We present a novel approach to learn binary classifiers when only positive and unlabeled instances are available (PU learning). This problem is routinely cast as a supervised task with label noise in the negative set. We use an ensemble of SVM models trained on bootstrap resamples of the training data for increased robustness against label noise. The approach can be considered in a bagging framework which provides an intuitive explanation for its mechanics in a semi-supervised setting. We compared our method to state-of-the-art approaches in simulations using multiple public benchmark data sets. The included benchmark comprises three settings with increasing label noise: (i) fully supervised, (ii) PU learning and (iii) PU learning with false positives. Our approach shows a marginal improvement over existing methods in the second setting and a significant improvement in the third. Frank De Smet is a member of the medical management department of the National Alliance of Christian Mutualities. Accepted at Neurocomputing: SI on Advances in Learning with Label Noise 20/10/2014 1. Introduction Training binary classifiers on positive and unlabeled data is referred to as PU learning [31]. The absence of known negative training instances warrants appropriate learning methods. Inaccurate label information can be more problematic than attribute noise [45]. Specialised PU learning approaches are recommended when (i) negative labels cannot be acquired, (ii) the training data contains a large amount of false negatives or (iii) the positive set has many outliers. Practical applications of PU learning typically feature large, imbalanced training sets with a small amount of labeled (positive) and a large amount of unlabeled training instances. The PU learning problem arises in various settings, including web page classification [44], intrusion detection [26] and bioinformatics tasks such as variant prioritization [42], gene prioritization [1, 35] and virtual screening of drug compounds [41]. Though these applications share a common underlying learning problem, the final evaluation criteria may be fundamentally different.

The classical approach to inverse problems is based on the optimization of a misfit function. Despite its computational appeal, such an approach suffers from many shortcomings, e.g., non-uniqueness of solutions, modeling prior knowledge, etc. The Bayesian formalism to inverse problems avoids most of the difficulties encountered by the optimization approach, albeit at an increased computational cost. In this work, we use information theoretic arguments to cast the Bayesian inference problem in terms of an optimization problem. The resulting scheme combines the theoretical soundness of fully Bayesian inference with the computational efficiency of a simple optimization.

Objective. The paper investigates the presence of autism using the functional brain connectivity measures derived from electro-encephalogram (EEG) of children during face perception tasks. Approach. Phase synchronized patterns from 128-channel EEG signals are obtained for typical children and children with autism spectrum disorder (ASD). The phase synchronized states or synchrostates temporally switch amongst themselves as an underlying process for the completion of a particular cognitive task. We used 12 subjects in each group (ASD and typical) for analyzing their EEG while processing fearful, happy and neutral faces. The minimal and maximally occurring synchrostates for each subject are chosen for extraction of brain connectivity features, which are used for classification between these two groups of subjects. Among different supervised learning techniques, we here explored the discriminant analysis and support vector machine both with polynomial kernels for the classification task. Main results. The leave one out cross-validation of the classification algorithm gives 94.7% accuracy as the best performance with corresponding sensitivity and specificity values as 85.7% and 100% respectively. Significance. The proposed method gives high classification accuracies and outperforms other contemporary research results. The effectiveness of the proposed method for classification of autistic and typical children suggests the possibility of using it on a larger population to validate it for clinical practice.

A number of representation schemes have been presented for use within Learning Classifier Systems, ranging from binary encodings to neural networks. This paper presents results from an investigation into using a discrete dynamical system representation within the XCS Learning Classifier System. In particular, asynchronous random Boolean networks are used to represent the traditional condition-action production system rules. It is shown possible to use self-adaptive, open-ended evolution to design an ensemble of such discrete dynamical systems within XCS to solve a number of well-known test problems.

We propose a mini-batching scheme for improving the theoretical complexity and practical performance of semi-stochastic gradient descent applied to the problem of minimizing a strongly convex composite function represented as the sum of an average of a large number of smooth convex functions, and simple nonsmooth convex function. Our method first performs a deterministic step (computation of the gradient of the objective function at the starting point), followed by a large number of stochastic steps. The process is repeated a few times with the last iterate becoming the new starting point. The novelty of our method is in introduction of mini-batching into the computation of stochastic steps. In each step, instead of choosing a single function, we sample $b$ functions, compute their gradients, and compute the direction based on this. We analyze the complexity of the method and show that the method benefits from two speedup effects. First, we prove that as long as $b$ is below a certain threshold, we can reach predefined accuracy with less overall work than without mini-batching. Second, our mini-batching scheme admits a simple parallel implementation, and hence is suitable for further acceleration by parallelization.

Logistic regression models with $n$ observations and $q$ linearly-independent covariates are shown to have Fisher information volumes which are bounded below by $\pi^q$ and above by ${n \choose q} \pi^q$. This is proved with a novel generalization of the classical theorems of Pythagoras and de Gua, which is of independent interest. The finding that the volume is always finite is new, and it implies that the volume can be directly interpreted as a measure of model complexity. The volume is shown to be a continuous function of the design matrix $X$ at generic $X$, but to be discontinuous in general. This means that models with sparse design matrices can be significantly less complex than nearby models, so the resulting model-selection criterion prefers sparse models. This is analogous to the way that $\ell^1$-regularisation tends to prefer sparse model fits, though in our case this behaviour arises spontaneously from general principles. Lastly, an unusual topological duality is shown to exist between the ideal boundaries of the natural and expectation parameter spaces of logistic regression models.

Lasso is a widely used regression technique to find sparse representations. When the dimension of the feature space and the number of samples are extremely large, solving the Lasso problem remains challenging. To improve the efficiency of solving large-scale Lasso problems, El Ghaoui and his colleagues have proposed the SAFE rules which are able to quickly identify the inactive predictors, i.e., predictors that have $0$ components in the solution vector. Then, the inactive predictors or features can be removed from the optimization problem to reduce its scale. By transforming the standard Lasso to its dual form, it can be shown that the inactive predictors include the set of inactive constraints on the optimal dual solution. In this paper, we propose an efficient and effective screening rule via Dual Polytope Projections (DPP), which is mainly based on the uniqueness and nonexpansiveness of the optimal dual solution due to the fact that the feasible set in the dual space is a convex and closed polytope. Moreover, we show that our screening rule can be extended to identify inactive groups in group Lasso. To the best of our knowledge, there is currently no "exact" screening rule for group Lasso. We have evaluated our screening rule using synthetic and real data sets. Results show that our rule is more effective in identifying inactive predictors than existing state-of-the-art screening rules for Lasso.

In this study we show that by the current state-of-the-art synthetically generated fingerprints can easily be discriminated from real fingerprints. We propose a method based on second order extended minutiae histograms (MHs) which can distinguish between real and synthetic prints with very high accuracy. MHs provide a fixed-length feature vector for a fingerprint which are invariant under rotation and translation. This 'test of realness' can be applied to synthetic fingerprints produced by any method. In this work, tests are conducted on the 12 publicly available databases of FVC2000, FVC2002 and FVC2004 which are well established benchmarks for evaluating the performance of fingerprint recognition algorithms; 3 of these 12 databases consist of artificial fingerprints generated by the SFinGe software. Additionally, we evaluate the discriminative performance on a database of synthetic fingerprints generated by the software of Bicz versus real fingerprint images. We conclude with suggestions for the improvement of synthetic fingerprint generation.

Frank-Wolfe algorithms for convex minimization have recently gained considerable attention from the Optimization and Machine Learning communities, as their properties make them a suitable choice in a variety of applications. However, as each iteration requires to optimize a linear model, a clever implementation is crucial to make such algorithms viable on large-scale datasets. For this purpose, approximation strategies based on a random sampling have been proposed by several researchers. In this work, we perform an experimental study on the effectiveness of these techniques, analyze possible alternatives and provide some guidelines based on our results.

A reliable human skin detection method that is adaptable to different human skin colours and illu- mination conditions is essential for better human skin segmentation. Even though different human skin colour detection solutions have been successfully applied, they are prone to false skin detection and are not able to cope with the variety of human skin colours across different ethnic. Moreover, existing methods require high computational cost. In this paper, we propose a novel human skin de- tection approach that combines a smoothed 2D histogram and Gaussian model, for automatic human skin detection in colour image(s). In our approach an eye detector is used to refine the skin model for a specific person. The proposed approach reduces computational costs as no training is required; and it improves the accuracy of skin detection despite wide variation in ethnicity and illumination. To the best of our knowledge, this is the first method to employ fusion strategy for this purpose. Qualitative and quantitative results on three standard public datasets and a comparison with state-of-the-art methods have shown the effectiveness and robustness of the proposed approach.