This paper considers networks where relationships between nodes are represented by directed dissimilarities. The goal is to study methods for the determination of hierarchical clusters, i.e., a family of nested partitions indexed by a connectivity parameter, induced by the given dissimilarity structures. Our construction of hierarchical clustering methods is based on defining admissible methods to be those methods that abide by the axioms of value - nodes in a network with two nodes are clustered together at the maximum of the two dissimilarities between them - and transformation - when dissimilarities are reduced, the network may become more clustered but not less. Several admissible methods are constructed and two particular methods, termed reciprocal and nonreciprocal clustering, are shown to provide upper and lower bounds in the space of admissible methods. Alternative clustering methodologies and axioms are further considered. Allowing the outcome of hierarchical clustering to be asymmetric, so that it matches the asymmetry of the original data, leads to the inception of quasi-clustering methods. The existence of a unique quasi-clustering method is shown. Allowing clustering in a two-node network to proceed at the minimum of the two dissimilarities generates an alternative axiomatic construction. There is a unique clustering method in this case too. The paper also develops algorithms for the computation of hierarchical clusters using matrix powers on a min-max dioid algebra and studies the stability of the methods proposed. We proved that most of the methods introduced in this paper are such that similar networks yield similar hierarchical clustering results. Algorithms are exemplified through their application to networks describing internal migration within states of the United States (U.S.) and the interrelation between sectors of the U.S. economy.

The support vector machine (SVM) is one of the most successful learning methods for solving classification problems. Despite its popularity, SVM has a serious drawback, that is sensitivity to outliers in training samples. The penalty on misclassification is defined by a convex loss called the hinge loss, and the unboundedness of the convex loss causes the sensitivity to outliers. To deal with outliers, robust variants of SVM have been proposed, such as the robust outlier detection algorithm and an SVM with a bounded loss called the ramp loss. In this paper, we propose a robust variant of SVM and investigate its robustness in terms of the breakdown point. The breakdown point is a robustness measure that is the largest amount of contamination such that the estimated classifier still gives information about the non-contaminated data. The main contribution of this paper is to show an exact evaluation of the breakdown point for the robust SVM. For learning parameters such as the regularization parameter in our algorithm, we derive a simple formula that guarantees the robustness of the classifier. When the learning parameters are determined with a grid search using cross validation, our formula works to reduce the number of candidate search points. The robustness of the proposed method is confirmed in numerical experiments. We show that the statistical properties of the robust SVM are well explained by a theoretical analysis of the breakdown point.

Information theory provides principled ways to analyze different inference and learning problems such as hypothesis testing, clustering, dimensionality reduction, classification, among others. However, the use of information theoretic quantities as test statistics, that is, as quantities obtained from empirical data, poses a challenging estimation problem that often leads to strong simplifications such as Gaussian models, or the use of plug in density estimators that are restricted to certain representation of the data. In this paper, a framework to non-parametrically obtain measures of entropy directly from data using operators in reproducing kernel Hilbert spaces defined by infinitely divisible kernels is presented. The entropy functionals, which bear resemblance with quantum entropies, are defined on positive definite matrices and satisfy similar axioms to those of Renyi's definition of entropy. Convergence of the proposed estimators follows from concentration results on the difference between the ordered spectrum of the Gram matrices and the integral operators associated to the population quantities. In this way, capitalizing on both the axiomatic definition of entropy and on the representation power of positive definite kernels, the proposed measure of entropy avoids the estimation of the probability distribution underlying the data. Moreover, estimators of kernel-based conditional entropy and mutual information are also defined. Numerical experiments on independence tests compare favourably with state of the art.

Multi-task learning (MTL) aims to improve generalization performance by learning multiple related tasks simultaneously. While sometimes the underlying task relationship structure is known, often the structure needs to be estimated from data at hand. In this paper, we present a novel family of models for MTL, applicable to regression and classification problems, capable of learning the structure of task relationships. In particular, we consider a joint estimation problem of the task relationship structure and the individual task parameters, which is solved using alternating minimization. The task relationship structure learning component builds on recent advances in structure learning of Gaussian graphical models based on sparse estimators of the precision (inverse covariance) matrix. We illustrate the effectiveness of the proposed model on a variety of synthetic and benchmark datasets for regression and classification. We also consider the problem of combining climate model outputs for better projections of future climate, with focus on temperature in South America, and show that the proposed model outperforms several existing methods for the problem.

This paper presents a new classification methods for Event Related Potentials (ERP) based on an Information geometry framework. Through a new estimation of covariance matrices, this work extend the use of Riemannian geometry, which was previously limited to SMR-based BCI, to the problem of classification of ERPs. As compared to the state-of-the-art, this new method increases performance, reduces the number of data needed for the calibration and features good generalisation across sessions and subjects. This method is illustrated on data recorded with the P300-based game brain invaders. Finally, an online and adaptive implementation is described, where the BCI is initialized with generic parameters derived from a database and continuously adapt to the individual, allowing the user to play the game without any calibration while keeping a high accuracy.

Subjective Well-being(SWB), which refers to how people experience the quality of their lives, is of great use to public policy-makers as well as economic, sociological research, etc. Traditionally, the measurement of SWB relies on time-consuming and costly self-report questionnaires. Nowadays, people are motivated to share their experiences and feelings on social media, so we propose to sense SWB from the vast user generated data on social media. By utilizing 1785 users' social media data with SWB labels, we train machine learning models that are able to "sense" individual SWB from users' social media. Our model, which attains the state-by-art prediction accuracy, can then be used to identify SWB of large population of social media users in time with very low cost.

The paper demonstrates that falsifiability is fundamental to learning. We prove the following theorem for statistical learning and sequential prediction: If a theory is falsifiable then it is learnable -- i.e. admits a strategy that predicts optimally. An analogous result is shown for universal induction.

The task of estimating a matrix given a sample of observed entries is known as the \emph{matrix completion problem}. Most works on matrix completion have focused on recovering an unknown real-valued low-rank matrix from a random sample of its entries. Here, we investigate the case of highly quantized observations when the measurements can take only a small number of values. These quantized outputs are generated according to a probability distribution parametrized by the unknown matrix of interest. This model corresponds, for example, to ratings in recommender systems or labels in multi-class classification. We consider a general, non-uniform, sampling scheme and give theoretical guarantees on the performance of a constrained, nuclear norm penalized maximum likelihood estimator. One important advantage of this estimator is that it does not require knowledge of the rank or an upper bound on the nuclear norm of the unknown matrix and, thus, it is adaptive. We provide lower bounds showing that our estimator is minimax optimal. An efficient algorithm based on lifted coordinate gradient descent is proposed to compute the estimator. A limited Monte-Carlo experiment, using both simulated and real data is provided to support our claims.

Extreme learning machine (ELM) as a neural network algorithm has shown its good performance, such as fast speed, simple structure etc, but also, weak robustness is an unavoidable defect in original ELM for blended data. We present a new machine learning framework called LARSEN-ELM for overcoming this problem. In our paper, we would like to show two key steps in LARSEN-ELM. In the first step, preprocessing, we select the input variables highly related to the output using least angle regression (LARS). In the second step, training, we employ Genetic Algorithm (GA) based selective ensemble and original ELM. In the experiments, we apply a sum of two sines and four datasets from UCI repository to verify the robustness of our approach. The experimental results show that compared with original ELM and other methods such as OP-ELM, GASEN-ELM and LSBoost, LARSEN-ELM significantly improve robustness performance while keeping a relatively high speed.

We use a semisupervised learning algorithm based on a topological data analysis approach to assign functional categories to yeast proteins using similarity graphs. This new approach to analyzing biological networks yields results that are as good as or better than state of the art existing approaches.