Network embedding aims to embed nodes into a low-dimensional space, while capturing the network structures and properties. Although quite a few promising network embedding methods have been proposed, most of them focus on static networks. In fact, temporal networks, which usually evolve over time in terms of microscopic and macroscopic dynamics, are ubiquitous. The micro-dynamics describe the formation process of network structures in a detailed manner, while the macro-dynamics refer to the evolution pattern of the network scale. Both micro- and macro-dynamics are the key factors to network evolution; however, how to elegantly capture both of them for temporal network embedding, especially macro-dynamics, has not yet been well studied. In this paper, we propose a novel temporal network embedding method with micro- and macro-dynamics, named $\rm{M^2DNE}$. Specifically, for micro-dynamics, we regard the establishments of edges as the occurrences of chronological events and propose a temporal attention point process to capture the formation process of network structures in a fine-grained manner. For macro-dynamics, we define a general dynamics equation parameterized with network embeddings to capture the inherent evolution pattern and impose constraints in a higher structural level on network embeddings. Mutual evolutions of micro- and macro-dynamics in a temporal network alternately affect the process of learning node embeddings. Extensive experiments on three real-world temporal networks demonstrate that $\rm{M^2DNE}$ significantly outperforms the state-of-the-arts not only in traditional tasks, e.g., network reconstruction, but also in temporal tendency-related tasks, e.g., scale prediction.

The Monte Carlo dropout method has proved to be a scalable and easy-to-use approach for estimating the uncertainty of deep neural network predictions. This approach was recently applied to Fault Detection and Di-agnosis (FDD) applications to improve the classification performance on incipient faults. In this paper, we propose a novel approach of augmenting the classification model with an additional unsupervised learning task. We justify our choice of algorithm design via an information-theoretical analysis. Our experimental results on three datasets from diverse application domains show that the proposed method leads to improved fault detection and diagnosis performance, especially on out-of-distribution examples including both incipient and unknown faults.

RESEARCH Static Force Field Representation of Environments Based on Agents' Nonlinear Motions Damian Campo 1*, Alejandro Betancourt 1,2, Lucio Marcenaro 1 and Carlo Regazzoni 1 Abstract This paper presents a methodology that aims at the incremental representation of areas inside environments in terms of attractive forces. It is proposed a parametric representation of velocity fields ruling the dynamics of moving agents. It is assumed that attractive spots in the environment are responsible for modifying the motion of agents. A switching model is used to describe near and far velocity fields, which in turn are used to learn attractive characteristics of environments. The effect of such areas is considered radial over all the scene. Based on the estimation of attractive areas, a map that describes their effects in terms of their localizations, ranges of action and intensities is derived in an online way . Information of static attractive areas is added dynamically into a set of filters that describes possible interactions between moving agents and an environment. The proposed approach is first evaluated on synthetic data, posteriorly, the method is applied on real trajectories coming from moving pedestrians in an indoor environment. Keywords: Kalman filtering; Interactive force models; T rajectory analysis; Representation of environments; Situation awareness1 Introduction Analysis of trajectories performed by moving entities in environments is an important topic for different fields such as video surveillance [1], crowd/vehicle analysis [2, 3] and in general for monitoring systems, on which the dynamics of agents can lead to a better understanding of patterns and situations of interest [4, 5]. Abnormality detection is one of the most explored applications that involves analysis of trajectories. In such approach, by characterizing agents' motions, it is possible to learn and identify normal/abnormal situations in a certain environment. In general, approaches for abnormality detection are based on a set of observations that define the regular behaviors in a scene. Afterwards, abnormalities are defined as behaviors that do not match with patterns previously learned as normal, i.e., behaviors that have not been observed before [6].

We propose a new approach to combine Restricted Boltzmann Machines (RBMs) that can be used to solve combinatorial optimization problems. This allows synthesis of larger models from smaller RBMs that have been pretrained, thus effectively bypassing the problem of learning in large RBMs, and creating a system able to model a large, complex multi-modal space. We validate this approach by using learned representations to create "invertible boolean logic", where we can use Markov chain Monte Carlo (MCMC) approaches to find the solution to large scale boolean satisfiability problems and show viability towards other combinatorial optimization problems. Using this method, we are able to solve 64 bit addition based problems, as well as factorize 16 bit numbers. We find that these combined representations can provide a more accurate result for the same sample size as compared to a fully trained model. The Ising Problem has long been known to be in the class of NP-Hard problems, with no exact polynomial solution existing. Because of this, a large class of combinatorial optimization problems can be reformulated as Ising problems and solved by finding the ground state of that system (Barahona, 1982; Kirkpatrick et al., 1983; Lucas, 2014). The Boltzmann Machine (Ackley et al., 1987) was originally introduced as a constraint satisfaction network based on the Ising model problem, where the weights would encode some global constraints, and stochastic units were used to escape local minima. The original Boltzmann Machine found favor as a method to solve various combinatorial optimization problems (Korst & Aarts, 1989). However, learning was very slow with this model due to the difficulties with sampling and convergence, as well as the inability to exactly calculate the partition function.

Driver identification has emerged as a vital research field, where both practitioners and researchers investigate the potential of driver identification to enable a personalized driving experience. Within recent years, a selection of studies have reported that individuals could be perfectly identified based on their driving behavior under controlled conditions. However, research investigating the potential of driver identification under naturalistic conditions claim accuracies only marginally higher than random guess. The paper at hand provides a comprehensive summary of the recent work, highlighting the main discrepancies in the design of the machine learning approaches, primarily the window length parameter that was considered. Key findings further indicate that the longitudinal vehicle control information is particularly useful for driver identification, leaving the research gap on the extent to which the lateral vehicle control can be used for reliable identification. Building upon existing work, we provide a novel approach for the design of the window length parameter that provides evidence that reliable driver identification can be achieved with data limited to the steering wheel only. The results and insights in this paper are based on data collected from the largest naturalistic driving study conducted in this field. Overall, a neural network based on GRUs was found to provide better identification performance than traditional methods, increasing the prediction accuracy from under 15\% to over 65\% for 15 drivers. When leveraging the full field study dataset, comprising 72 drivers, the accuracy of identification prediction of the approach improved a random guess approach by a factor of 25.

Learning the parameters of a Gaussian mixtures models is a fundamental and widely studied problem with numerous applications. In this work, we give new algorithms for learning the parameters of a high-dimensional, well separated, Gaussian mixture model subject to the strong constraint of differential privacy. In particular, we give a differentially private analogue of the algorithm of Achlioptas and McSherry. Our algorithm has two key properties not achieved by prior work: (1) The algorithm's sample complexity matches that of the corresponding non-private algorithm up to lower order terms in a wide range of parameters. (2) The algorithm does not require strong a priori bounds on the parameters of the mixture components.

A new meta-algorithm for estimating the conditional average treatment effects is proposed in the paper. The main idea underlying the algorithm is to consider a new dataset consisting of feature vectors produced by means of concatenation of examples from control and treatment groups, which are close to each other. Outcomes of new data are defined as the difference between outcomes of the corresponding examples comprising new feature vectors. The second idea is based on the assumption that the number of controls is rather large and the control outcome function is precisely determined. This assumption allows us to augment treatments by generating feature vectors which are closed to available treatments. The outcome regression function constructed on the augmented set of concatenated feature vectors can be viewed as an estimator of the conditional average treatment effects. A simple modification of the Co-learner based on the random subspace method or the feature bagging is also proposed. Various numerical simulation experiments illustrate the proposed algorithm and show its outperformance in comparison with the well-known T-learner and X-learner for several types of the control and treatment outcome functions. Keywords: treatment effect, meta-learner, regression, treatment, control, simulation 1 Introduction One the most important problems in medicine is to choose the most appropriate treatment for a certain patient which may differ from other patients in her/his clinical or other characteristics [25]. With the increase of the amount of data and with the developing the electronic health record concept in medicine, there is a growing interest to apply machine learning methods to solve the problem of the most appropriate treatment by estimating treatment effects directly from observational data. The main peculiarity of observational data is that it contains past actions, their outcomes, but without direct access to the mechanism which gave rise to the action. Shalit at al. [34] give a clear example of observational data, when we have patient characteristics, medications (action), and outcomes, 1 arXiv:1909.03894v1

We present Graph Random Neural Features (GRNF), a novel embedding method from graph-structured data to real vectors based on a family of graph neural networks. The embedding naturally deals with graph isomorphism and preserves, in probability, the metric structure of graph domain. In addition to being an explicit embedding method, it also allows to efficiently and effectively approximate graph metric distances (as well as complete kernel functions); a criterion to select the embedding dimension trading off the approximation accuracy with the computational cost is also provided. Derived GRNF can be used within traditional processing methods or as input layer of a larger graph neural network. The theoretical guarantees that accompany GRNF ensure that the considered graph distance is metric, hence allowing to distinguish any pair of non-isomorphic graphs. 1 Introduction Inference on graph-structured data is one of the hottest topics in machine learning, thanks to successes achieved in several scientific fields, like neurosciences, chemistry, computational biology and social sciences [1-3]. One of the major research challenges there consists of building a practical solution able to process graphs, yet managing the graph isomorphism problem. A way to address this latter problem passes through metric distances and complete kernels, however, it has been shown to be at least as hard as deciding whether two graphs are isomorphic [4].

A trade-off exists between reconstruction quality and the prior regularisation in the Evidence Lower Bound (ELBO) loss that Variational Autoencoder (VAE) models use for learning. There are few satisfactory approaches to deal with a balance between the prior and reconstruction objective, with most methods dealing with this problem through heuristics. In this paper, we show that the noise variance (often set as a fixed value) in the Gaussian likelihood p(x|z) for real-valued data can naturally act to provide such a balance. By learning this noise variance so as to maximise the ELBO loss, we automatically obtain an optimal trade-off between the reconstruction error and the prior constraint on the posteriors. This variance can be interpreted intuitively as the necessary noise level for the current model to be the best explanation of the observed dataset. Further, by allowing the variance inference to be more flexible it can conveniently be used as an uncertainty estimator for reconstructed or generated samples. We demonstrate that optimising the noise variance is a crucial component of VAE learning, and showcase the performance on MNIST, Fashion MNIST and CelebA datasets. We find our approach can significantly improve the quality of generated samples whilst maintaining a smooth latent-space manifold to represent the data. The method also offers an indication of uncertainty in the final generative model.

We consider the problem of the recovery of a k-sparse vector from compressed linear measurements when data are corrupted by a quantization noise. When the number of measurements is not sufficiently large, different $k$-sparse solutions may be present in the feasible set, and the classical l1 approach may be unsuccessful. For this motivation, we propose a non-convex quadratic programming method, which exploits prior information on the magnitude of the non-zero parameters. This results in a more efficient support recovery. We provide sufficient conditions for successful recovery and numerical simulations to illustrate the practical feasibility of the proposed method.