Biomedical subjects

Gavin C Cawley

Publications and source records attributed to Gavin C Cawley.

4 recordsLinked to original sources

PubMed2006

Gene selection in cancer classification using sparse logistic regression with Bayesian regularization.

MOTIVATION: Gene selection algorithms for cancer classification, based on the expression of a small number of biomarker genes, have been the subject of considerable research in recent years. Shevade and Keerthi propose a gene selection algorithm based on sparse logistic regression (SLogReg) incorporating a Laplace prior to promote sparsity in the model parameters, and provide a simple but efficient training procedure. The degree of sparsity obtained is determined by the value of a regularization parameter, which must be carefully tuned in order to optimize performance. This normally involves a model selection stage, based on a computationally intensive search for the minimizer of the cross-validation error. In this paper, we demonstrate that a simple Bayesian approach can be taken to eliminate this regularization parameter entirely, by integrating it out analytically using an uninformative Jeffrey's prior. The improved algorithm (BLogReg) is then typically two or three orders of magnitude faster than the original algorithm, as there is no longer a need for a model selection step. The BLogReg algorithm is also free from selection bias in performance estimation, a common pitfall in the application of machine learning algorithms in cancer classification. RESULTS: The SLogReg, BLogReg and Relevance Vector Machine (RVM) gene selection algorithms are evaluated over the well-studied colon cancer and leukaemia benchmark datasets. The leave-one-out estimates of the probability of test error and cross-entropy of the BLogReg and SLogReg algorithms are very similar, however the BlogReg algorithm is found to be considerably faster than the original SLogReg algorithm. Using nested cross-validation to avoid selection bias, performance estimation for SLogReg on the leukaemia dataset takes almost 48 h, whereas the corresponding result for BLogReg is obtained in only 1 min 24 s, making BLogReg by far the more practical algorithm. BLogReg also demonstrates better estimates of conditional probability than the RVM, which are of great importance in medical applications, with similar computational expense. AVAILABILITY: A MATLAB implementation of the sparse logistic regression algorithm with Bayesian regularization (BLogReg) is available from http://theoval.cmp.uea.ac.uk/~gcc/cbl/blogreg/

Algorithms↗

PubMed2006

Sparse Bayesian kernel survival analysis for modeling the growth domain of microbial pathogens.

Survival analysis is a branch of statistics concerned with the time elapsing before "failure," with diverse applications in medical statistics and the analysis of the reliability of electrical or mechanical components. We introduce a parametric accelerated life survival analysis model based on kernel learning methods that, at least in principal, is able to learn arbitrary dependencies between a vector of explanatory variables and the scale of the distribution of survival times. The proposed kernel survival analysis method is then used to model the growth domain of Clostridium botulinum, the food processing and storage conditions permitting the growth of this foodborne microbial pathogen, leading to the production of the neurotoxin responsible for botulism. A Bayesian training procedure, based on the evidence framework, is used for model selection and to provide a credible interval on model predictions. The kernel survival analysis models are found to be more accurate than models based on more traditional survival analysis techniques but also suggest a risk assessment of the foodborne botulism hazard would benefit from the collection of additional data.

Artificial Intelligence↗

PubMed2004

Fast exact leave-one-out cross-validation of sparse least-squares support vector machines.

Leave-one-out cross-validation has been shown to give an almost unbiased estimator of the generalisation properties of statistical models, and therefore provides a sensible criterion for model selection and comparison. In this paper we show that exact leave-one-out cross-validation of sparse Least-Squares Support Vector Machines (LS-SVMs) can be implemented with a computational complexity of only O(ln2) floating point operations, rather than the O(l2n2) operations of a naïve implementation, where l is the number of training patterns and n is the number of basis vectors. As a result, leave-one-out cross-validation becomes a practical proposition for model selection in large scale applications. For clarity the exposition concentrates on sparse least-squares support vector machines in the context of non-linear regression, but is equally applicable in a pattern recognition setting.

Algorithms↗

PubMedDate not supplied

Constructing Bayesian formulations of sparse kernel learning methods.

We present here a simple technique that simplifies the construction of Bayesian treatments of a variety of sparse kernel learning algorithms. An incomplete Cholesky factorisation is employed to modify the dual parameter space, such that the Gaussian prior over the dual model parameters is whitened. The regularisation term then corresponds to the usual weight-decay regulariser, allowing the Bayesian analysis to proceed via the evidence framework of MacKay. There is in addition a useful by-product associated with the incomplete Cholesky factorisation algorithm, it also identifies a subset of the training data forming an approximate basis for the entire dataset in the kernel-induced feature space, resulting in a sparse model. Bayesian treatments of the kernel ridge regression (KRR) algorithm, with both constant and heteroscedastic (input dependent) variance structures, and kernel logistic regression (KLR) are provided as illustrative examples of the proposed method, which we hope will be more widely applicable.

Algorithms↗