In this paper, we elaborate on the use of the Sugeno integral in the context of machine learning. More specifically, we propose a method for binary classification, in which the Sugeno integral is used as an aggregation function that combines several local evaluations of an instance, pertaining to different features or measurements, into a single global evaluation. Due to the specific nature of the Sugeno integral, this approach is especially suitable for learning from ordinal data, that is, when measurements are taken from ordinal scales. This is a topic that has not received much attention in machine learning so far. The core of the learning problem itself consists of identifying the capacity underlying the Sugeno integral. To tackle this problem, we develop an algorithm based on linear programming. The algorithm also includes a suitable technique for transforming the original feature values into local evaluations (local utility scores), as well as a method for tuning a threshold on the global evaluation. To control the flexibility of the classifier and mitigate the problem of overfitting the training data, we generalize our approach toward $k$-maxitive capacities, where $k$ plays the role of a hyper-parameter of the learner. We present experimental studies, in which we compare our method with competing approaches on several benchmark data sets.

We apply the algorithm Neuroevolution learning literature [5, 6]. of Augmenting Topologies (NEAT) which has not been widely In this paper, we describe development and application of a applied generally in the credit evaluation domain. In addition to technique for learning online (or frequently updated) credit scoring comparing the methodology with other widely applied machine models as new data is read record by record. We describe the learning techniques, we develop and evaluate several approach developed as Online NEAT for Credit Scoring. The enhancements to the algorithm which make it suitable for the approach applies neuro-evolution, a technique that combines neural particular aspects of online learning that are relevant in the networks with evolutionary computation [7].

In this paper we consider an online learning version of the Facility location problem where users need to be served one at a time in a sequence of trials. The goal is to select, at each trial, a subset of a given set of sites, and then pay a loss equal to their total "opening cost" plus the minimum "connection cost" for connecting the user to one of the sites in the subset. More precisely, we are given a set of N sites. At the beginning of each trial, an opening cost and a connection cost for the arriving user are associated with each site and are unknown. At each trial, the learner has to select a subset of sites and incurs a loss given by the minimum connection cost over the selected sites plus the sum of the opening costs of all selected sites. After each subset selection, the opening and connection costs of all sites are revealed. To solve this problem, we design and rigorously analyse an algorithm which belongs to the class of online learning algorithms that make use of the Exponentiated gradient method [15]. We measure, and rigorously analyse, the performance of our method by comparing its cumulative loss with that of any fixed subset of sites.

We investigate whether Jacobi preconditioning, accounting for the bootstrap term in temporal difference (TD) learning, can help boost performance of adaptive optimizers. Our method, TDprop, computes a per parameter learning rate based on the diagonal preconditioning of the TD update rule. We show how this can be used in both $n$-step returns and TD($\lambda$). Our theoretical findings demonstrate that including this additional preconditioning information is, surprisingly, comparable to normal semi-gradient TD if the optimal learning rate is found for both via a hyperparameter search. In Deep RL experiments using Expected SARSA, TDprop meets or exceeds the performance of Adam in all tested games under near-optimal learning rates, but a well-tuned SGD can yield similar improvements -- matching our theory. Our findings suggest that Jacobi preconditioning may improve upon typical adaptive optimization methods in Deep RL, but despite incorporating additional information from the TD bootstrap term, may not always be better than SGD.

Given a convex and differentiable objective $Q(\M)$ for a real, symmetric matrix $\M$ in the positive definite (PD) cone---used to compute Mahalanobis distances---we propose a fast general metric learning framework that is entirely projection-free. We first assume that $\M$ resides in a space $\cS$ of generalized graph Laplacian matrices (graph metric matrices) corresponding to balanced signed graphs. Unlike low-rank metric matrices common in the literature, $\cS$ includes the important diagonal-only matrices as a special case. The key theorem to circumvent full eigen-decomposition and enable fast metric matrix optimization is Gershgorin disc alignment (GDA): given graph metric matrix $\M \in \cS$ and diagonal matrix $\S$, where $S_{ii} = 1/v_i$ and $\v$ is the first eigenvector of $\M$, we prove that Gershgorin disc left-ends of similar transform $\B = \S \M \S^{-1}$ are perfectly aligned at the smallest eigenvalue $\lambda_{\min}$. Using this theorem, we replace the PD cone constraint in the metric learning problem with tightest possible linear constraints per iteration, so that the alternating optimization of the diagonal / off-diagonal terms in $\M$ can be solved efficiently as linear programs via Frank-Wolfe iterations. We update $\v$ using Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) with warm start as matrix entries in $\M$ are optimized successively. Experiments show that our graph metric optimization is significantly faster than cone-projection methods, and produces competitive binary classification performance.

Deep neural networks demonstrated their ability to provide remarkable performances on a wide range of supervised learning tasks (e.g., image classification) when trained on extensive collections of labeled data (e.g., ImageNet). However, creating such large datasets requires a considerable amount of resources, time, and effort. Such resources may not be available in many practical cases, limiting the adoption and the application of many deep learning methods. In a search for more data-efficient deep learning methods to overcome the need for large annotated datasets, there is a rising research interest in semi-supervised learning and its applications to deep neural networks to reduce the amount of labeled data required, by either developing novel methods or adopting existing semi-supervised learning frameworks for a deep learning setting. In this paper, we provide a comprehensive overview of deep semi-supervised learning, starting with an introduction to the field, followed by a summarization of the dominant semi-supervised approaches in deep learning.

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