Multivariate Spatiotemporal Hawkes Processes and Network Reconstruction

There is often latent network structure in spatial and temporal data and the tools of network analysis can yield fascinating insights into such data. In this paper, we develop a nonparametric method for network reconstruction from spatiotemporal data sets using multivariate Hawkes processes. In contrast to prior work on network reconstruction with point-process models, which has often focused on exclusively temporal information, our approach uses both temporal and spatial information and does not assume a specific parametric form of network dynamics. This leads to an effective way of recovering an underlying network. We illustrate our approach using both synthetic networks and networks constructed from real-world data sets (a location-based social media network, a narrative of crime events, and violent gang crimes). Our results demonstrate that, in comparison to using only temporal data, our spatiotemporal approach yields improved network reconstruction, providing a basis for meaningful subsequent analysis --- such as community structure and motif analysis --- of the reconstructed networks

Mobile Agent Trajectory Prediction using Bayesian Nonparametric Reachability Trees

This paper presents an efficient trajectory prediction algorithm that has been developed to improve the performance of future collision avoidance and detection systems. The main idea is to embed the inferred intention information of surrounding agents into their estimated reachability sets to obtain a probabilistic description of their future paths. More specifically, the proposed approach combines the recently developed RRT-Reach algorithm and mixtures of Gaussian Processes. RRT-Reach was introduced by the authors as an extension of the closed-loop rapidly-exploring random tree (CL-RRT) algorithm to compute reachable sets of moving objects in real-time. A mixture of Gaussian processes (GP) is a flexible nonparametric Bayesian model used to represent a distribution over trajectories and have been previously demonstrated by the authors in a UAV interception and tracking of ground vehicles planning scheme. The mixture is trained using typical maneuvers learned from statistical data, and RRT-Reach utilizes samples from the GP to grow probabilistically weighted feasible paths of the surrounding vehicles. The resulting approach, denoted as RR-GP, has RRTReach's benefits of computing trajectories that are dynamically feasible by construction, therefore efficiently approximating the reachability set of surrounding vehicles following typical patterns. RRT-GP also features the GP mixture's benefits of providing a probabilistic weighting on the feasible trajectories produced by RRTReach, allowing our system to systematically weight trajectories by their likelihood. A demonstrative example on a car-like vehicle illustrates the advantages of the RR-GP approach by comparing it to two other GP-based algorithms. © 2011 by Professor Jonathan P. How, Massachusetts Institute of Technology. Published by the American Institute of Aeronautics and Astronautics, Inc

Interfirm Job Mobility of Two Cohorts of Young German Men 1979 - 1990: An analysis of the (West-)German Employment Statistic Register Sample concerning multivariate failure times and unobserved heterogeneity

The OECD (1993) has documented that the majority of workers in industrialised countries can look forward to finding a stable employment relationship. However new entrants into the labor force experience high turnover. Promoting institutions which support longer tenures and worker participation (or ''voice`` in the firm) utilize strategies to encourage enterprise and employee efforts in skill formation and training. The results of the OECD (1993) study show that attachments between employee and employer are more likely to endure for Japanese, French and German workers. Furthermore Germany has the highest share of young new recruits who received any formal training from their employer. In Germany, 71.5 % of young new recruits were trained at any job within 7 years after leaving school, whereas in the U.S. only 10.2 % of young new recruits were similarly trained (cf. OECD 1993, 137). It is sometimes assumed that employment protection policies have been exogenously imposed and thus probably impair efficiency. However, research on the micro-economics of labor markets has shown that employers may be interested in long-term employment relationships (cf. Levine 1991). Here, the job training model focusing on the importance of human capital investment, specifically the job shopping and matching model stressing the process of information gathering through employment experience should be mentioned. In such models employment protection legislation has not only desirable distributional effects but also help to ensure efficient outcomes. Therefore, it is important to assess the relevance of micro- economic theories empirically. This paper provides an empirical analysis of job durations in Western Germany using information from two cohorts of new entrants to the labor force documented in the (West-)German employment statistic register sample (cf. Bender and Hilzendegen 1996). The appropriate empirical technique to study job length is event history or survival analysis. In labor market research, survival analysis has primarily focused on explaining the length of unemployment spells. Application of this technique to employment is less common 1 , because huge longitudinal data sets are needed. Apart from testing hypotheses about the effect of personal characteristics and labor demand variables (e.g. firm size and industry affiliation), we will assess the influence of heterogeneity of the members of the two cohorts on their duration profile. The applied model and estimation method allow for unobserved heterogeneity and correlation between the clustered failure times of one employee as well as for right-censored spells. Our analysis is not restricted to the beginning of the working life of the employees. The individual retirement decision is affected by employment protection and early retirement regulations which differ widely between the firms. The respective data are missing in the employment statistic register, so that the retirement decision cannot be modelled explicitly

Symbol Emergence in Robotics: A Survey

Humans can learn the use of language through physical interaction with their environment and semiotic communication with other people. It is very important to obtain a computational understanding of how humans can form a symbol system and obtain semiotic skills through their autonomous mental development. Recently, many studies have been conducted on the construction of robotic systems and machine-learning methods that can learn the use of language through embodied multimodal interaction with their environment and other systems. Understanding human social interactions and developing a robot that can smoothly communicate with human users in the long term, requires an understanding of the dynamics of symbol systems and is crucially important. The embodied cognition and social interaction of participants gradually change a symbol system in a constructive manner. In this paper, we introduce a field of research called symbol emergence in robotics (SER). SER is a constructive approach towards an emergent symbol system. The emergent symbol system is socially self-organized through both semiotic communications and physical interactions with autonomous cognitive developmental agents, i.e., humans and developmental robots. Specifically, we describe some state-of-art research topics concerning SER, e.g., multimodal categorization, word discovery, and a double articulation analysis, that enable a robot to obtain words and their embodied meanings from raw sensory--motor information, including visual information, haptic information, auditory information, and acoustic speech signals, in a totally unsupervised manner. Finally, we suggest future directions of research in SER.Comment: submitted to Advanced Robotic

Probabilistically Safe Avoidance of Dynamic Obstacles with Uncertain Motion Patterns

This paper presents a real-time path planning algorithm which can guarantee probabilistic feasibility for autonomous robots subject to process noise and an uncertain environment, including dynamic obstacles with uncertain motion patterns. The key contribution of the work is the integration of a novel method for modeling dynamic obstacles with uncertain future trajectories. The method, denoted as RR-GP, uses a learned motion pattern model of the dynamic obstacles to make long-term predictions of their future paths. This is done by combining the flexibility of Gaussian processes (GP) with the efficiency of RRT-Reach, a sampling-based reachability computation method which ensures dynamic feasibility. This prediction model is then utilized within chance-constrained rapidly-exploring random trees (CC-RRT), which uses chance constraints to explicitly achieve probabilistic constraint satisfaction while maintaining the computational benefits of sampling-based algorithms. With RR-GP embedded in the CC-RRT framework, theoretical guarantees can be demonstrated for linear systems subject to Gaussian uncertainty, though the extension to nonlinear systems is also considered. Simulation results show that the resulting approach can be used in real-time to efficiently and accurately execute safe paths

A Bayesian Nonparametric Approach to Modeling Motion Patterns

The most difficult—and often most essential— aspect of many interception and tracking tasks is constructing motion models of the targets to be found. Experts can often provide only partial information, and fitting parameters for complex motion patterns can require large amounts of training data. Specifying how to parameterize complex motion patterns is in itself a difficult task. In contrast, nonparametric models are very flexible and generalize well with relatively little training data. We propose modeling target motion patterns as a mixture of Gaussian processes (GP) with a Dirichlet process (DP) prior over mixture weights. The GP provides a flexible representation for each individual motion pattern, while the DP assigns observed trajectories to particular motion patterns. Both automatically adjust the complexity of the motion model based on the available data. Our approach outperforms several parametric models on a helicopter-based car-tracking task on data collected from the greater Boston area