The relationship between statistical dependency and causality lies at the heart of all statistical approaches to causal inference. Recent results in the ChaLearn cause-effect pair challenge have shown that causal directionality can be inferred with good accuracy also in Markov indistinguishable configurations thanks to data driven approaches. This paper proposes a supervised machine learning approach to infer the existence of a directed causal link between two variables in multivariate settings with $n>2$ variables. The approach relies on the asymmetry of some conditional (in)dependence relations between the members of the Markov blankets of two variables causally connected. Our results show that supervised learning methods may be successfully used to extract causal information on the basis of asymmetric statistical descriptors also for $n>2$ variate distributions.

The problem of resource allocation of nonlinear networked control systems is investigated, where, unlike the well discussed case of triggering for stability, the objective is optimal triggering. An approximate dynamic programming approach is developed for solving problems with fixed final times initially and then it is extended to infinite horizon problems. Different cases including Zero-Order-Hold, Generalized Zero-Order-Hold, and stochastic networks are investigated. Afterwards, the developments are extended to the case of problems with unknown dynamics and a model-free scheme is presented for learning the (approximate) optimal solution. After detailed analyses of convergence, optimality, and stability of the results, the performance of the method is demonstrated through different numerical examples.

Detecting faults in electrical power grids is of paramount importance, either from the electricity operator and consumer viewpoints. Modern electric power grids (smart grids) are equipped with smart sensors that allow to gather real-time information regarding the physical status of all the component elements belonging to the whole infrastructure (e.g., cables and related insulation, transformers, breakers and so on). In real-world smart grid systems, usually, additional information that are related to the operational status of the grid itself are collected such as meteorological information. Designing a suitable recognition (discrimination) model of faults in a real-world smart grid system is hence a challenging task. This follows from the heterogeneity of the information that actually determine a typical fault condition. The second point is that, for synthesizing a recognition model, in practice only the conditions of observed faults are usually meaningful. Therefore, a suitable recognition model should be synthesized by making use of the observed fault conditions only. In this paper, we deal with the problem of modeling and recognizing faults in a real-world smart grid system, which supplies the entire city of Rome, Italy. Recognition of faults is addressed by following a combined approach of multiple dissimilarity measures customization and one-class classification techniques. We provide here an in-depth study related to the available data and to the models synthesized by the proposed one-class classifier. We offer also a comprehensive analysis of the fault recognition results by exploiting a fuzzy set based reliability decision rule.

The process of multiple criteria decision making (MCDM) is of determining the best choice among all of the probable alternatives. The problem of supplier selection on which decision maker has usually vague and imprecise knowledge is a typical example of multi criteria group decision-making problem. The conventional crisp techniques has not much effective for solving MCDM problems because of imprecise or fuzziness nature of the linguistic assessments. To find the exact values for MCDM problems is both difficult and impossible in more cases in real world. So, it is more reasonable to consider the values of alternatives according to the criteria as single valued neutrosophic sets (SVNS). This paper deal with the technique for order preference by similarity to ideal solution (TOPSIS) approach and extend the TOPSIS method to MCDM problem with single valued neutrosophic information. The value of each alternative and the weight of each criterion are characterized by single valued neutrosophic numbers. Here, the importance of criteria and alternatives is identified by aggregating individual opinions of decision makers (DMs) via single valued neutrosophic weighted averaging (IFWA) operator. The proposed method is, easy use, precise and practical for solving MCDM problem with single valued neutrosophic data. Finally, to show the applicability of the developed method, a numerical experiment for supplier choice is given as an application of single valued neutrosophic TOPSIS method at end of this paper.

In this work we introduce a new optimisation method called SAGA in the spirit of SAG, SDCA, MISO and SVRG, a set of recently proposed incremental gradient algorithms with fast linear convergence rates. SAGA improves on the theory behind SAG and SVRG, with better theoretical convergence rates, and has support for composite objectives where a proximal operator is used on the regulariser. Unlike SDCA, SAGA supports non-strongly convex problems directly, and is adaptive to any inherent strong convexity of the problem. We give experimental results showing the effectiveness of our method.

Variational methods in imaging are nowadays developing towards a quite universal and flexible tool, allowing for highly successful approaches on tasks like denoising, deblurring, inpainting, segmentation, super-resolution, disparity, and optical flow estimation. The overall structure of such approaches is of the form ${\cal D}(Ku) + \alpha {\cal R} (u) \rightarrow \min_u$ ; where the functional ${\cal D}$ is a data fidelity term also depending on some input data $f$ and measuring the deviation of $Ku$ from such and ${\cal R}$ is a regularization functional. Moreover $K$ is a (often linear) forward operator modeling the dependence of data on an underlying image, and $\alpha$ is a positive regularization parameter. While ${\cal D}$ is often smooth and (strictly) convex, the current practice almost exclusively uses nonsmooth regularization functionals. The majority of successful techniques is using nonsmooth and convex functionals like the total variation and generalizations thereof or $\ell_1$-norms of coefficients arising from scalar products with some frame system. The efficient solution of such variational problems in imaging demands for appropriate algorithms. Taking into account the specific structure as a sum of two very different terms to be minimized, splitting algorithms are a quite canonical choice. Consequently this field has revived the interest in techniques like operator splittings or augmented Lagrangians. Here we shall provide an overview of methods currently developed and recent results as well as some computational studies providing a comparison of different methods and also illustrating their success in applications.

Statistical machine learning methods are increasingly used for neuroimaging data analysis. Their main virtue is their ability to model high-dimensional datasets, e.g. multivariate analysis of activation images or resting-state time series. Supervised learning is typically used in decoding or encoding settings to relate brain images to behavioral or clinical observations, while unsupervised learning can uncover hidden structures in sets of images (e.g. resting state functional MRI) or find sub-populations in large cohorts. By considering different functional neuroimaging applications, we illustrate how scikit-learn, a Python machine learning library, can be used to perform some key analysis steps. Scikit-learn contains a very large set of statistical learning algorithms, both supervised and unsupervised, and its application to neuroimaging data provides a versatile tool to study the brain.

In this paper we consider the problem of minimizing a convex function using a randomized block coordinate descent method. One of the key steps at each iteration of the algorithm is determining the update to a block of variables. Existing algorithms assume that in order to compute the update, a particular subproblem is solved exactly. In his work we relax this requirement, and allow for the subproblem to be solved inexactly, leading to an inexact block coordinate descent method. Our approach incorporates the best known results for exact updates as a special case. Moreover, these theoretical guarantees are complemented by practical considerations: the use of iterative techniques to determine the update as well as the use of preconditioning for further acceleration.

We present a new approach for transferring knowledge from groups to individuals that comprise them. We evaluate our method in text, by inferring the ratings of individual sentences using full-review ratings. This approach, which combines ideas from transfer learning, deep learning and multi-instance learning, reduces the need for laborious human labelling of fine-grained data when abundant labels are available at the group level.

Bayesian methods suffer from the problem of how to specify prior beliefs. One interesting idea is to consider worst-case priors. This requires solving a stochastic zero-sum game. In this paper, we extend well-known results from bandit theory in order to discover minimax-Bayes policies and discuss when they are practical.