Graph Neural Networks (GNNs) have been a latest hot research topic in data science, due to the fact that they use the ubiquitous data structure graphs as the underlying elements for constructing and training neural networks. In a GNN, each node has numerous features associated with it. The entire task (for example, classification, or clustering) utilizes the features of the nodes to make decisions, at node level or graph level. In this paper, (1) we extend the feature selection algorithm presented in via Gumbel Softmax to GNNs. We conduct a series of experiments on our feature selection algorithms, using various benchmark datasets: Cora, Citeseer and Pubmed. (2) We implement a mechanism to rank the extracted features. We demonstrate the effectiveness of our algorithms, for both feature selection and ranking. For the Cora dataset, (1) we use the algorithm to select 225 features out of 1433 features. Our experimental results demonstrate their effectiveness for the same classification problem. (2) We extract features such that they are linear combinations of the original features, where the coefficients for each extracted features are non-negative and sum up to one. We propose an algorithm to rank the extracted features in the sense that when using them for the same classification problem, the accuracy goes down gradually for the extracted features within the rank 1 - 50, 51 - 100, 100 - 150, and 151 - 200.

Anomaly detection in networks often boils down to identifying an underlying graph structure on which the abnormal occurrence rests on. Financial fraud schemes are one such example, where more or less intricate schemes are employed in order to elude transaction security protocols. We investigate the problem of learning graph structure representations using adaptations of dictionary learning aimed at encoding connectivity patterns. In particular, we adapt dictionary learning strategies to the specificity of network topologies and propose new methods that impose Laplacian structure on the dictionaries themselves. In one adaption we focus on classifying topologies by working directly on the graph Laplacian and cast the learning problem to accommodate its 2D structure. We tackle the same problem by learning dictionaries which consist of vectorized atomic Laplacians, and provide a block coordinate descent scheme to solve the new dictionary learning formulation. Imposing Lapla-cian structure on the dictionaries is also proposed in an adaptation of the Single Block Orthogonal learning method. Results on synthetic graph datasets comprising different graph topologies confirm the potential of dictionaries to directly represent graph structure information. Keywords: anomaly detection, dictionary learning, graph Laplacian classification, money laundering. 1 Introduction The benefits of global inter-connectivity and the general increase of the quality of life led to the democratization of the general population's access to banking resources such as accounts, cards and cash machines.

Financial fraud detection represents the challenge of finding anomalies in networks of financial transactions. In general, the anomaly detection (AD) is the problem of distinguishing between normal data samples with well defined patterns or signatures and those that do not conform to the expected profiles. The fraudulent behaviour in money laundering may manifest itself through unusual patterns in financial transaction networks. In such networks, nodes represents customers and the edges are transactions: a directed edge between two nodes illustrates that there is a money transfer in the respective direction, where the weight on the edge is the transferred amount. In this paper we present a survey on the fundamental anomaly detection techniques and then present briefly the relevant literature in connection with fraud detection context.

We begin by reiterating that common neural network activation functions have simple Bayesian origins. In this spirit, we go on to show that Bayes's theorem also implies a simple recurrence relation; this leads to a Bayesian recurrent unit with a prescribed feedback formulation. We show that introduction of a context indicator leads to a variable feedback that is similar to the forget mechanism in conventional recurrent units. A similar approach leads to a probabilistic input gate. The Bayesian formulation leads naturally to the two pass algorithm of the Kalman smoother or forward-backward algorithm, meaning that inference naturally depends upon future inputs as well as past ones. Experiments on speech recognition confirm that the resulting architecture can perform as well as a bidirectional recurrent network with the same number of parameters as a unidirectional one. Further, when configured explicitly bidirectionally, the architecture can exceed the performance of a conventional bidirectional recurrence.

This article introduces a Bayesian nonparametric method for quantifying the relative evidence in a dataset in favour of the dependence or independence of two variables conditional on a third. The approach uses P olya tree priors on spaces of conditional probability densities, accounting for uncertainty in the form of the underlying distributions in a nonparametric way. The Bayesian perspective provides an inherently symmetric probability measure of conditional dependence or independence, a feature particularly advantageous in causal discovery and not employed by any previous procedure of this type.

Combining insights from machine learning and quantum Monte Carlo, the stochastic reconfiguration method with neural network Ansatz states is a promising new direction for high precision ground state estimation of quantum many body problems. At present, the method is heuristic, lacking a proper theoretical foundation. We initiate a thorough analysis of the learning landscape, and show that it reveals universal behavior reflecting a combination of the underlying physics and of the learning dynamics. In particular, the spectrum of the quantum Fisher matrix of complex restricted Boltzmann machine states can dramatically change across a phase transition. In contrast to the spectral properties of the quantum Fisher matrix, the actual weights of the network at convergence do not reveal much information about the system or the dynamics. Furthermore, we identify a new measure of correlation in the state by analyzing entanglement the eigenvectors. We show that, generically, the learning landscape modes with least entanglement have largest eigenvalue, suggesting that correlations are encoded in large flat valleys of the learning landscape, favoring stable representations of the ground state.

Neural networks are becoming more and more popular for the analysis of physiological time-series. The most successful deep learning systems in this domain combine convolutional and recurrent layers to extract useful features to model temporal relations. Unfortunately, these recurrent models are difficult to tune and optimize. In our experience, they often require task-specific modifications, which makes them challenging to use for non-experts. We propose U-Time, a fully feed-forward deep learning approach to physiological time series segmentation developed for the analysis of sleep data. U-Time is a temporal fully convolutional network based on the U-Net architecture that was originally proposed for image segmentation. U-Time maps sequential inputs of arbitrary length to sequences of class labels on a freely chosen temporal scale. This is done by implicitly classifying every individual time-point of the input signal and aggregating these classifications over fixed intervals to form the final predictions. We evaluated U-Time for sleep stage classification on a large collection of sleep electroencephalography (EEG) datasets. In all cases, we found that U-Time reaches or outperforms current state-of-the-art deep learning models while being much more robust in the training process and without requiring architecture or hyperparameter adaptation across tasks.

There has recently been an increasing desire to evaluate neural networks locally on computationally-limited devices in order to exploit their recent effectiveness for several applications; such effectiveness has nevertheless come together with a considerable increase in the size of modern neural networks, which constitute a major downside in several of the aforementioned computationally-limited settings. There has thus been a demand of compression techniques for neural networks. Several proposal in this direction have been made, which famously include hashing-based methods and pruning-based ones. However, the evaluation of the efficacy of these techniques has so far been heterogeneous, with no clear evidence in favor of any of them over the others. The goal of this work is to address this latter issue by providing a comparative study. While most previous studies test the capability of a technique in reducing the number of parameters of state-of-the-art networks , we follow [CWT + 15] in evaluating their performance on basic ar-chitectures on the MNIST dataset and variants of it, which allows for a clearer analysis of some aspects of their behavior. To the best of our knowledge, we are the first to directly compare famous approaches such as HashedNet, Optimal Brain Damage (OBD), and magnitude-based pruning with L1 and L2 regularization among them and against equivalent-size feed-forward neural networks with simple (fully-connected) and structural (convolutional) neural networks. Rather surprisingly, our experiments show that (iterative) pruning-based methods are substantially better than the HashedNet architecture, whose compression doesn't appear advantageous to a carefully chosen convolutional network. We also show that, when the compression level is high, the famous OBD pruning heuristics deteriorates to the point of being less efficient than simple magnitude-based techniques.

We consider functions defined by deep neural networks as definab le objects in an o-miminal expansion of the real field, and derive an almost linear ( in the number of weights) bound on sample complexity of such networks.

Angular measurements are often modeled as circular random variables, where there are natural circular analogues of moments, including correlation. Because a product of circles is a torus, a d-dimensional vector of circular random variables lies on a d-dimensional torus. For such vectors we present here a class of graphical models, which we call torus graphs, based on the full exponential family with pairwise interactions. The topological distinction between a torus and Euclidean space has several important consequences. Our development was motivated by the problem of identifying phase coupling among oscillatory signals recorded from multiple electrodes in the brain: oscillatory phases across electrodes might tend to advance or recede together, indicating coordination across brain areas. The data analyzed here consisted of 24 phase angles measured repeatedly across 840 experimental trials (replications) during a memory task, where the electrodes were in 4 distinct brain regions, all known to be active while memories are being stored or retrieved. In realistic numerical simulations, we found that a standard pairwise assessment, known as phase locking value, is unable to describe multivariate phase interactions, but that torus graphs can accurately identify conditional associations. Torus graphs generalize several more restrictive approaches that have appeared in various scientific literatures, and produced intuitive results in the data we analyzed. Torus graphs thus unify multivariate analysis of circular data and present fertile territory for future research.