The \textit{sampling policy} of stage $t$, formally expressed as a probability density function $q_t$, stands for the distribution of the sample $(x_{t,1},\ldots, x_{t,n_t})$ generated at $t$. From the past samples, some information depending on some \textit{objective} is derived leading eventually to update the sampling policy to $q_{t+1}$. This generic approach characterizes \textit{adaptive importance sampling} (AIS) schemes. Each stage $t$ is formed with two steps : (i) to explore the space with $n_t$ points according to $q_t$ and (ii) to exploit the current amount of information to update the sampling policy. The very fundamental question raised in the paper concerns the behavior of empirical sums based on AIS. Without making any assumption on the \textit{allocation policy} $n_t$, the theory developed involves no restriction on the split of computational resources between the explore (i) and the exploit (ii) step. It is shown that AIS is efficient : the asymptotic behavior of AIS is the same as some "oracle" strategy that knows the optimal sampling policy from the beginning. From a practical perspective, weighted AIS is introduced, a new method that allows to forget poor samples from early stages.

The construction of a meaningful graph topology plays a crucial role in the effective representation, processing, analysis and visualization of structured data. When a natural choice of the graph is not readily available from the datasets, it is thus desirable to infer or learn a graph topology from the data. In this tutorial overview, we survey solutions to the problem of graph learning, including classical viewpoints from statistics and physics, and more recent approaches that adopt a graph signal processing (GSP) perspective. We further emphasize the conceptual similarities and differences between classical and GSP graph inference methods and highlight the potential advantage of the latter in a number of theoretical and practical scenarios. We conclude with several open issues and challenges that are keys to the design of future signal processing and machine learning algorithms for learning graphs from data.

Resilient supplier selection problem is a key decision problem for an organization to gain competitive advantage. In the presence of multiple conflicting evaluation criteria, contradicting decision makers, and imprecise information sources, this problem becomes even more difficult to solve with the classical optimization approaches. Multi-Criteria Decision Analysis (MCDA) is a viable alternative approach for handling the imprecise information associated with the evaluation proffered by the decision makers. In this work, we present a comprehensive algorithm for ranking a set of suppliers based on aggregated information obtained from crisp numerical assessments and reliability adjusted linguistic appraisals from a group of decision makers. We adapted two popular tools - Single Valued Neutrosophic Sets (SVNS) and Interval-valued fuzzy sets (IVFS) and extended them to incorporate both crisp and linguistic evaluations from the decision makers to obtain aggregated SVNS and IVFS. This information is then used to rank the suppliers by using TOPSIS method. We present a case study to illustrate the mechanism of the proposed algorithm and show sensitivity of the supplier ranking with respect to the priorities of evaluation criteria.

We extend the decomposition approach for learning Bayesian networks (BN) proposed by (Xie et al., 2006) to learning multivariate regression chain graphs (MVR CGs), which include BNs as a special case. The same advantages of this decomposition approach hold in the more general setting: reduces complexity and increased power of computational independence tests. Moreover, latent (hidden) variables can be represented in MVR CGs by using bidirected edges, and our algorithm correctly recovers any independence structure that is faithful to a MVR CG, thus greatly extending the range of applications of decomposition-based model selection techniques. While our new algorithm has the same complexity as the one in (Xie et al., 2006) for BNs, it requires larger components for general MVR CGs, to insure that sufficient data is present to estimate parameters.

In classification applications such as severe disease diagnosis and fraud detection, people have clear priorities over the two types of classification errors. For instance, diagnosing a patient with cancer to be healthy may lead to loss of life, which incurs a much higher cost than the other way around. The classical binary classification paradigm does not take into account such priorities, as it aims to minimize the overall classification error. In contrast, the Neyman-Pearson (NP) paradigm seeks classifiers with a minimal type II error while having the prioritized type I error constrained under a user-specified level, addressing asymmetric type I/II error priorities in the previously mentioned scenarios. Despite recent advances in the NP classification literature, two essential issues pose challenges: i) current theoretical framework assumes bounded feature support, which does not admit parametric settings; ii) in practice, existing NP classifiers involve splitting class 0 samples into two parts using a pre-fixed split proportion. To address the first challenge, we present NP-sLDA that adapts the popular sparse linear discriminant analysis (sLDA, Mai et al. (2012)) to the NP paradigm. On the theoretical front, this is the first theoretically justified NP classifier that takes parametric assumptions and unbounded feature support. We formulate a new conditional margin assumption and a new conditional detection condition to accommodate unbounded feature support and show that NP-sLDA satisfies the NP oracle inequalities. Numerical results show that NP-sLDA is a valuable addition to the existing NP classifiers. To address the second challenge, we construct a general data-adaptive sample splitting scheme that improves the classification performance upon the default half-half class 0 split used in Tong et al. (2018).

In this study, we present a hierarchical fuzzy system by evaluating the risk state for a Driver Assistance System in order to contribute in reducing the road accident's number. A key component of this system is its ability to continually detect and test the inside and outside risks in real time: The outside car risks by detecting various road moving objects; this proposed system stands on computer vision approaches. The inside risks by presenting an automatic system for drowsy driving identification or detection by evaluating EEG signals of the driver; this developed system is based on computer vision techniques and biometrics factors (electroencephalogram EEG). This proposed system is then composed of three main modules. The first module is responsible for identifying the driver drowsiness state through his eye movements (physical drowsiness). The second one is responsible for detecting and analysing his physiological signals to also identify his drowsiness state (moral drowsiness). The third module is responsible to evaluate the road driving risks by detecting of the road different moving objects in a real time. The final decision will be obtained by merging of the three detection systems through the use of fuzzy decision rules. Finally, the proposed approach has been improved on ten samples from a proposed dataset.

This note considers softmax parameter estimation when little/no labeled training data is available, but a priori information about the relative geometry of class label log-odds boundaries is available. It is shown that `data-free' softmax model synthesis corresponds to solving a linear system of parameter equations, wherein desired dominant class log-odds boundaries are encoded via convex polytopes that decompose the input feature space. When solvable, the linear equations yield closed-form softmax parameter solution families using class boundary polytope specifications only. This allows softmax parameter learning to be implemented without expensive brute force data sampling and numerical optimization. The linear equations can also be adapted to constrained maximum likelihood estimation in data-sparse settings. Since solutions may also fail to exist for the linear parameter equations derived from certain polytope specifications, it is thus also shown that there exist probabilistic classification problems over m convexly separable classes for which the log-odds boundaries cannot be learned using an m-class softmax model.

Classical clustering algorithms typically either lack an underlying probability framework to make them predictive or focus on parameter estimation rather than defining and minimizing a notion of error. Recent work addresses these issues by developing a probabilistic framework based on the theory of random labeled point processes and characterizing a Bayes clusterer that minimizes the number of misclustered points. The Bayes clusterer is analogous to the Bayes classifier. Whereas determining a Bayes classifier requires full knowledge of the feature-label distribution, deriving a Bayes clusterer requires full knowledge of the point process. When uncertain of the point process, one would like to find a robust clusterer that is optimal over the uncertainty, just as one may find optimal robust classifiers with uncertain feature-label distributions. Herein, we derive an optimal robust clusterer by first finding an effective random point process that incorporates all randomness within its own probabilistic structure and from which a Bayes clusterer can be derived that provides an optimal robust clusterer relative to the uncertainty. This is analogous to the use of effective class-conditional distributions in robust classification. After evaluating the performance of robust clusterers in synthetic mixtures of Gaussians models, we apply the framework to granular imaging, where we make use of the asymptotic granulometric moment theory for granular images to relate robust clustering theory to the application.

In the last three decades, we have seen a significant increase in trading goods and services through online auctions. However, this business created an attractive environment for malicious moneymakers who can commit different types of fraud activities, such as Shill Bidding (SB). The latter is predominant across many auctions but this type of fraud is difficult to detect due to its similarity to normal bidding behaviour. The unavailability of SB datasets makes the development of SB detection and classification models burdensome. Furthermore, to implement efficient SB detection models, we should produce SB data from actual auctions of commercial sites. In this study, we first scraped a large number of eBay auctions of a popular product. After preprocessing the raw auction data, we build a high-quality SB dataset based on the most reliable SB strategies. The aim of our research is to share the preprocessed auction dataset as well as the SB training (unlabelled) dataset, thereby researchers can apply various machine learning techniques by using authentic data of auctions and fraud.

Complex performance measures, beyond the popular measure of accuracy, are increasingly being used in the context of binary classification. These complex performance measures are typically not even decomposable, that is, the loss evaluated on a batch of samples cannot typically be expressed as a sum or average of losses evaluated at individual samples, which in turn requires new theoretical and methodological developments beyond standard treatments of supervised learning. In this paper, we advance this understanding of binary classification for complex performance measures by identifying two key properties: a so-called Karmic property, and a more technical threshold-quasi-concavity property, which we show is milder than existing structural assumptions imposed on performance measures. Under these properties, we show that the Bayes optimal classifier is a threshold function of the conditional probability of positive class. We then leverage this result to come up with a computationally practical plug-in classifier, via a novel threshold estimator, and further, provide a novel statistical analysis of classification error with respect to complex performance measures.