The present paper considers a finite sequence of graphs, e.g., coming from technological, biological, and social networks, each of which is modelled as a realization of a graph-valued random variable, and proposes a methodology to identify possible changes in stationarity in its generating stochastic process. In order to cover a large class of applications, we consider a general family of attributed graphs, chatacterized by a possible variable topology (edges and vertices) also in the stationary case. A Change Point Method (CPM) approach is proposed, that (i) maps graphs into a vector domain; (ii) applies a suitable statistical test; (iii) detects the change --if any-- according to a confidence level and provides an estimate for its time of occurrence. Two specific CPMs are proposed: one detecting shifts in the distribution mean, the other addressing generic changes affecting the distribution. We ground our proposal with theoretical results showing how to relate the inference attained in the numerical vector space to the graph domain, and vice versa. Finally, simulations on epileptic-seizure detection problems are conducted on real-world data providing evidence for the CPMs effectiveness.

A latent force model is a Gaussian process with a covariance function inspired by a differential operator. Such covariance function is obtained by performing convolution integrals between Green's functions associated to the differential operators, and covariance functions associated to latent functions. In the classical formulation of latent force models, the covariance functions are obtained analytically by solving a double integral, leading to expressions that involve numerical solutions of different types of error functions. In consequence, the covariance matrix calculation is considerably expensive, because it requires the evaluation of one or more of these error functions. In this paper, we use random Fourier features to approximate the solution of these double integrals obtaining simpler analytical expressions for such covariance functions. We show experimental results using ordinary differential operators and provide an extension to build general kernel functions for convolved multiple output Gaussian processes.

The Kullback-Leilber divergence from model to data is a classic goodness of fit measure but can be intractable in many cases. In this paper, we estimate the ratio function between a data density and a model density with the help of Stein operator. The estimated density ratio allows us to compute the likelihood ratio function which is a surrogate to the actual Kullback-Leibler divergence from model to data. By minimizing this surrogate, we can perform model fitting and inference from either frequentist or Bayesian point of view. This paper discusses methods, theories and algorithms for performing such tasks. Our theoretical claims are verified by experiments and examples are given demonstrating the usefulness of our methods.

Numerous methods have been proposed in the statistics and machine learning literature to sum up information and represent data by condensed and simpler to understand quantities. Among those methods, Principal Component Analysis (PCA) aims at identifying the maximal variance axes of data. This serves as a way to represent data in a more compact fashion and hopefully reveal as well as possible their variability. PCA has been introduced by Pearson (1901) and Spearman (1904) and further developed by Hotelling (1933). This is one of the most widely used procedures in multivariate exploratory analysis targeting dimension reduction or features extraction. Nonetheless, PCA is a linear procedure and the need for more sophisticated nonlinear techniques has led to the notion of principal curve. Principal curves may be seen as a nonlinear generalization of the first principal component. The goal is to obtain a curve which passes "in the middle" of data, as illustrated by Figure 1. This notion has been at the heart of numerous applications in many different domains, such as physics (Brunsdon, 2007; Friedsam and Oren, 1989), character and speech recognition (Kégl and Krzyżak, 2002; Reinhard and Niranjan, 1999), mapping and geology (Banfield and Raftery, 1992; Brunsdon, 2007; Stanford and Raftery, 2000), to name but a few.

Recurrent neural networks are strong dynamic systems, but they are very sensitive to their hyper-parameter configuration. Moreover, training properly a recurrent neural network is a tough task, therefore selecting an appropriate configuration is critical. There have been proposed varied strategies to tackle this issue, however most of them are still impractical because of the time/resources needed. In this study, we propose a low computational cost model to evaluate the expected performance of a given architecture based on the distribution of the error of random samples.

We establish, for the first time, connections between feedforward neural networks with ReLU activation and tropical geometry --- we show that the family of such neural networks is equivalent to the family of tropical rational maps. Among other things, we deduce that feedforward ReLU neural networks with one hidden layer can be characterized by zonotopes, which serve as building blocks for deeper networks; we relate decision boundaries of such neural networks to tropical hypersurfaces, a major object of study in tropical geometry; and we prove that linear regions of such neural networks correspond to vertices of polytopes associated with tropical rational functions. An insight from our tropical formulation is that a deeper network is exponentially more expressive than a shallow network.

Machine learning shows promise for improving our understanding of many-body problems. Tackling an unsolved problem, or classifying intricate phases, remains however a daunting task. Building on a recently introduced interpretable supervised learning scheme, we introduce a generic protocol to probe and identify nonlinear orientational spin order, and extract the analytical form of the tensorial order parameter up to rank 6. Moreover, we find that our approach yields reliable results already for a modest amount of training data and without knowledge of the exact phase boundary. Our approach may prove useful for identifying novel spin order and ruling out spurious spin liquid candidates.

Big data has had a great share in the success of deep learning in computer vision. Recent works suggest that there is significant further potential to increase object detection performance by utilizing even bigger datasets. In this paper, we introduce the EuroCity Persons dataset, which provides a large number of highly diverse, accurate and detailed annotations of pedestrians, cyclists and other riders in urban traffic scenes. The images for this dataset were collected on-board a moving vehicle in 31 cities of 12 European countries. With over 238200 person instances manually labeled in over 47300 images, EuroCity Persons is nearly one order of magnitude larger than person datasets used previously for benchmarking. The dataset furthermore contains a large number of person orientation annotations (over 211200). We optimize four state-of-the-art deep learning approaches (Faster R-CNN, R-FCN, SSD and YOLOv3) to serve as baselines for the new object detection benchmark. In experiments with previous datasets we analyze the generalization capabilities of these detectors when trained with the new dataset. We furthermore study the effect of the training set size, the dataset diversity (day- vs. night-time, geographical region), the dataset detail (i.e. availability of object orientation information) and the annotation quality on the detector performance. Finally, we analyze error sources and discuss the road ahead.

Technology may have brought the music industry to its knees 20 years ago, but these days pop stars and record labels are using computing power to find new audiences and take fresh creative decisions. The benefits and pitfalls of this new technology are being debated at The Great Escape music festival in Brighton, in a day-long conference. Here are some of the things we learned. Virtual reality could allow fans to experience Glastonbury from the comfort of their sofa, simply by plugging in a headset. In fact, Melody VR - a London-based tech start-up - launched earlier this month, offering concerts by stars like The Who, Royal Blood and Rag'N'Bone Man through VR sets like Oculus Go and Samsung's Gear VR.

You must have heard about how artificial intelligence is being used in industries like Travel, Health, e-commerce etc. but a company in the United States have started the use of Artificial Intelligence in a totally different industry. Connecterra, a Dutch company, has implemented the technology in the dairy farming sector. They have induced two technologies - motion sensor and AI - with the aim of making barnyards functional in the 21st century. The company has already started its IDA system or'The Intelligent Dairy Farmers System'in Europe for several years. A motion-sensing device is attached to a cow's neck to convey its movements to a program that uses the technology of Artificial intelligence.