There has been an increasing interest in semi-supervised learning in the recent years because of the great number of datasets with a large number of unlabeled data but only a few labeled samples. Semi-supervised learning algorithms can work with both types of data, combining them to obtain better performance for both clustering and classification. Also, these datasets commonly have a high number of dimensions. This article presents a new semi-supervised method based on self-organizing maps (SOMs) for clustering and classification, called Semi-Supervised Self-Organizing Map (SS-SOM). The method can dynamically switch between supervised and unsupervised learning during the training according to the availability of the class labels for each pattern. Our results show that the SS-SOM outperforms other semi-supervised methods in conditions in which there is a low amount of labeled samples, also achieving good results when all samples are labeled.

Delay embedding---a method for reconstructing dynamical systems by delay coordinates---is widely used to forecast nonlinear time series as a model-free approach. When multivariate time series are observed, several existing frameworks can be applied to yield a single forecast combining multiple forecasts derived from various embeddings. However, the performance of these frameworks is not always satisfactory because they randomly select embeddings or use brute force and do not consider the diversity of the embeddings to combine. Herein, we develop a forecasting framework that overcomes these existing problems. The framework exploits various "suboptimal embeddings" obtained by minimizing the in-sample error via combinatorial optimization. The framework achieves the best results among existing frameworks for sample toy datasets and a real-world flood dataset. We show that the framework is applicable to a wide range of data lengths and dimensions. Therefore, the framework can be applied to various fields such as neuroscience, ecology, finance, fluid dynamics, weather, and disaster prevention.

Mixtures of Gaussian distributions are a popular choice in model-based clustering. Outliers can affect parameters estimation and, as such, must be accounted for. Algorithms such as TCLUST discern the most likely outliers, but only when the proportion of outlying points is known \textit{a priori}. It is proved that, for a finite Gaussian mixture model, the log-likelihoods of the subset models are beta-distributed. An algorithm is then proposed that predicts the proportion of outliers by measuring the adherence of a set of subset log-likelihoods to a beta reference distribution. This algorithm removes the least likely points, which are deemed outliers, until model assumptions are met.

This work aims at solving the problems with intractable sparsity-inducing norms that are often encountered in various machine learning tasks, such as multi-task learning, subspace clustering, feature selection, robust principal component analysis, and so on. Specifically, an Iteratively Re-Weighted method (IRW) with solid convergence guarantee is provided. We investigate its convergence speed via numerous experiments on real data. Furthermore, in order to validate the practicality of IRW, we use it to solve a concrete robust feature selection model with complicated objective function. The experimental results show that the model coupled with proposed optimization method outperforms alternative methods significantly.

Tensor (multidimensional arrays) are generalizations of vectors and matrices, which can be used as a powerful tool in modeling multidimensional data such as videos [29], color images [36, 40], hyperspectral images [11, 35, 49], and electroencephalography (EEG) [8]. Based on its multilinear algebraic properties, a tensor can take full advantage of its structures to provide better understanding and higher accuracy of the multidimensional data. In many tensor data applications [9, 20, 27, 33, 37, 40, 41, 47, 50], tensor data sets are often corrupted and/or incomplete owing to various unpredictable or unavoidable situations. It is motivated us to perform tensor completion and tensor robust principal component analysis for multidimensional data processing. Compared with matrix completion and robust principal component analysis, tensor completion and tensor robust principal component analysis are far from being well-studied. The main issues are the definitions of tensor ranks and tensor decompositions.

Large scale online kernel learning aims to build an efficient and scalable kernel-based predictive model incrementally from a sequence of potentially infinite data points. To achieve this aim, the method must be able to deal with a potentially infinite number of support vectors. The current state-of-the-art is unable to deal with even a moderate number of support vectors. This paper identifies the root cause of the current methods, i.e., the type of kernel used which has a feature map of infinite dimensionality. With this revelation and together with our discovery that a recently introduced Isolation Kernel has a finite feature map, to achieve the above aim of large scale online kernel learning becomes extremely simple---simply use Isolation Kernel instead of kernels having infinite feature map. We show for the first time that online kernel learning is able to deal with a potentially infinite number of support vectors.

Many computational models were proposed to extract temporal patterns from clinical time series for each patient and among patient group for predictive healthcare. However, the common relations among patients (e.g., share the same doctor) were rarely considered. In this paper, we represent patients and clinicians relations by bipartite graphs addressing for example from whom a patient get a diagnosis. We then solve for the top eigenvectors of the graph Laplacian, and include the eigenvectors as latent representations of the similarity between patient-clinician pairs into a time-sensitive prediction model. We conducted experiments using real-world data to predict the initiation of first-line treatment for Chronic Lymphocytic Leukemia (CLL) patients. Results show that relational similarity can improve prediction over multiple baselines, for example a 5% incremental over long-short term memory baseline in terms of area under precision-recall curve.

In the recent years, there is a growing interest in semi-supervised learning, since, in many learning tasks, there is a plentiful supply of unlabeled data, but insufficient labeled ones. Hence, Semi-Supervised learning models can benefit from both types of data to improve the obtained performance. Also, it is important to develop methods that are easy to parameterize in a way that is robust to the different characteristics of the data at hand. This article presents a new method based on Self-Organizing Map (SOM) for clustering and classification, called Adaptive Local Thresholds Semi-Supervised Self-Organizing Map (ALTSS-SOM). It can dynamically switch between two forms of learning at training time, according to the availability of labels, as in previous models, and can automatically adjust itself to the local variance observed in each data cluster. The results show that the ALTSS-SOM surpass the performance of other semi-supervised methods in terms of classification, and other pure clustering methods when there are no labels available, being also less sensitive than previous methods to the parameters values.

New methods for time-to-event prediction are proposed by extending the Cox proportional hazards model with neural networks. Building on methodology from nested case-control studies, we propose a loss function that scales well to large data sets, and enables fitting of both proportional and non-proportional extensions of the Cox model. Through simulation studies, the proposed loss function is verified to be a good approximation for the Cox partial log-likelihood. The proposed methodology is compared to existing methodologies on real-world data sets, and is found to be highly competitive, typically yielding the best performance in terms of Brier score and binomial log-likelihood. A python package for the proposed methods is available at https://github.com/havakv/pycox.

Many sequential decision-making tasks require choosing at each decision step the right action out of the vast set of possibilities by extracting actionable intelligence from high-dimensional data streams. Most of the times, the high-dimensionality of actions and data makes learning of the optimal actions by traditional learning methods impracticable. In this work, we investigate how to discover and leverage the low-dimensional structure in actions and data to enable fast learning. As our learning model, we consider a structured contextual multi-armed bandit (CMAB) with high-dimensional arm (action) and context (data) sets, where the rewards depend only on a few relevant dimensions of the joint context-arm set. We depart from the prior work by assuming a high-dimensional and uncountable arm set, and allow relevant context dimensions to vary for each arm. We propose a new online learning algorithm called CMAB with Relevance Learning (CMAB-RL) and prove that its time-averaged regret asymptotically goes to zero. CMAB-RL enjoys a substantially improved regret bound compared to classical CMAB algorithms whose regrets depend on the dimensions $d_x$ and $d_a$ of the context and arm sets. Importantly, we show that if the learner knows upper bounds $\overline{d}_x$ and $\overline{d}_a$ on the number of relevant context and arm dimensions, then CMAB-RL achieves $\tilde{O}(T^{1 - 1 /(2 + 2\overline{d}_x + \overline{d}_a)})$ regret. Finally, we illustrate how CMAB algorithms can be used for optimal personalized blood glucose control in type 1 diabetes mellitus patients, and show that CMAB-RL outperforms other contextual MAB algorithms in this task, where the contexts represent multimodal physiological data streams obtained from sensor readings and the arms represent bolus insulin doses that are appropriate for injection.