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Emerging distributed cloud architectures, e.g., fog and mobile edge computing, are playing an increasingly important role in the efficient delivery of real-time stream-processing applications such as augmented reality, multiplayer gaming, and industrial automation. While such applications require processed streams to be shared and simultaneously consumed by multiple users/devices, existing technologies lack efficient mechanisms to deal with their inherent multicast nature, leading to unnecessary traffic redundancy and network congestion. In this paper, we establish a unified framework for distributed cloud network control with generalized (mixed-cast) traffic flows that allows optimizing the distributed execution of the required packet processing, forwarding, and replication operations. We first characterize the enlarged multicast network stability region under the new control framework (with respect to its unicast counterpart). We then design a novel queuing system that allows scheduling data packets according to their current destination sets, and leverage Lyapunov drift-plus-penalty theory to develop the first fully decentralized, throughput- and cost-optimal algorithm for multicast cloud network flow control. Numerical experiments validate analytical results and demonstrate the performance gain of the proposed design over existing cloud network control techniques.

Linear mixed models (LMMs) are instrumental for regression analysis with structured dependence, such as grouped, clustered, or multilevel data. However, selection among the covariates--while accounting for this structured dependence--remains a challenge. We introduce a Bayesian decision analysis for subset selection with LMMs. Using a Mahalanobis loss function that incorporates the structured dependence, we derive optimal linear coefficients for (i) any given subset of variables and (ii) all subsets of variables that satisfy a cardinality constraint. Crucially, these estimates inherit shrinkage or regularization and uncertainty quantification from the underlying Bayesian model, and apply for any well-specified Bayesian LMM. More broadly, our decision analysis strategy deemphasizes the role of a single "best" subset, which is often unstable and limited in its information content, and instead favors a collection of near-optimal subsets. This collection is summarized by key member subsets and variable-specific importance metrics. Customized subset search and out-of-sample approximation algorithms are provided for more scalable computing. These tools are applied to simulated data and a longitudinal physical activity dataset, and demonstrate excellent prediction, estimation, and selection ability.

Collision avoidance is a widely investigated topic in robotic applications. When applying collision avoidance techniques to a mobile robot, how to deal with the spatial structure of the robot still remains a challenge. In this paper, we design a configuration-aware safe control law by solving a Quadratic Programming (QP) with designed Control Barrier Functions (CBFs) constraints, which can safely navigate a mobile robotic arm to a desired region while avoiding collision with environmental obstacles. The advantage of our approach is that it correctly and in an elegant way incorporates the spatial structure of the mobile robotic arm. This is achieved by merging geometric restrictions among mobile robotic arm links into CBFs constraints. Simulations on a rigid rod and the modeled mobile robotic arm are performed to verify the feasibility and time-efficiency of proposed method. Numerical results about the time consuming for different degrees of freedom illustrate that our method scales well with dimension.

Autonomous marine vessels are expected to avoid inter-vessel collisions and comply with the international regulations for safe voyages. This paper presents a stepwise path planning method using stream functions. The dynamic flow of fluids is used as a guidance model, where the collision avoidance in static environments is achieved by applying the circular theorem in the sink flow. We extend this method to dynamic environments by adding vortex flows in the flow field. The stream function is recursively updated to enable on the fly waypoint decisions. The vessel avoids collisions and also complies with several rules of the Convention on the International Regulations for Preventing Collisions at Sea. The method is conceptually and computationally simple and convenient to tune, and yet versatile to handle complex and dense marine traffic with multiple dynamic obstacles. The ship dynamics are taken into account, by using B\'{e}zier curves to generate a sufficiently smooth path with feasible curvature. Numerical simulations are conducted to verify the proposed method.

We introduce the first algorithm for distributed decision-making that provably balances the trade-off of centralization, for global near-optimality, vs. decentralization, for near-minimal on-board computation, communication, and memory resources. We are motivated by the future of autonomy that involves heterogeneous robots collaborating in complex~tasks, such as image covering, target tracking, and area monitoring. Current algorithms, such as consensus algorithms, are insufficient to fulfill this future: they achieve distributed communication only, at the expense of high communication, computation, and memory overloads. A shift to resource-aware algorithms is needed, that can account for each robot's on-board resources, independently. We provide the first resource-aware algorithm, Resource-Aware distributed Greedy (RAG). We focus on maximization problems involving monotone and "doubly" submodular functions, a diminishing returns property. RAG has near-minimal on-board resource requirements. Each agent can afford to run the algorithm by adjusting the size of its neighborhood, even if that means selecting actions in complete isolation. RAG has provable approximation performance, where each agent can independently determine its contribution. All in all, RAG is the first algorithm to quantify the trade-off of centralization, for global near-optimality, vs. decentralization, for near-minimal on-board resource requirements. To capture the trade-off, we introduce the notion of Centralization Of Information among non-Neighbors (COIN). We validate RAG in simulated scenarios of image covering with mobile robots.

Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal likelihood (model evidence), which is computationally challenging, prohibiting its use in many high-dimensional Bayesian inverse problems. With Bayesian imaging applications in mind, in this work we present the proximal nested sampling methodology to objectively compare alternative Bayesian imaging models for applications that use images to inform decisions under uncertainty. The methodology is based on nested sampling, a Monte Carlo approach specialised for model comparison, and exploits proximal Markov chain Monte Carlo techniques to scale efficiently to large problems and to tackle models that are log-concave and not necessarily smooth (e.g., involving l_1 or total-variation priors). The proposed approach can be applied computationally to problems of dimension O(10^6) and beyond, making it suitable for high-dimensional inverse imaging problems. It is validated on large Gaussian models, for which the likelihood is available analytically, and subsequently illustrated on a range of imaging problems where it is used to analyse different choices of dictionary and measurement model.

One of the most important problems in system identification and statistics is how to estimate the unknown parameters of a given model. Optimization methods and specialized procedures, such as Empirical Minimization (EM) can be used in case the likelihood function can be computed. For situations where one can only simulate from a parametric model, but the likelihood is difficult or impossible to evaluate, a technique known as the Two-Stage (TS) Approach can be applied to obtain reliable parametric estimates. Unfortunately, there is currently a lack of theoretical justification for TS. In this paper, we propose a statistical decision-theoretical derivation of TS, which leads to Bayesian and Minimax estimators. We also show how to apply the TS approach on models for independent and identically distributed samples, by computing quantiles of the data as a first step, and using a linear function as the second stage. The proposed method is illustrated via numerical simulations.

We propose a new fast streaming algorithm for the tensor completion problem of imputing missing entries of a low-tubal-rank tensor using the tensor singular value decomposition (t-SVD) algebraic framework. We show the t-SVD is a specialization of the well-studied block-term decomposition for third-order tensors, and we present an algorithm under this model that can track changing free submodules from incomplete streaming 2-D data. The proposed algorithm uses principles from incremental gradient descent on the Grassmann manifold of subspaces to solve the tensor completion problem with linear complexity and constant memory in the number of time samples. We provide a local expected linear convergence result for our algorithm. Our empirical results are competitive in accuracy but much faster in compute time than state-of-the-art tensor completion algorithms on real applications to recover temporal chemo-sensing and MRI data under limited sampling.

In the pooled data problem we are given a set of $n$ agents, each of which holds a hidden state bit, either $0$ or $1$. A querying procedure returns for a query set the sum of the states of the queried agents. The goal is to reconstruct the states using as few queries as possible. In this paper we consider two noise models for the pooled data problem. In the noisy channel model, the result for each agent flips with a certain probability. In the noisy query model, each query result is subject to random Gaussian noise. Our results are twofold. First, we present and analyze for both error models a simple and efficient distributed algorithm that reconstructs the initial states in a greedy fashion. Our novel analysis pins down the range of error probabilities and distributions for which our algorithm reconstructs the exact initial states with high probability. Secondly, we present simulation results of our algorithm and compare its performance with approximate message passing (AMP) algorithms that are conjectured to be optimal in a number of related problems.

Effective multi-robot teams require the ability to move to goals in complex environments in order to address real-world applications such as search and rescue. Multi-robot teams should be able to operate in a completely decentralized manner, with individual robot team members being capable of acting without explicit communication between neighbors. In this paper, we propose a novel game theoretic model that enables decentralized and communication-free navigation to a goal position. Robots each play their own distributed game by estimating the behavior of their local teammates in order to identify behaviors that move them in the direction of the goal, while also avoiding obstacles and maintaining team cohesion without collisions. We prove theoretically that generated actions approach a Nash equilibrium, which also corresponds to an optimal strategy identified for each robot. We show through extensive simulations that our approach enables decentralized and communication-free navigation by a multi-robot system to a goal position, and is able to avoid obstacles and collisions, maintain connectivity, and respond robustly to sensor noise.