions contrasted in space and disciplines. It includes the latest developments in sequential concepts, coding, atypical datasets and time patterns, optimal matching and alternative algorithms, survey optimization, and visualization. Field studies include original sequential material related to parenting in 19th-century Belgium, higher education and work in Finland and Italy, family formation before and after German reunification, French Jews persecuted in occupied France, long-term trends in electoral participation, and regime democratization. Overall the book reassesses the classical uses of sequences and it promotes new ways of collecting, formatting, representing and processing them. The introduction provides basic sequential concepts and tools, as well as a history of the method. Chapters are presented in a way that is both accessible to the beginner and informative to the expert.

ROBETH: un logiciel pour les procédés statistiques robustes [ROBETH: a library for robust statistical procedures].

In the past 20 years the theory of robust estimation has become an important topic of mathematical statistics. We discuss here some basic concepts of this theory with the help of simple examples. Furthermore we describe a subroutine library for the application of robust statistical procedures, which was developed with the support of the Swiss National Science Foundation.

P value and the theory of hypothesis testing: an explanation for new researchers.

In the 1920s, Ronald Fisher developed the theory behind the p value and Jerzy Neyman and Egon Pearson developed the theory of hypothesis testing. These distinct theories have provided researchers important quantitative tools to confirm or refute their hypotheses. The p value is the probability to obtain an effect equal to or more extreme than the one observed presuming the null hypothesis of no effect is true; it gives researchers a measure of the strength of evidence against the null hypothesis. As commonly used, investigators will select a threshold p value below which they will reject the null hypothesis. The theory of hypothesis testing allows researchers to reject a null hypothesis in favor of an alternative hypothesis of some effect. As commonly used, investigators choose Type I error (rejecting the null hypothesis when it is true) and Type II error (accepting the null hypothesis when it is false) levels and determine some critical region. If the test statistic falls into that critical region, the null hypothesis is rejected in favor of the alternative hypothesis. Despite similarities between the two, the p value and the theory of hypothesis testing are different theories that often are misunderstood and confused, leading researchers to improper conclusions. Perhaps the most common misconception is to consider the p value as the probability that the null hypothesis is true rather than the probability of obtaining the difference observed, or one that is more extreme, considering the null is true. Another concern is the risk that an important proportion of statistically significant results are falsely significant. Researchers should have a minimum understanding of these two theories so that they are better able to plan, conduct, interpret, and report scientific experiments.

Implementing statistical learning methods through Bayesian networks. Part 1: a guide to Bayesian parameter estimation using forensic science data

As a thorough aggregation of probability and graph theory, Bayesian networks currently enjoy widespread interest as a means for studying factors that affect the coherent evaluation of scientific evidence in forensic science. Paper I of this series of papers intends to contribute to the discussion of Bayesian networks as a framework that is helpful for both illustrating and implementing statistical procedures that are commonly employed for the study of uncertainties (e.g. the estimation of unknown quantities). While the respective statistical procedures are widely described in literature, the primary aim of this paper is to offer an essentially non-technical introduction on how interested readers may use these analytical approaches - with the help of Bayesian networks - for processing their own forensic science data. Attention is mainly drawn to the structure and underlying rationale of a series of basic and context-independent network fragments that users may incorporate as building blocs while constructing larger inference models. As an example of how this may be done, the proposed concepts will be used in a second paper (Part II) for specifying graphical probability networks whose purpose is to assist forensic scientists in the evaluation of scientific evidence encountered in the context of forensic document examination (i.e. results of the analysis of black toners present on printed or copied documents).