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In this paper we consider the spatial semi-discretization of conservative PDEs. Such finite dimensional approximations of infinite dimensional dynamical systems can be described as flows in suitable matrix spaces, which in turn leads to the need to solve polynomial matrix equations, a classical and important topic both in theoretical and in applied mathematics. Solving numerically these equations is challenging due to the presence of several conservation laws which our finite models incorporate and which must be retained while integrating the equations of motion. In the last thirty years, the theory of geometric integration has provided a variety of techniques to tackle this problem. These numerical methods require to solve both direct and inverse problems in matrix spaces. We present two algorithms to solve a cubic matrix equation arising in the geometric integration of isospectral flows. This type of ODEs includes finite models of ideal hydrodynamics, plasma dynamics, and spin particles, which we use as test problems for our algorithms.

Large observational data are increasingly available in disciplines such as health, economic and social sciences, where researchers are interested in causal questions rather than prediction. In this paper, we examine the problem of estimating heterogeneous treatment effects using non-parametric regression-based methods, starting from an empirical study aimed at investigating the effect of participation in school meal programs on health indicators. Firstly, we introduce the setup and the issues related to conducting causal inference with observational or non-fully randomized data, and how these issues can be tackled with the help of statistical learning tools. Then, we review and develop a unifying taxonomy of the existing state-of-the-art frameworks that allow for individual treatment effects estimation via non-parametric regression models. After presenting a brief overview on the problem of model selection, we illustrate the performance of some of the methods on three different simulated studies. We conclude by demonstrating the use of some of the methods on an empirical analysis of the school meal program data.

Human speech production encompasses physiological processes that naturally react to physic stress. Stress caused by physical activity (PA), e.g., running, may lead to significant changes in a person's speech. The major changes are related to the aspects of pitch level, speaking rate, pause pattern, and breathiness. The extent of change depends presumably on physical fitness and well-being of the person, as well as intensity of PA. The general wellness of a person is further related to his/her physical literacy (PL), which refers to a holistic description of engagement in PA. This paper presents the development of a Cantonese speech database that contains audio recordings of speech before and after physical exercises of different intensity levels. The corpus design and data collection process are described. Preliminary results of acoustical analysis are presented to illustrate the impact of PA on pitch level, pitch range, speaking and articulation rate, and time duration of pauses. It is also noted that the effect of PA is correlated to some of the PA and PL measures.

The focus of disentanglement approaches has been on identifying independent factors of variation in data. However, the causal variables underlying real-world observations are often not statistically independent. In this work, we bridge the gap to real-world scenarios by analyzing the behavior of the most prominent disentanglement approaches on correlated data in a large-scale empirical study (including 4260 models). We show and quantify that systematically induced correlations in the dataset are being learned and reflected in the latent representations, which has implications for downstream applications of disentanglement such as fairness. We also demonstrate how to resolve these latent correlations, either using weak supervision during training or by post-hoc correcting a pre-trained model with a small number of labels.

This paper defines a new visual reasoning paradigm by introducing an important factor, i.e., transformation. The motivation comes from the fact that most existing visual reasoning tasks, such as CLEVR in VQA, are solely defined to test how well the machine understands the concepts and relations within static settings, like one image. We argue that this kind of state driven visual reasoning approach has limitations in reflecting whether the machine has the ability to infer the dynamics between different states, which has been shown as important as state-level reasoning for human cognition in Piaget's theory. To tackle this problem, we propose a novel transformation driven visual reasoning task. Given both the initial and final states, the target is to infer the corresponding single-step or multi-step transformation, represented as a triplet (object, attribute, value) or a sequence of triplets, respectively. Following this definition, a new dataset namely TRANCE is constructed on the basis of CLEVR, including three levels of settings, i.e., Basic (single-step transformation), Event (multi-step transformation), and View (multi-step transformation with variant views). Experimental results show that the state-of-the-art visual reasoning models perform well on Basic, but are still far from human-level intelligence on Event and View. We believe the proposed new paradigm will boost the development of machine visual reasoning. More advanced methods and real data need to be investigated in this direction. Code is available at: //github.com/hughplay/TVR.

Point cloud is point sets defined in 3D metric space. Point cloud has become one of the most significant data format for 3D representation. Its gaining increased popularity as a result of increased availability of acquisition devices, such as LiDAR, as well as increased application in areas such as robotics, autonomous driving, augmented and virtual reality. Deep learning is now the most powerful tool for data processing in computer vision, becoming the most preferred technique for tasks such as classification, segmentation, and detection. While deep learning techniques are mainly applied to data with a structured grid, point cloud, on the other hand, is unstructured. The unstructuredness of point clouds makes use of deep learning for its processing directly very challenging. Earlier approaches overcome this challenge by preprocessing the point cloud into a structured grid format at the cost of increased computational cost or lost of depth information. Recently, however, many state-of-the-arts deep learning techniques that directly operate on point cloud are being developed. This paper contains a survey of the recent state-of-the-art deep learning techniques that mainly focused on point cloud data. We first briefly discussed the major challenges faced when using deep learning directly on point cloud, we also briefly discussed earlier approaches which overcome the challenges by preprocessing the point cloud into a structured grid. We then give the review of the various state-of-the-art deep learning approaches that directly process point cloud in its unstructured form. We introduced the popular 3D point cloud benchmark datasets. And we also further discussed the application of deep learning in popular 3D vision tasks including classification, segmentation and detection.

Graphical causal inference as pioneered by Judea Pearl arose from research on artificial intelligence (AI), and for a long time had little connection to the field of machine learning. This article discusses where links have been and should be established, introducing key concepts along the way. It argues that the hard open problems of machine learning and AI are intrinsically related to causality, and explains how the field is beginning to understand them.

In recent years with the rise of Cloud Computing (CC), many companies providing services in the cloud, are empowered a new series of services to their catalog, such as data mining (DM) and data processing, taking advantage of the vast computing resources available to them. Different service definition proposals have been proposed to address the problem of describing services in CC in a comprehensive way. Bearing in mind that each provider has its own definition of the logic of its services, and specifically of DM services, it should be pointed out that the possibility of describing services in a flexible way between providers is fundamental in order to maintain the usability and portability of this type of CC services. The use of semantic technologies based on the proposal offered by Linked Data (LD) for the definition of services, allows the design and modelling of DM services, achieving a high degree of interoperability. In this article a schema for the definition of DM services on CC is presented, in addition are considered all key aspects of service in CC, such as prices, interfaces, Software Level Agreement, instances or workflow of experimentation, among others. The proposal presented is based on LD, so that it reuses other schemata obtaining a best definition of the service. For the validation of the schema, a series of DM services have been created where some of the best known algorithms such as \textit{Random Forest} or \textit{KMeans} are modeled as services.

The era of big data provides researchers with convenient access to copious data. However, people often have little knowledge about it. The increasing prevalence of big data is challenging the traditional methods of learning causality because they are developed for the cases with limited amount of data and solid prior causal knowledge. This survey aims to close the gap between big data and learning causality with a comprehensive and structured review of traditional and frontier methods and a discussion about some open problems of learning causality. We begin with preliminaries of learning causality. Then we categorize and revisit methods of learning causality for the typical problems and data types. After that, we discuss the connections between learning causality and machine learning. At the end, some open problems are presented to show the great potential of learning causality with data.