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Both capacity and latency are crucial performance metrics for the optimal operation of most networking services and applications, from online gaming to futuristic holographic-type communications. Networks worldwide have witnessed important breakthroughs in terms of capacity, including fibre introduction everywhere, new radio technologies and faster core networks. However, the impact of these capacity upgrades on end-to-end delay is not straightforward as traffic has also grown exponentially. This article overviews the current status of end-to-end latency on different regions and continents worldwide and how far these are from the theoretical minimum baseline, given by the speed of light propagation over an optical fibre. We observe that the trend in the last decade goes toward latency reduction (in spite of the ever-increasing annual traffic growth), but still there are important differences between countries.

This paper presents a novel approach to Bayesian nonparametric spectral analysis of stationary multivariate time series. Starting with a parametric vector-autoregressive model, the parametric likelihood is nonparametrically adjusted in the frequency domain to account for potential deviations from parametric assumptions. We show mutual contiguity of the nonparametrically corrected likelihood, the multivariate Whittle likelihood approximation and the exact likelihood for Gaussian time series. A multivariate extension of the nonparametric Bernstein-Dirichlet process prior for univariate spectral densities to the space of Hermitian positive definite spectral density matrices is specified directly on the correction matrices. An infinite series representation of this prior is then used to develop a Markov chain Monte Carlo algorithm to sample from the posterior distribution. The code is made publicly available for ease of use and reproducibility. With this novel approach we provide a generalization of the multivariate Whittle-likelihood-based method of Meier et al. (2020) as well as an extension of the nonparametrically corrected likelihood for univariate stationary time series of Kirch et al. (2019) to the multivariate case. We demonstrate that the nonparametrically corrected likelihood combines the efficiencies of a parametric with the robustness of a nonparametric model. Its numerical accuracy is illustrated in a comprehensive simulation study. We illustrate its practical advantages by a spectral analysis of two environmental time series data sets: a bivariate time series of the Southern Oscillation Index and fish recruitment and time series of windspeed data at six locations in California.

The use of quantum processing units (QPUs) promises speed-ups for solving computational problems. Yet, current devices are limited by the number of qubits and suffer from significant imperfections, which prevents achieving quantum advantage. To step towards practical utility, one approach is to apply hardware-software co-design methods. This can involve tailoring problem formulations and algorithms to the quantum execution environment, but also entails the possibility of adapting physical properties of the QPU to specific applications. In this work, we follow the latter path, and investigate how key figures - circuit depth and gate count - required to solve four cornerstone NP-complete problems vary with tailored hardware properties. Our results reveal that achieving near-optimal performance and properties does not necessarily require optimal quantum hardware, but can be satisfied with much simpler structures that can potentially be realised for many hardware approaches. Using statistical analysis techniques, we additionally identify an underlying general model that applies to all subject problems. This suggests that our results may be universally applicable to other algorithms and problem domains, and tailored QPUs can find utility outside their initially envisaged problem domains. The substantial possible improvements nonetheless highlight the importance of QPU tailoring to progress towards practical deployment and scalability of quantum software.

Given the exponential growth of the volume of the ball w.r.t. its radius, the hyperbolic space is capable of embedding trees with arbitrarily small distortion and hence has received wide attention for representing hierarchical datasets. However, this exponential growth property comes at a price of numerical instability such that training hyperbolic learning models will sometimes lead to catastrophic NaN problems, encountering unrepresentable values in floating point arithmetic. In this work, we carefully analyze the limitation of two popular models for the hyperbolic space, namely, the Poincar\'e ball and the Lorentz model. We first show that, under the 64 bit arithmetic system, the Poincar\'e ball has a relatively larger capacity than the Lorentz model for correctly representing points. Then, we theoretically validate the superiority of the Lorentz model over the Poincar\'e ball from the perspective of optimization. Given the numerical limitations of both models, we identify one Euclidean parametrization of the hyperbolic space which can alleviate these limitations. We further extend this Euclidean parametrization to hyperbolic hyperplanes and exhibits its ability in improving the performance of hyperbolic SVM.

The adaptive processing of structured data is a long-standing research topic in machine learning that investigates how to automatically learn a mapping from a structured input to outputs of various nature. Recently, there has been an increasing interest in the adaptive processing of graphs, which led to the development of different neural network-based methodologies. In this thesis, we take a different route and develop a Bayesian Deep Learning framework for graph learning. The dissertation begins with a review of the principles over which most of the methods in the field are built, followed by a study on graph classification reproducibility issues. We then proceed to bridge the basic ideas of deep learning for graphs with the Bayesian world, by building our deep architectures in an incremental fashion. This framework allows us to consider graphs with discrete and continuous edge features, producing unsupervised embeddings rich enough to reach the state of the art on several classification tasks. Our approach is also amenable to a Bayesian nonparametric extension that automatizes the choice of almost all model's hyper-parameters. Two real-world applications demonstrate the efficacy of deep learning for graphs. The first concerns the prediction of information-theoretic quantities for molecular simulations with supervised neural models. After that, we exploit our Bayesian models to solve a malware-classification task while being robust to intra-procedural code obfuscation techniques. We conclude the dissertation with an attempt to blend the best of the neural and Bayesian worlds together. The resulting hybrid model is able to predict multimodal distributions conditioned on input graphs, with the consequent ability to model stochasticity and uncertainty better than most works. Overall, we aim to provide a Bayesian perspective into the articulated research field of deep learning for graphs.

Graph machine learning has been extensively studied in both academic and industry. However, as the literature on graph learning booms with a vast number of emerging methods and techniques, it becomes increasingly difficult to manually design the optimal machine learning algorithm for different graph-related tasks. To tackle the challenge, automated graph machine learning, which aims at discovering the best hyper-parameter and neural architecture configuration for different graph tasks/data without manual design, is gaining an increasing number of attentions from the research community. In this paper, we extensively discuss automated graph machine approaches, covering hyper-parameter optimization (HPO) and neural architecture search (NAS) for graph machine learning. We briefly overview existing libraries designed for either graph machine learning or automated machine learning respectively, and further in depth introduce AutoGL, our dedicated and the world's first open-source library for automated graph machine learning. Last but not least, we share our insights on future research directions for automated graph machine learning. This paper is the first systematic and comprehensive discussion of approaches, libraries as well as directions for automated graph machine learning.

We address the task of automatically scoring the competency of candidates based on textual features, from the automatic speech recognition (ASR) transcriptions in the asynchronous video job interview (AVI). The key challenge is how to construct the dependency relation between questions and answers, and conduct the semantic level interaction for each question-answer (QA) pair. However, most of the recent studies in AVI focus on how to represent questions and answers better, but ignore the dependency information and interaction between them, which is critical for QA evaluation. In this work, we propose a Hierarchical Reasoning Graph Neural Network (HRGNN) for the automatic assessment of question-answer pairs. Specifically, we construct a sentence-level relational graph neural network to capture the dependency information of sentences in or between the question and the answer. Based on these graphs, we employ a semantic-level reasoning graph attention network to model the interaction states of the current QA session. Finally, we propose a gated recurrent unit encoder to represent the temporal question-answer pairs for the final prediction. Empirical results conducted on CHNAT (a real-world dataset) validate that our proposed model significantly outperforms text-matching based benchmark models. Ablation studies and experimental results with 10 random seeds also show the effectiveness and stability of our models.

Modeling multivariate time series has long been a subject that has attracted researchers from a diverse range of fields including economics, finance, and traffic. A basic assumption behind multivariate time series forecasting is that its variables depend on one another but, upon looking closely, it is fair to say that existing methods fail to fully exploit latent spatial dependencies between pairs of variables. In recent years, meanwhile, graph neural networks (GNNs) have shown high capability in handling relational dependencies. GNNs require well-defined graph structures for information propagation which means they cannot be applied directly for multivariate time series where the dependencies are not known in advance. In this paper, we propose a general graph neural network framework designed specifically for multivariate time series data. Our approach automatically extracts the uni-directed relations among variables through a graph learning module, into which external knowledge like variable attributes can be easily integrated. A novel mix-hop propagation layer and a dilated inception layer are further proposed to capture the spatial and temporal dependencies within the time series. The graph learning, graph convolution, and temporal convolution modules are jointly learned in an end-to-end framework. Experimental results show that our proposed model outperforms the state-of-the-art baseline methods on 3 of 4 benchmark datasets and achieves on-par performance with other approaches on two traffic datasets which provide extra structural information.

In this monograph, I introduce the basic concepts of Online Learning through a modern view of Online Convex Optimization. Here, online learning refers to the framework of regret minimization under worst-case assumptions. I present first-order and second-order algorithms for online learning with convex losses, in Euclidean and non-Euclidean settings. All the algorithms are clearly presented as instantiation of Online Mirror Descent or Follow-The-Regularized-Leader and their variants. Particular attention is given to the issue of tuning the parameters of the algorithms and learning in unbounded domains, through adaptive and parameter-free online learning algorithms. Non-convex losses are dealt through convex surrogate losses and through randomization. The bandit setting is also briefly discussed, touching on the problem of adversarial and stochastic multi-armed bandits. These notes do not require prior knowledge of convex analysis and all the required mathematical tools are rigorously explained. Moreover, all the proofs have been carefully chosen to be as simple and as short as possible.