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We study distributed estimation and learning problems in a networked environment in which agents exchange information to estimate unknown statistical properties of random variables from their privately observed samples. By exchanging information about their private observations, the agents can collectively estimate the unknown quantities, but they also face privacy risks. The goal of our aggregation schemes is to combine the observed data efficiently over time and across the network, while accommodating the privacy needs of the agents and without any coordination beyond their local neighborhoods. Our algorithms enable the participating agents to estimate a complete sufficient statistic from private signals that are acquired offline or online over time, and to preserve the privacy of their signals and network neighborhoods. This is achieved through linear aggregation schemes with adjusted randomization schemes that add noise to the exchanged estimates subject to differential privacy (DP) constraints. In every case, we demonstrate the efficiency of our algorithms by proving convergence to the estimators of a hypothetical, omniscient observer that has central access to all of the signals. We also provide convergence rate analysis and finite-time performance guarantees and show that the noise that minimizes the convergence time to the best estimates is the Laplace noise, with parameters corresponding to each agent's sensitivity to their signal and network characteristics. Finally, to supplement and validate our theoretical results, we run experiments on real-world data from the US Power Grid Network and electric consumption data from German Households to estimate the average power consumption of power stations and households under all privacy regimes.

We present a new approach to approximate nearest-neighbor queries in fixed dimension under a variety of non-Euclidean distances. We are given a set $S$ of $n$ points in $\mathbb{R}^d$, an approximation parameter $\varepsilon > 0$, and a distance function that satisfies certain smoothness and growth-rate assumptions. The objective is to preprocess $S$ into a data structure so that for any query point $q$ in $\mathbb{R}^d$, it is possible to efficiently report any point of $S$ whose distance from $q$ is within a factor of $1+\varepsilon$ of the actual closest point. Prior to this work, the most efficient data structures for approximate nearest-neighbor searching in spaces of constant dimensionality applied only to the Euclidean metric. This paper overcomes this limitation through a method called convexification. For admissible distance functions, the proposed data structures answer queries in logarithmic time using $O(n \log (1 / \varepsilon) / \varepsilon^{d/2})$ space, nearly matching the best known bounds for the Euclidean metric. These results apply to both convex scaling distance functions (including the Mahalanobis distance and weighted Minkowski metrics) and Bregman divergences (including the Kullback-Leibler divergence and the Itakura-Saito distance).

We present a novel and easy-to-use method for calibrating error-rate based confidence intervals to evidence-based support intervals. Support intervals are obtained from inverting Bayes factors based on a parameter estimate and its standard error. A $k$ support interval can be interpreted as "the observed data are at least $k$ times more likely under the included parameter values than under a specified alternative". Support intervals depend on the specification of prior distributions for the parameter under the alternative, and we present several types that allow different forms of external knowledge to be encoded. We also show how prior specification can to some extent be avoided by considering a class of prior distributions and then computing so-called minimum support intervals which, for a given class of priors, have a one-to-one mapping with confidence intervals. We also illustrate how the sample size of a future study can be determined based on the concept of support. Finally, we show how the bound for the type I error rate of Bayes factors leads to a bound for the coverage of support intervals. An application to data from a clinical trial illustrates how support intervals can lead to inferences that are both intuitive and informative.

In this paper, we first introduce the multilayer random dot product graph (MRDPG) model, which can be seen as an extension of the random dot product graph model to multilayer networks. The MRDPG model is convenient for incorporating nodes' latent positions when understanding connectivity. By modelling a multilayer network as an MRDPG, we further deploy a tensor-based method and demonstrate its superiority over the state-of-the-art methods. We then move from a static to a dynamic MRDPG and are concerned with online change point detection problems. At every time point, we observe a realisation from an $L$-layered MRDPG. Across layers, we assume shared common node sets and latent positions, but allow for different connectivity matrices. In this paper we unfold a comprehensive picture concerning a range of problems. For both fixed and random latent position cases, we propose efficient online change point detection algorithms, minimising the delay in detection while controlling the false alarms. Notably, in the random latent position case, we devise a novel nonparametric change point detection algorithm with a kernel estimator in its core, allowing for the case when the density does not exist, accommodating stochastic block models as special cases. Our theoretical findings are supported by extensive numerical experiments, with the code available online //github.com/MountLee/MRDPG.

Eigenspace estimation is fundamental in machine learning and statistics, which has found applications in PCA, dimension reduction, and clustering, among others. The modern machine learning community usually assumes that data come from and belong to different organizations. The low communication power and the possible privacy breaches of data make the computation of eigenspace challenging. To address these challenges, we propose a class of algorithms called \textsf{FedPower} within the federated learning (FL) framework. \textsf{FedPower} leverages the well-known power method by alternating multiple local power iterations and a global aggregation step, thus improving communication efficiency. In the aggregation, we propose to weight each local eigenvector matrix with {\it Orthogonal Procrustes Transformation} (OPT) for better alignment. To ensure strong privacy protection, we add Gaussian noise in each iteration by adopting the notion of \emph{differential privacy} (DP). We provide convergence bounds for \textsf{FedPower} that are composed of different interpretable terms corresponding to the effects of Gaussian noise, parallelization, and random sampling of local machines. Additionally, we conduct experiments to demonstrate the effectiveness of our proposed algorithms.

Missing data is frequently encountered in many areas of statistics. Imputation and propensity score weighting are two popular methods for handling missing data. These methods employ some model assumptions, either the outcome regression or the response propensity model. However, correct specification of the statistical model can be challenging in the presence of missing data. Doubly robust estimation is attractive as the consistency of the estimator is guaranteed when either the outcome regression model or the propensity score model is correctly specified. In this paper, we first employ information projection to develop an efficient and doubly robust estimator under indirect model calibration constraints. The resulting propensity score estimator can be equivalently expressed as a doubly robust regression imputation estimator by imposing the internal bias calibration condition in estimating the regression parameters. In addition, we generalize the information projection to allow for outlier-robust estimation. Thus, we achieve triply robust estimation by adding the outlier robustness condition to the double robustness condition. Some asymptotic properties are presented. The simulation study confirms that the proposed method allows robust inference against not only the violation of various model assumptions, but also outliers.

Grey-box fuzzing is the lightweight approach of choice for finding bugs in sequential programs. It provides a balance between efficiency and effectiveness by conducting a biased random search over the domain of program inputs using a feedback function from observed test executions. For distributed system testing, however, the state-of-practice is represented today by only black-box tools that do not attempt to infer and exploit any knowledge of the system's past behaviours to guide the search for bugs. In this work, we present Mallory: the first framework for grey-box fuzz-testing of distributed systems. Unlike popular black-box distributed system fuzzers, such as Jepsen, that search for bugs by randomly injecting network partitions and node faults or by following human-defined schedules, Mallory is adaptive. It exercises a novel metric to learn how to maximize the number of observed system behaviors by choosing different sequences of faults, thus increasing the likelihood of finding new bugs. The key enablers for our approach are the new ideas of timeline-driven testing and timeline abstraction that provide the feedback function guiding a biased random search for failures. Mallory dynamically constructs Lamport timelines of the system behaviour, abstracts these timelines into happens-before summaries, and introduces faults guided by its real-time observation of the summaries. We have evaluated Mallory on a diverse set of widely-used industrial distributed systems. Compared to the start-of-the-art black-box fuzzer Jepsen, Mallory explores more behaviours and takes less time to find bugs. Mallory discovered 22 zero-day bugs (of which 18 were confirmed by developers), including 10 new vulnerabilities, in rigorously-tested distributed systems such as Braft, Dqlite, and Redis. 6 new CVEs have been assigned.

Separating signals from an additive mixture may be an unnecessarily hard problem when one is only interested in specific properties of a given signal. In this work, we tackle simpler "statistical component separation" problems that focus on recovering a predefined set of statistical descriptors of a target signal from a noisy mixture. Assuming access to samples of the noise process, we investigate a method devised to match the statistics of the solution candidate corrupted by noise samples with those of the observed mixture. We first analyze the behavior of this method using simple examples with analytically tractable calculations. Then, we apply it in an image denoising context employing 1) wavelet-based descriptors, 2) ConvNet-based descriptors on astrophysics and ImageNet data. In the case of 1), we show that our method better recovers the descriptors of the target data than a standard denoising method in most situations. Additionally, despite not constructed for this purpose, it performs surprisingly well in terms of peak signal-to-noise ratio on full signal reconstruction. In comparison, representation 2) appears less suitable for image denoising. Finally, we extend this method by introducing a diffusive stepwise algorithm which gives a new perspective to the initial method and leads to promising results for image denoising under specific circumstances.

Evaluating the impact of policy interventions on respondents who are embedded in a social network is often challenging due to the presence of network interference within the treatment groups, as well as between treatment and non-treatment groups throughout the network. In this paper, we propose a modeling strategy that combines existing work on stochastic actor-oriented models (SAOM) and diffusion contagion models with a novel network sampling method based on the identification of independent sets. By assigning respondents from an independent set to the treatment, we are able to block any direct spillover of the treatment, thereby allowing us to isolate the direct effect of the treatment from the indirect network-induced effects. As a result, our method allows for the estimation of both the direct as well as the net effect of a chosen policy intervention, in the presence of network effects in the population. We perform a comparative simulation analysis to show that the choice of sampling technique leads to significantly distinct estimates for both direct and net effects of the policy, as well as for the relevant network effects, such as homophily. Furthermore, using a modified diffusion contagion model, we show that our proposed sampling technique leads to greater and faster spread of the policy-linked behavior through the network. This study highlights the importance of network sampling techniques in improving policy evaluation studies and has the potential to help researchers and policymakers with better planning, designing, and anticipating policy responses in a networked society.

This paper aims to mitigate straggler effects in synchronous distributed learning for multi-agent reinforcement learning (MARL) problems. Stragglers arise frequently in a distributed learning system, due to the existence of various system disturbances such as slow-downs or failures of compute nodes and communication bottlenecks. To resolve this issue, we propose a coded distributed learning framework, which speeds up the training of MARL algorithms in the presence of stragglers, while maintaining the same accuracy as the centralized approach. As an illustration, a coded distributed version of the multi-agent deep deterministic policy gradient(MADDPG) algorithm is developed and evaluated. Different coding schemes, including maximum distance separable (MDS)code, random sparse code, replication-based code, and regular low density parity check (LDPC) code are also investigated. Simulations in several multi-robot problems demonstrate the promising performance of the proposed framework.