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As the coronavirus disease 2019 outbreak evolves, statistical network analysis is playing an essential role in informing policy decisions. Therefore, researchers who are new to such studies need to understand the techniques available to them. As a field, statistical network analysis aims to develop methods that account for the complex dependencies found in network data. Over the last few decades, the area has rapidly accumulated methods, including techniques for network modelling and simulating the spread of infectious disease. This article reviews these network modelling techniques and their applications to the coronavirus disease 2019 pandemic.

 

We consider a multi-agent multi-armed bandit setting in which n honest agents collaborate over a network to minimize regret but m malicious agents can disrupt learning arbitrarily. Assuming the network is the complete graph, existing algorithms incur O((m + K/n) łog (T) / Δ ) regret in this setting, where K is the number of arms and Δ is the arm gap. For m łl K, this improves over the single-agent baseline regret of O(Kłog(T)/Δ). In this work, we show the situation is murkier beyond the case of a complete graph. In particular, we prove that if the state-of-the-art algorithm is used on the undirected line graph, honest agents can suffer (nearly) linear regret until time is doubly exponential in K and n . In light of this negative result, we propose a new algorithm for which the i -th agent has regret O(( dmal (i) + K/n) łog(T)/Δ) on any connected and undirected graph, where dmal(i) is the number of i 's neighbors who are malicious. Thus, we generalize existing regret bounds beyond the complete graph (where dmal(i) = m), and show the effect of malicious agents is entirely local (in the sense that only the dmal (i) malicious agents directly connected to i affect its long-term regret). 

Distributed machine learning is primarily motivated by the promise of increased computation power for accelerating training and mitigating privacy concerns. Unlike machine learning on a single device, distributed machine learning requires collaboration and communication among the devices. This creates several new challenges: (1) the heavy communication overhead can be a bottleneck that slows down the training, and (2) the unreliable communication and weaker control over the remote entities make the distributed system vulnerable to systematic failures and malicious attacks. This paper presents a variant of stochastic gradient descent (SGD) with improved communication efficiency and security in distributed environments. Our contributions include (1) a new technique called error reset to adapt both infrequent synchronization and message compression for communication reduction in both synchronous and asynchronous training, (2) new score-based approaches for validating the updates, and (3) integration with both error reset and score-based validation. The proposed system provides communication reduction, both synchronous and asynchronous training, Byzantine tolerance, and local privacy preservation. We evaluate our techniques both theoretically and empirically. 

We propose a flexible, yet interpretable model for high-dimensional data with time-varying second-order statistics, motivated and applied to functional neuroimaging data. Our approach implements the neuroscientific hypothesis of discrete cognitive processes by factorizing covariances into sparse spatial and smooth temporal components. Although this factorization results in parsimony and domain interpretability, the resulting estimation problem is nonconvex. We design a two-stage optimization scheme with a tailored spectral initialization, combined with iteratively refined alternating projected gradient descent. We prove a linear convergence rate up to a nontrivial statistical error for the proposed descent scheme and establish sample complexity guarantees for the estimator. Empirical results using simulated data and brain imaging data illustrate that our approach outperforms existing baselines.