Kernel learning at the first level of inference

Kernel learning methods, whether Bayesian or frequentist, typically involve multiple levels of inference, with the coefficients of the kernel expansion being determined at the first level and the kernel and regularisation parameters carefully tuned at the second level, a process known as model selection. Model selection for kernel machines is commonly performed via optimisation of a suitable model selection criterion, often based on cross-validation or theoretical performance bounds. However, if there are a large number of kernel parameters, as for instance in the case of automatic relevance determination (ARD), there is a substantial risk of over-fitting the model selection criterion, resulting in poor generalisation performance. In this paper we investigate the possibility of learning the kernel, for the Least-Squares Support Vector Machine (LS-SVM) classifier, at the first level of inference, i.e.parameter optimisation. The kernel parameters and the coefficients of the kernel expansion are jointly optimised at the first level of inference, minimising a training criterion with an additional regularisation term acting on the kernel parameters. The key advantage of this approach is that the values of only two regularisation parameters need be determined in model selection, substantially alleviating the problem of over-fitting the model selection criterion. The benefits of this approach are demonstrated using a suite of synthetic and real-world binary classification benchmark problems, where kernel learning at the first level of inference is shown to be statistically superior to the conventional approach, improves on our previous work (Cawley and Talbot, 2007) and is competitive with Multiple Kernel Learning approaches, but with reduced computational expense

Outcome prediction based on microarray analysis: a critical perspective on methods

<p>Abstract</p> <p>Background</p> <p>Information extraction from microarrays has not yet been widely used in diagnostic or prognostic decision-support systems, due to the diversity of results produced by the available techniques, their instability on different data sets and the inability to relate statistical significance with biological relevance. Thus, there is an urgent need to address the statistical framework of microarray analysis and identify its drawbacks and limitations, which will enable us to thoroughly compare methodologies under the same experimental set-up and associate results with confidence intervals meaningful to clinicians. In this study we consider gene-selection algorithms with the aim to reveal inefficiencies in performance evaluation and address aspects that can reduce uncertainty in algorithmic validation.</p> <p>Results</p> <p>A computational study is performed related to the performance of several gene selection methodologies on publicly available microarray data. Three basic types of experimental scenarios are evaluated, i.e. the independent test-set and the 10-fold cross-validation (CV) using maximum and average performance measures. Feature selection methods behave differently under different validation strategies. The performance results from CV do not mach well those from the independent test-set, except for the support vector machines (SVM) and the least squares SVM methods. However, these wrapper methods achieve variable (often low) performance, whereas the hybrid methods attain consistently higher accuracies. The use of an independent test-set within CV is important for the evaluation of the predictive power of algorithms. The optimal size of the selected gene-set also appears to be dependent on the evaluation scheme. The consistency of selected genes over variation of the training-set is another aspect important in reducing uncertainty in the evaluation of the derived gene signature. In all cases the presence of outlier samples can seriously affect algorithmic performance.</p> <p>Conclusion</p> <p>Multiple parameters can influence the selection of a gene-signature and its predictive power, thus possible biases in validation methods must always be accounted for. This paper illustrates that independent test-set evaluation reduces the bias of CV, and case-specific measures reveal stability characteristics of the gene-signature over changes of the training set. Moreover, frequency measures on gene selection address the algorithmic consistency in selecting the same gene signature under different training conditions. These issues contribute to the development of an objective evaluation framework and aid the derivation of statistically consistent gene signatures that could eventually be correlated with biological relevance. The benefits of the proposed framework are supported by the evaluation results and methodological comparisons performed for several gene-selection algorithms on three publicly available datasets.</p

Kernel-imbedded Gaussian processes for disease classification using microarray gene expression data

BACKGROUND: Designing appropriate machine learning methods for identifying genes that have a significant discriminating power for disease outcomes has become more and more important for our understanding of diseases at genomic level. Although many machine learning methods have been developed and applied to the area of microarray gene expression data analysis, the majority of them are based on linear models, which however are not necessarily appropriate for the underlying connection between the target disease and its associated explanatory genes. Linear model based methods usually also bring in false positive significant features more easily. Furthermore, linear model based algorithms often involve calculating the inverse of a matrix that is possibly singular when the number of potentially important genes is relatively large. This leads to problems of numerical instability. To overcome these limitations, a few non-linear methods have recently been introduced to the area. Many of the existing non-linear methods have a couple of critical problems, the model selection problem and the model parameter tuning problem, that remain unsolved or even untouched. In general, a unified framework that allows model parameters of both linear and non-linear models to be easily tuned is always preferred in real-world applications. Kernel-induced learning methods form a class of approaches that show promising potentials to achieve this goal. RESULTS: A hierarchical statistical model named kernel-imbedded Gaussian process (KIGP) is developed under a unified Bayesian framework for binary disease classification problems using microarray gene expression data. In particular, based on a probit regression setting, an adaptive algorithm with a cascading structure is designed to find the appropriate kernel, to discover the potentially significant genes, and to make the optimal class prediction accordingly. A Gibbs sampler is built as the core of the algorithm to make Bayesian inferences. Simulation studies showed that, even without any knowledge of the underlying generative model, the KIGP performed very close to the theoretical Bayesian bound not only in the case with a linear Bayesian classifier but also in the case with a very non-linear Bayesian classifier. This sheds light on its broader usability to microarray data analysis problems, especially to those that linear methods work awkwardly. The KIGP was also applied to four published microarray datasets, and the results showed that the KIGP performed better than or at least as well as any of the referred state-of-the-art methods did in all of these cases. CONCLUSION: Mathematically built on the kernel-induced feature space concept under a Bayesian framework, the KIGP method presented in this paper provides a unified machine learning approach to explore both the linear and the possibly non-linear underlying relationship between the target features of a given binary disease classification problem and the related explanatory gene expression data. More importantly, it incorporates the model parameter tuning into the framework. The model selection problem is addressed in the form of selecting a proper kernel type. The KIGP method also gives Bayesian probabilistic predictions for disease classification. These properties and features are beneficial to most real-world applications. The algorithm is naturally robust in numerical computation. The simulation studies and the published data studies demonstrated that the proposed KIGP performs satisfactorily and consistently

Information Theory and Its Application in Machine Condition Monitoring

Condition monitoring of machinery is one of the most important aspects of many modern industries. With the rapid advancement of science and technology, machines are becoming increasingly complex. Moreover, an exponential increase of demand is leading an increasing requirement of machine output. As a result, in most modern industries, machines have to work for 24 hours a day. All these factors are leading to the deterioration of machine health in a higher rate than before. Breakdown of the key components of a machine such as bearing, gearbox or rollers can cause a catastrophic effect both in terms of financial and human costs. In this perspective, it is important not only to detect the fault at its earliest point of inception but necessary to design the overall monitoring process, such as fault classification, fault severity assessment and remaining useful life (RUL) prediction for better planning of the maintenance schedule. Information theory is one of the pioneer contributions of modern science that has evolved into various forms and algorithms over time. Due to its ability to address the non-linearity and non-stationarity of machine health deterioration, it has become a popular choice among researchers. Information theory is an effective technique for extracting features of machines under different health conditions. In this context, this book discusses the potential applications, research results and latest developments of information theory-based condition monitoring of machineries

Geo-Information Technology and Its Applications

Geo-information technology has been playing an ever more important role in environmental monitoring, land resource quantification and mapping, geo-disaster damage and risk assessment, urban planning and smart city development. This book focuses on the fundamental and applied research in these domains, aiming to promote exchanges and communications, share the research outcomes of scientists worldwide and to put these achievements better social use. This Special Issue collects fourteen high-quality research papers and is expected to provide a useful reference and technical support for graduate students, scientists, civil engineers and experts of governments to valorize scientific research