The path inference filter: model-based low-latency map matching of probe vehicle data

We consider the problem of reconstructing vehicle trajectories from sparse sequences of GPS points, for which the sampling interval is between 10 seconds and 2 minutes. We introduce a new class of algorithms, called altogether path inference filter (PIF), that maps GPS data in real time, for a variety of trade-offs and scenarios, and with a high throughput. Numerous prior approaches in map-matching can be shown to be special cases of the path inference filter presented in this article. We present an efficient procedure for automatically training the filter on new data, with or without ground truth observations. The framework is evaluated on a large San Francisco taxi dataset and is shown to improve upon the current state of the art. This filter also provides insights about driving patterns of drivers. The path inference filter has been deployed at an industrial scale inside the Mobile Millennium traffic information system, and is used to map fleets of data in San Francisco, Sacramento, Stockholm and Porto.Comment: Preprint, 23 pages and 23 figure

Herding as a Learning System with Edge-of-Chaos Dynamics

Herding defines a deterministic dynamical system at the edge of chaos. It generates a sequence of model states and parameters by alternating parameter perturbations with state maximizations, where the sequence of states can be interpreted as "samples" from an associated MRF model. Herding differs from maximum likelihood estimation in that the sequence of parameters does not converge to a fixed point and differs from an MCMC posterior sampling approach in that the sequence of states is generated deterministically. Herding may be interpreted as a"perturb and map" method where the parameter perturbations are generated using a deterministic nonlinear dynamical system rather than randomly from a Gumbel distribution. This chapter studies the distinct statistical characteristics of the herding algorithm and shows that the fast convergence rate of the controlled moments may be attributed to edge of chaos dynamics. The herding algorithm can also be generalized to models with latent variables and to a discriminative learning setting. The perceptron cycling theorem ensures that the fast moment matching property is preserved in the more general framework

Hamiltonian Monte Carlo Acceleration Using Surrogate Functions with Random Bases

For big data analysis, high computational cost for Bayesian methods often limits their applications in practice. In recent years, there have been many attempts to improve computational efficiency of Bayesian inference. Here we propose an efficient and scalable computational technique for a state-of-the-art Markov Chain Monte Carlo (MCMC) methods, namely, Hamiltonian Monte Carlo (HMC). The key idea is to explore and exploit the structure and regularity in parameter space for the underlying probabilistic model to construct an effective approximation of its geometric properties. To this end, we build a surrogate function to approximate the target distribution using properly chosen random bases and an efficient optimization process. The resulting method provides a flexible, scalable, and efficient sampling algorithm, which converges to the correct target distribution. We show that by choosing the basis functions and optimization process differently, our method can be related to other approaches for the construction of surrogate functions such as generalized additive models or Gaussian process models. Experiments based on simulated and real data show that our approach leads to substantially more efficient sampling algorithms compared to existing state-of-the art methods

CT-Mapper: Mapping Sparse Multimodal Cellular Trajectories using a Multilayer Transportation Network

Mobile phone data have recently become an attractive source of information about mobility behavior. Since cell phone data can be captured in a passive way for a large user population, they can be harnessed to collect well-sampled mobility information. In this paper, we propose CT-Mapper, an unsupervised algorithm that enables the mapping of mobile phone traces over a multimodal transport network. One of the main strengths of CT-Mapper is its capability to map noisy sparse cellular multimodal trajectories over a multilayer transportation network where the layers have different physical properties and not only to map trajectories associated with a single layer. Such a network is modeled by a large multilayer graph in which the nodes correspond to metro/train stations or road intersections and edges correspond to connections between them. The mapping problem is modeled by an unsupervised HMM where the observations correspond to sparse user mobile trajectories and the hidden states to the multilayer graph nodes. The HMM is unsupervised as the transition and emission probabilities are inferred using respectively the physical transportation properties and the information on the spatial coverage of antenna base stations. To evaluate CT-Mapper we collected cellular traces with their corresponding GPS trajectories for a group of volunteer users in Paris and vicinity (France). We show that CT-Mapper is able to accurately retrieve the real cell phone user paths despite the sparsity of the observed trace trajectories. Furthermore our transition probability model is up to 20% more accurate than other naive models.Comment: Under revision in Computer Communication Journa