Huge amount of applications in various fields, such as gene expression analysis or computer vision, undergo data sets with high-dimensional low-sample-size (HDLSS), which has putted forward great challenges for standard statistical and modern machine learning methods. In this paper, we propose a novel classification criterion on HDLSS, tolerance similarity, which emphasizes the maximization of within-class variance on the premise of class separability. According to this criterion, a novel linear binary classifier is designed, denoted by No-separated Data Maximum Dispersion classifier (NPDMD). The objective of NPDMD is to find a projecting direction w in which all of training samples scatter in as large an interval as possible. NPDMD has several characteristics compared to the state-of-the-art classification methods. First, it works well on HDLSS. Second, it combines the sample statistical information and local structural information (supporting vectors) into the objective function to find the solution of projecting direction in the whole feature spaces. Third, it solves the inverse of high dimensional matrix in low dimensional space. Fourth, it is relatively simple to be implemented based on Quadratic Programming. Fifth, it is robust to the model specification for various real applications. The theoretical properties of NPDMD are deduced. We conduct a series of evaluations on one simulated and six real-world benchmark data sets, including face classification and mRNA classification. NPDMD outperforms those widely used approaches in most cases, or at least obtains comparable results.

The recent advent of powerful generative models has triggered the renewed development of quantitative measures to assess the proximity of two probability distributions. As the scalar Frechet inception distance remains popular, several methods have explored computing entire curves, which reveal the trade-off between the fidelity and variability of the first distribution with respect to the second one. Several of such variants have been proposed independently and while intuitively similar, their relationship has not yet been made explicit. In an effort to make the emerging picture of generative evaluation more clear, we propose a unification of four curves known respectively as: the precision-recall (PR) curve, the Lorenz curve, the receiver operating characteristic (ROC) curve and a special case of R\'enyi divergence frontiers.

Deep Convolutional Neural Networks (DCNNs) are currently the method of choice both for generative, as well as for discriminative learning in computer vision and machine learning. The success of DCNNs can be attributed to the careful selection of their building blocks (e.g., residual blocks, rectifiers, sophisticated normalization schemes, to mention but a few). In this paper, we propose $\Pi$-Nets, a new class of DCNNs. $\Pi$-Nets are polynomial neural networks, i.e., the output is a high-order polynomial of the input. The unknown parameters, which are naturally represented by high-order tensors, are estimated through a collective tensor factorization with factors sharing. We introduce three tensor decompositions that significantly reduce the number of parameters and show how they can be efficiently implemented by hierarchical neural networks. We empirically demonstrate that $\Pi$-Nets are very expressive and they even produce good results without the use of non-linear activation functions in a large battery of tasks and signals, i.e., images, graphs, and audio. When used in conjunction with activation functions, $\Pi$-Nets produce state-of-the-art results in three challenging tasks, i.e. image generation, face verification and 3D mesh representation learning.

Fast reactions to changes in the surrounding visual environment require efficient attention mechanisms to reallocate computational resources to most relevant locations in the visual field. While current computational models keep improving their predictive ability thanks to the increasing availability of data, they still struggle approximating the effectiveness and efficiency exhibited by foveated animals. In this paper, we present a biologically-plausible computational model of focus of attention that exhibits spatiotemporal locality and that is very well-suited for parallel and distributed implementations. Attention emerges as a wave propagation process originated by visual stimuli corresponding to details and motion information. The resulting field obeys the principle of "inhibition of return" so as not to get stuck in potential holes. An accurate experimentation of the model shows that it achieves top level performance in scanpath prediction tasks. This can easily be understood at the light of a theoretical result that we establish in the paper, where we prove that as the velocity of wave propagation goes to infinity, the proposed model reduces to recently proposed state of the art gravitational models of focus of attention.

Motivated by industrial-scale applications, we consider two specific areas of fairness, one connected to the notion of equality of opportunity, and the other one generally tied to fair model performance. Throughout the paper, we consider only methods that can be scaled to Internet-industry size datasets. With this in mind, we propose a simple post-processing method to achieve equality of opportunity and discuss challenges and some solutions in the specific cases of recommendation systems and rankings. We then discuss a class of model performance fairness measures based on conditional ROC curves. We propose both scalable uncertainty assessment tools (that improve upon recent research) as well as scalable penalized methods to improve fairness with respect to these metrics. We provide fast algorithms with an emphasis on making few passes over the data when possible.

Background/introduction: Cross-validation is still uncommon in time series modeling. Echo State Networks (ESNs), as a prime example of Reservoir Computing (RC) models, are known for their fast and precise one-shot learning, that often benefit from good hyper-parameter tuning. This makes them ideal to change the status quo. Methods: We suggest several schemes for cross-validating ESNs and introduce an efficient algorithm for implementing them. This algorithm is presented as two levels of optimizations of doing $k$-fold cross-validation. Training an RC model typically consists of two stages: (i) running the reservoir with the data and (ii) computing the optimal readouts. The first level of our proposed optimization addresses the most computationally expensive part (i) and makes it remain constant irrespective of $k$. It dramatically reduces reservoir computations in any type of RC system and is enough if $k$ is small. The second level of optimization also makes the (ii) part remain constant irrespective of large $k$, as long as the dimension of the output is low. We discuss when the proposed validation schemes for ESNs could be beneficial, three options for producing the final model and empirically investigate them on six different real-world datasets, as well as do empirical computation time experiments. We provide the code in an online repository. Results: Proposed cross-validation schemes give better and more stable test performance in all the six different real-world datasets, three task types. Empirical run times confirm our complexity analysis. Conclusions: In most situations $k$-fold cross-validation of ESNs and many other RC models can be done for virtually the same time complexity as a simple single-split validation. Space complexity can also remain the same in all the cases. This enables cross-validation to become a standard practice in reservoir computing.

Exploratory landscape analysis (ELA) supports supervised learning approaches for automated algorithm selection and configuration by providing sets of features that quantify the most relevant characteristics of the optimization problem at hand. In black-box optimization, where an explicit problem representation is not available, the feature values need to be approximated from a small number of sample points. In practice, uniformly sampled random point sets and Latin hypercube constructions are commonly used sampling strategies. In this work, we analyze how the sampling method and the sample size influence the quality of the feature value approximations and how this quality impacts the accuracy of a standard classification task. While, not unexpectedly, increasing the number of sample points gives more robust estimates for the feature values, to our surprise we find that the feature value approximations for different sampling strategies do not converge to the same value. This implies that approximated feature values cannot be interpreted independently of the underlying sampling strategy. As our classification experiments show, this also implies that the feature approximations used for training a classifier must stem from the same sampling strategy as those used for the actual classification tasks. As a side result we show that classifiers trained with feature values approximated by Sobol' sequences achieve higher accuracy than any of the standard sampling techniques. This may indicate improvement potential for ELA-trained machine learning models.

Classifiers are often tested on relatively small data sets, which should lead to uncertain performance metrics. Nevertheless, these metrics are usually taken at face value. We present an approach to quantify the uncertainty of classification performance metrics, based on a probability model of the confusion matrix. Application of our approach to classifiers from the scientific literature and a classification competition shows that uncertainties can be surprisingly large and limit performance evaluation. In fact, some published classifiers are likely to be misleading. The application of our approach is simple and requires only the confusion matrix. It is agnostic of the underlying classifier. Our method can also be used for the estimation of sample sizes that achieve a desired precision of a performance metric.

Dependability assurance of systems embedding machine learning(ML) components---so called learning-enabled systems (LESs)---is a key step for their use in safety-critical applications. In emerging standardization and guidance efforts, there is a growing consensus in the value of using assurance cases for that purpose. This paper develops a quantitative notion of assurance that an LES is dependable, as a core component of its assurance case, also extending our prior work that applied to ML components. Specifically, we characterize LES assurance in the form of assurance measures: a probabilistic quantification of confidence that an LES possesses system-level properties associated with functional capabilities and dependability attributes. We illustrate the utility of assurance measures by application to a real world autonomous aviation system, also describing their role both in i) guiding high-level, runtime risk mitigation decisions and ii) as a core component of the associated dynamic assurance case.

There exist significant gaps in research about how to design efficient in-bed lying posture tracking systems. These gaps can be articulated through several research questions as follows. First, can we design a single-sensor, pervasive, and inexpensive system that can accurately detect lying postures? Second, what computational models are most effective in the accurate detection of lying postures? Finally, what physical configuration of the sensor system is most effective for lying posture tracking? To answer these important research questions, in this article, we propose a comprehensive approach to design a sensor system that uses a single accelerometer along with machine learning algorithms for in-bed lying posture classification. We design two categories of machine learning algorithms based on deep learning and traditional classification with handcrafted features to detect lying postures. We also investigate what wearing sites are most effective in accurate detection of lying postures. We extensively evaluate the performance of the proposed algorithms on nine different body locations and four human lying postures using two datasets. Our results show that a system with a single accelerometer can be used with either deep learning or traditional classifiers to accurately detect lying postures. The best models in our approach achieve an F-Score that ranges from 95.2% to 97.8% with 0.03 to 0.05 coefficient of variation. The results also identify the thighs and chest as the most salient body sites for lying posture tracking. Our findings in this article suggest that because accelerometers are ubiquitous and inexpensive sensors, they can be a viable source of information for pervasive monitoring of in-bed postures.