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In a number of application domains, one observes a sequence of network data; for example, repeated measurements between users interactions in social media platforms, financial correlation networks over time, or across subjects, as in multi-subject studies of brain connectivity. One way to analyze such data is by stacking networks into a third-order array or tensor. We propose a principal components analysis (PCA) framework for sequence network data, based on a novel decomposition for semi-symmetric tensors. We derive efficient algorithms for computing our proposed "Coupled CP" decomposition and establish estimation consistency of our approach under an analogue of the spiked covariance model with rates the same as the matrix case up to a logarithmic term. Our framework inherits many of the strengths of classical PCA and is suitable for a wide range of unsupervised learning tasks, including identifying principal networks, isolating meaningful changepoints or outliers across observations, and for characterizing the "variability network" of the most varying edges. Finally, we demonstrate the effectiveness of our proposal on simulated data and on examples from political science and financial economics. The proof techniques used to establish our main consistency results are surprisingly straight-forward and may find use in a variety of other matrix and tensor decomposition problems.

Deep neural network models are used today in various applications of artificial intelligence, the strengthening of which, in the face of adversarial attacks is of particular importance. An appropriate solution to adversarial attacks is adversarial training, which reaches a trade-off between robustness and generalization. This paper introduces a novel framework (Layer Sustainability Analysis (LSA)) for the analysis of layer vulnerability in a given neural network in the scenario of adversarial attacks. LSA can be a helpful toolkit to assess deep neural networks and to extend adversarial training approaches towards improving the sustainability of model layers via layer monitoring and analysis. The LSA framework identifies a list of Most Vulnerable Layers (MVL list) of a given network. The relative error, as a comparison measure, is used to evaluate the representation sustainability of each layer against adversarial attack inputs. The proposed approach for obtaining robust neural networks to fend off adversarial attacks is based on a layer-wise regularization (LR) over LSA proposal(s) for adversarial training (AT); i.e. the AT-LR procedure. AT-LR could be used with any benchmark adversarial attack to reduce the vulnerability of network layers and to improve conventional adversarial training approaches. The proposed idea performs well theoretically and experimentally for state-of-the-art multilayer perceptron and convolutional neural network architectures. Compared with the AT-LR and its corresponding base adversarial training, the classification accuracy of more significant perturbations increased by 16.35%, 21.79%, and 10.730% on Moon, MNIST, and CIFAR-10 benchmark datasets in comparison with the AT-LR and its corresponding base adversarial training, respectively. The LSA framework is available and published at //github.com/khalooei/LSA.

Precision phenomenological studies of high-multiplicity scattering processes at collider experiments present a substantial theoretical challenge and are vitally important ingredients in experimental measurements. Machine learning technology has the potential to dramatically optimise simulations for complicated final states. We investigate the use of neural networks to approximate matrix elements, studying the case of loop-induced diphoton production through gluon fusion. We train neural network models on one-loop amplitudes from the NJet C++ library and interface them with the Sherpa Monte Carlo event generator to provide the matrix element within a realistic hadronic collider simulation. Computing some standard observables with the models and comparing to conventional techniques, we find excellent agreement in the distributions and a reduced total simulation time by a factor of thirty.

Spatial statistics is concerned with the analysis of data that have spatial locations associated with them, and those locations are used to model statistical dependence between the data. The spatial data are treated as a single realisation from a probability model that encodes the dependence through both fixed effects and random effects, where randomness is manifest in the underlying spatial process and in the noisy, incomplete, measurement process. The focus of this review article is on the use of basis functions to provide an extremely flexible and computationally efficient way to model spatial processes that are possibly highly non-stationary. Several examples of basis-function models are provided to illustrate how they are used in Gaussian, non-Gaussian, multivariate, and spatio-temporal settings, with applications in geophysics. Our aim is to emphasise the versatility of these spatial statistical models and to demonstrate that they are now centre-stage in a number of application domains. The review concludes with a discussion and illustration of software currently available to fit spatial-basis-function models and implement spatial-statistical prediction.

The COVID-19 pandemic continues to affect the conduct of clinical trials globally. Complications may arise from pandemic-related operational challenges such as site closures, travel limitations and interruptions to the supply chain for the investigational product, or from health-related challenges such as COVID-19 infections. Some of these complications lead to unforeseen intercurrent events in the sense that they affect either the interpretation or the existence of the measurements associated with the clinical question of interest. In this article, we demonstrate how the ICH E9(R1) Addendum on estimands and sensitivity analyses provides a rigorous basis to discuss potential pandemic-related trial disruptions and to embed these disruptions in the context of study objectives and design elements. We introduce several hypothetical estimand strategies and review various causal inference and missing data methods, as well as a statistical method that combines unbiased and possibly biased estimators for estimation. To illustrate, we describe the features of a stylized trial, and how it may have been impacted by the pandemic. This stylized trial will then be re-visited by discussing the changes to the estimand and the estimator to account for pandemic disruptions. Finally, we outline considerations for designing future trials in the context of unforeseen disruptions.

The study of generalisation in deep Reinforcement Learning (RL) aims to produce RL algorithms whose policies generalise well to novel unseen situations at deployment time, avoiding overfitting to their training environments. Tackling this is vital if we are to deploy reinforcement learning algorithms in real world scenarios, where the environment will be diverse, dynamic and unpredictable. This survey is an overview of this nascent field. We provide a unifying formalism and terminology for discussing different generalisation problems, building upon previous works. We go on to categorise existing benchmarks for generalisation, as well as current methods for tackling the generalisation problem. Finally, we provide a critical discussion of the current state of the field, including recommendations for future work. Among other conclusions, we argue that taking a purely procedural content generation approach to benchmark design is not conducive to progress in generalisation, we suggest fast online adaptation and tackling RL-specific problems as some areas for future work on methods for generalisation, and we recommend building benchmarks in underexplored problem settings such as offline RL generalisation and reward-function variation.

Causal inference is a critical research topic across many domains, such as statistics, computer science, education, public policy and economics, for decades. Nowadays, estimating causal effect from observational data has become an appealing research direction owing to the large amount of available data and low budget requirement, compared with randomized controlled trials. Embraced with the rapidly developed machine learning area, various causal effect estimation methods for observational data have sprung up. In this survey, we provide a comprehensive review of causal inference methods under the potential outcome framework, one of the well known causal inference framework. The methods are divided into two categories depending on whether they require all three assumptions of the potential outcome framework or not. For each category, both the traditional statistical methods and the recent machine learning enhanced methods are discussed and compared. The plausible applications of these methods are also presented, including the applications in advertising, recommendation, medicine and so on. Moreover, the commonly used benchmark datasets as well as the open-source codes are also summarized, which facilitate researchers and practitioners to explore, evaluate and apply the causal inference methods.

A key component to the success of deep learning is the availability of massive amounts of training data. Building and annotating large datasets for solving medical image classification problems is today a bottleneck for many applications. Recently, capsule networks were proposed to deal with shortcomings of Convolutional Neural Networks (ConvNets). In this work, we compare the behavior of capsule networks against ConvNets under typical datasets constraints of medical image analysis, namely, small amounts of annotated data and class-imbalance. We evaluate our experiments on MNIST, Fashion-MNIST and medical (histological and retina images) publicly available datasets. Our results suggest that capsule networks can be trained with less amount of data for the same or better performance and are more robust to an imbalanced class distribution, which makes our approach very promising for the medical imaging community.

The field of Multi-Agent System (MAS) is an active area of research within Artificial Intelligence, with an increasingly important impact in industrial and other real-world applications. Within a MAS, autonomous agents interact to pursue personal interests and/or to achieve common objectives. Distributed Constraint Optimization Problems (DCOPs) have emerged as one of the prominent agent architectures to govern the agents' autonomous behavior, where both algorithms and communication models are driven by the structure of the specific problem. During the last decade, several extensions to the DCOP model have enabled them to support MAS in complex, real-time, and uncertain environments. This survey aims at providing an overview of the DCOP model, giving a classification of its multiple extensions and addressing both resolution methods and applications that find a natural mapping within each class of DCOPs. The proposed classification suggests several future perspectives for DCOP extensions, and identifies challenges in the design of efficient resolution algorithms, possibly through the adaptation of strategies from different areas.

This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as positive-semidefiniteness, and they can produce approximations with a user-specified rank. The algorithms are simple, accurate, numerically stable, and provably correct. Moreover, each method is accompanied by an informative error bound that allows users to select parameters a priori to achieve a given approximation quality. These claims are supported by numerical experiments with real and synthetic data.