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In the single winner determination problem, we have n voters and m candidates and each voter j incurs a cost c(i, j) if candidate i is chosen. Our objective is to choose a candidate that minimizes the expected total cost incurred by the voters; however as we only have access to the agents' preference rankings over the outcomes, a loss of efficiency is inevitable. This loss of efficiency is quantified by distortion. We give an instance of the metric single winner determination problem for which any randomized social choice function has distortion at least 2.063164. This disproves the long-standing conjecture that there exists a randomized social choice function that has a worst-case distortion of at most 2.

In this paper, we present a framework that unites obstacle avoidance and deliberate physical interaction for robotic manipulators. As humans and robots begin to coexist in work and household environments, pure collision avoidance is insufficient, as human-robot contact is inevitable and, in some situations, desired. Our work enables manipulators to anticipate, detect, and act on contact. To achieve this, we allow limited deviation from the robot's original trajectory through velocity reduction and motion restrictions. Then, if contact occurs, a robot can detect it and maneuver based on a novel dynamic contact thresholding algorithm. The core contribution of this work is dynamic contact thresholding, which allows a manipulator with onboard proximity sensors to track nearby objects and reduce contact forces in anticipation of a collision. Our framework elicits natural behavior during physical human-robot interaction. We evaluate our system on a variety of scenarios using the Franka Emika Panda robot arm; collectively, our results demonstrate that our contribution is not only able to avoid and react on contact, but also anticipate it.

There has been a rich development of vector autoregressive (VAR) models for modeling temporally correlated multivariate outcomes. However, the existing VAR literature has largely focused on single subject parametric analysis, with some recent extensions to multi-subject modeling with known subgroups. Motivated by the need for flexible Bayesian methods that can pool information across heterogeneous samples in an unsupervised manner, we develop a novel class of non-parametric Bayesian VAR models based on heterogeneous multi-subject data. In particular, we propose a product of Dirichlet process mixture priors that enables separate clustering at multiple scales, which result in partially overlapping clusters that provide greater flexibility. We develop several variants of the method to cater to varying levels of heterogeneity. We implement an efficient posterior computation scheme and illustrate posterior consistency properties under reasonable assumptions on the true density. Extensive numerical studies show distinct advantages over competing methods in terms of estimating model parameters and identifying the true clustering and sparsity structures. Our analysis of resting state fMRI data from the Human Connectome Project reveals biologically interpretable differences between distinct fluid intelligence groups, and reproducible parameter estimates. In contrast, single-subject VAR analyses followed by permutation testing result in negligible differences, which is biologically implausible.

The geometric median of a tuple of vectors is the vector that minimizes the sum of Euclidean distances to the vectors of the tuple. Classically called the Fermat-Weber problem and applied to facility location, it has become a major component of the robust learning toolbox. It is typically used to aggregate the (processed) inputs of different data providers, whose motivations may diverge, especially in applications like content moderation. Interestingly, as a voting system, the geometric median has well-known desirable properties: it is a provably good average approximation, it is robust to a minority of malicious voters, and it satisfies the "one voter, one unit force" fairness principle. However, what was not known is the extent to which the geometric median is strategyproof. Namely, can a strategic voter significantly gain by misreporting their preferred vector? We prove in this paper that, perhaps surprisingly, the geometric median is not even $\alpha$-strategyproof, where $\alpha$ bounds what a voter can gain by deviating from truthfulness. But we also prove that, in the limit of a large number of voters with i.i.d. preferred vectors, the geometric median is asymptotically $\alpha$-strategyproof. We show how to compute this bound $\alpha$. We then generalize our results to voters who care more about some dimensions. Roughly, we show that, if some dimensions are more polarized and regarded as more important, then the geometric median becomes less strategyproof. Interestingly, we also show how the skewed geometric medians can improve strategyproofness. Nevertheless, if voters care differently about different dimensions, we prove that no skewed geometric median can achieve strategyproofness for all. Overall, our results constitute a coherent set of insights into the extent to which the geometric median is suitable to aggregate high-dimensional disagreements.

In this paper, we propose a method for generating a hierarchical, volumetric topological map from 3D point clouds. There are three basic hierarchical levels in our map: $storey - region - volume$. The advantages of our method are reflected in both input and output. In terms of input, we accept multi-storey point clouds and building structures with sloping roofs or ceilings. In terms of output, we can generate results with metric information of different dimensionality, that are suitable for different robotics applications. The algorithm generates the volumetric representation by generating $volumes$ from a 3D voxel occupancy map. We then add $passage$s (connections between $volumes$), combine small $volumes$ into a big $region$ and use a 2D segmentation method for better topological representation. We evaluate our method on several freely available datasets. The experiments highlight the advantages of our approach.

This paper presents a distributed algorithm applicable to a wide range of practical multi-robot applications. In such multi-robot applications, the user-defined objectives of the mission can be cast as a general optimization problem, without explicit guidelines of the subtasks per different robot. Owing to the unknown environment, unknown robot dynamics, sensor nonlinearities, etc., the analytic form of the optimization cost function is not available a priori. Therefore, standard gradient-descent-like algorithms are not applicable to these problems. To tackle this, we introduce a new algorithm that carefully designs each robot's subcost function, the optimization of which can accomplish the overall team objective. Upon this transformation, we propose a distributed methodology based on the cognitive-based adaptive optimization (CAO) algorithm, that is able to approximate the evolution of each robot's cost function and to adequately optimize its decision variables (robot actions). The latter can be achieved by online learning only the problem-specific characteristics that affect the accomplishment of mission objectives. The overall, low-complexity algorithm can straightforwardly incorporate any kind of operational constraint, is fault tolerant, and can appropriately tackle time-varying cost functions. A cornerstone of this approach is that it shares the same convergence characteristics as those of block coordinate descent algorithms. The proposed algorithm is evaluated in three heterogeneous simulation set-ups under multiple scenarios, against both general-purpose and problem-specific algorithms. Source code is available at \url{//github.com/athakapo/A-distributed-plug-n-play-algorithm-for-multi-robot-applications}.

We consider the problem of secure distributed matrix computation (SDMC), where a \textit{user} queries a function of data matrices generated at distributed \textit{source} nodes. We assume the availability of $N$ honest but curious computation servers, which are connected to the sources, the user, and each other through orthogonal and reliable communication links. Our goal is to minimize the amount of data that must be transmitted from the sources to the servers, called the \textit{upload cost}, while guaranteeing that no $T$ colluding servers can learn any information about the source matrices, and the user cannot learn any information beyond the computation result. We first focus on secure distributed matrix multiplication (SDMM), considering two matrices, and propose a novel polynomial coding scheme using the properties of finite field discrete Fourier transform, which achieves an upload cost significantly lower than the existing results in the literature. We then generalize the proposed scheme to include straggler mitigation, and to the multiplication of multiple matrices while keeping the input matrices, the intermediate computation results, as well as the final result secure against any $T$ colluding servers. We also consider a special case, called computation with own data, where the data matrices used for computation belong to the user. In this case, we drop the security requirement against the user, and show that the proposed scheme achieves the minimal upload cost. We then propose methods for performing other common matrix computations securely on distributed servers, including changing the parameters of secret sharing, matrix transpose, matrix exponentiation, solving a linear system, and matrix inversion, which are then used to show how arbitrary matrix polynomials can be computed securely on distributed servers using the proposed procedure.

We present R-LINS, a lightweight robocentric lidar-inertial state estimator, which estimates robot ego-motion using a 6-axis IMU and a 3D lidar in a tightly-coupled scheme. To achieve robustness and computational efficiency even in challenging environments, an iterated error-state Kalman filter (ESKF) is designed, which recursively corrects the state via repeatedly generating new corresponding feature pairs. Moreover, a novel robocentric formulation is adopted in which we reformulate the state estimator concerning a moving local frame, rather than a fixed global frame as in the standard world-centric lidar-inertial odometry(LIO), in order to prevent filter divergence and lower computational cost. To validate generalizability and long-time practicability, extensive experiments are performed in indoor and outdoor scenarios. The results indicate that R-LINS outperforms lidar-only and loosely-coupled algorithms, and achieve competitive performance as the state-of-the-art LIO with close to an order-of-magnitude improvement in terms of speed.

Network embedding aims to learn a latent, low-dimensional vector representations of network nodes, effective in supporting various network analytic tasks. While prior arts on network embedding focus primarily on preserving network topology structure to learn node representations, recently proposed attributed network embedding algorithms attempt to integrate rich node content information with network topological structure for enhancing the quality of network embedding. In reality, networks often have sparse content, incomplete node attributes, as well as the discrepancy between node attribute feature space and network structure space, which severely deteriorates the performance of existing methods. In this paper, we propose a unified framework for attributed network embedding-attri2vec-that learns node embeddings by discovering a latent node attribute subspace via a network structure guided transformation performed on the original attribute space. The resultant latent subspace can respect network structure in a more consistent way towards learning high-quality node representations. We formulate an optimization problem which is solved by an efficient stochastic gradient descent algorithm, with linear time complexity to the number of nodes. We investigate a series of linear and non-linear transformations performed on node attributes and empirically validate their effectiveness on various types of networks. Another advantage of attri2vec is its ability to solve out-of-sample problems, where embeddings of new coming nodes can be inferred from their node attributes through the learned mapping function. Experiments on various types of networks confirm that attri2vec is superior to state-of-the-art baselines for node classification, node clustering, as well as out-of-sample link prediction tasks. The source code of this paper is available at //github.com/daokunzhang/attri2vec.

Importance sampling is one of the most widely used variance reduction strategies in Monte Carlo rendering. In this paper, we propose a novel importance sampling technique that uses a neural network to learn how to sample from a desired density represented by a set of samples. Our approach considers an existing Monte Carlo rendering algorithm as a black box. During a scene-dependent training phase, we learn to generate samples with a desired density in the primary sample space of the rendering algorithm using maximum likelihood estimation. We leverage a recent neural network architecture that was designed to represent real-valued non-volume preserving ('Real NVP') transformations in high dimensional spaces. We use Real NVP to non-linearly warp primary sample space and obtain desired densities. In addition, Real NVP efficiently computes the determinant of the Jacobian of the warp, which is required to implement the change of integration variables implied by the warp. A main advantage of our approach is that it is agnostic of underlying light transport effects, and can be combined with many existing rendering techniques by treating them as a black box. We show that our approach leads to effective variance reduction in several practical scenarios.