The classical problem of learning a classifier relies on a set of labelled examples, without ever questioning the correctness of the provided label assignments. However, there is an increasing realisation that labelling errors are not uncommon in real situations. In this paper we consider a label-noise robust version of the logistic regression and multinomial logistic regression classifiers and develop the following contributions: (i) We derive efficient multiplicative updates to estimate the label flipping probabilities, and we give a proof of convergence for our algorithm. (ii) We develop a novel sparsity-promoting regularisation approach which allows us to tackle challenging high dimensional noisy settings. (iii) Finally, we throughly evaluate the performance of our approach in synthetic experiments and we demonstrate several real applications including gene expression analysis, class topology discovery and learning from crowdsourcing data.

Estimations of distribution algorithms (EDAs) are a major branch of evolutionary algorithms (EA) with some unique advantages in principle. They are able to take advantage of correlation structure to drive the search more efficiently, and they are able to provide insights about the structure of the search space. However, model building in high dimensions is extremely challenging, and as a result existing EDAs may become less attractive in large-scale problems because of the associated large computational requirements. Large-scale continuous global optimisation is key to many modern-day real-world problems. Scaling up EAs to large-scale problems has become one of the biggest challenges of the field. This paper pins down some fundamental roots of the problem and makes a start at developing a new and generic framework to yield effective and efficient EDA-type algorithms for large-scale continuous global optimisation problems. Our concept is to introduce an ensemble of random projections to low dimensions of the set of fittest search points as a basis for developing a new and generic divide-and-conquer methodology. Our ideas are rooted in the theory of random projections developed in theoretical computer science, and in developing and analysing our framework we exploit some recent results in nonasymptotic random matrix theory.

Supplementary data are available at Bioinformatics online.

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The classical machinery of supervised learning machines relies on a correct set of training labels. Unfortunately, there is no guarantee that all of the labels are correct. Labelling errors are increasingly noticeable in today's classification tasks, as the scale and difficulty of these tasks increases so much that perfect label assignment becomes nearly impossible. Several algorithms have been proposed to alleviate the problem, of which a robust Kernel Fisher Discriminant is a successful example. However, for classification, discriminative models are of primary interest, and rather curiously, the very few existing label-robust discriminative classifiers are limited to linear problems.In this paper, we build on the widely used and successful kernelising technique to introduce a label-noise robust Kernel Logistic Regression classifier. The main difficulty that we need to bypass is how to determine the model complexity parameters when no trusted validation set is available. We propose to adapt the Multiple Kernel Learning approach for this new purpose, together with a Bayesian regularisation scheme. Empirical results on 13 benchmark data sets and two real-world applications demonstrate the success of our approach.