The bias-variance trade-off is a well-known problem in machine learning that only gets more pronounced the less available data there is. In active learning, where labeled data is scarce or difficult to obtain, neglecting this trade-off can cause inefficient and non-optimal querying, leading to unnecessary data labeling. In this paper, we focus on active learning with Gaussian Processes (GPs). For the GP, the bias-variance trade-off is made by optimization of the two hyperparameters: the length scale and noise-term. Considering that the optimal mode of the joint posterior of the hyperparameters is equivalent to the optimal bias-variance trade-off, we approximate this joint posterior and utilize it to design two new acquisition functions. The first one is a Bayesian variant of Query-by-Committee (B-QBC), and the second is an extension that explicitly minimizes the predictive variance through a Query by Mixture of Gaussian Processes (QB-MGP) formulation. Across six simulators, we empirically show that B-QBC, on average, achieves the best marginal likelihood, whereas QB-MGP achieves the best predictive performance. We show that incorporating the bias-variance trade-off in the acquisition functions mitigates unnecessary and expensive data labeling.

Urban environments are systems of overwhelming complexity and dynamism, involving numerous variables and idiosyncrasies which not usually easy to model from a functional perspective. Simulation modeling is a common and well-accepted approach to study such systems, specially those that prove to be too complex to be analyzed by standard analytic methods. However, such urban simulation models can become computationally very expensive to run. To address this drawback, simulation metamodels can be employed to approximate the underlying simulation function. In this paper, we propose a batch-mode active learning strategy based on Gaussian Processes metamodeling that searches for the most informative data points in batches with respect to their corresponding predictive variances. These points are selected in such a way that they originate from different high variance neighborhoods. Eventually, this allows us to analyze the simulation output behavior with fewer simulation requests. Using an illustrative traffic simulation example, the results show that the proposed restricted batch-mode strategy is able to increase the simulation input space exploration efficiency in comparison with standard batch-mode strategies.

Simulation modeling is a well-known and recurrent approach to study the performance of urban systems. Taking into account the recent and continuous transformations within increasingly complex and multidimensional cities, the use of simulation tools is, in many cases, the only feasible and reliable approach to analyze such dynamic systems. However, simulation models can become very time consuming when detailed input-space exploration is needed. To tackle this problem, simulation metamodels are often used to approximate the simulators' results. In this paper, we propose an active learning algorithm based on the Gaussian process (GP) framework that gathers the most informative simulation data points in batches, according to both their predictive variances and to the relative distance between them. This allows us to explore the simulators' input space with fewer data points and in parallel, and thus in a more efficient way, while avoiding computationally expensive simulation runs in the process. We take advantage of the closeness notion encoded into the GP to select batches of points in such a way that they do not belong to the same high-variance neighborhoods. In addition, we also suggest two simple and practical user-defined stopping criteria so that the iterative learning procedure can be fully automated. We illustrate this methodology using three experimental settings. The results show that the proposed methodology is able to improve the exploration efficiency of the simulation input space in comparison with non-restricted batch-mode active learning procedures.

A rise in population, along with urbanization, has been causing an increase in demand for urban transportation services in the sub-Saharan Africa countries. In these countries, mobility of people is mainly ensured by bus services and a large-scale informal public transport service, which is known as paratransit (e.g., car rapides in Senegal, Tro Tros in Ghana, taxis in Uganda and Ethiopia, and Matatus in Kenya). Transport demand estimation is a challenging task, particularly in developing countries, mainly due to its expensive and time-consuming data collection requirements. Without accurate demand estimation, it is difficult for transport operators to provide their services and make other important decisions. In this paper, we present a methodology to estimate passenger demand for public transport services using cell phone data. Significant origins and destinations of inhabitants are extracted and used to build origin-destination matrices that resemble travel demand. Based on the inferred travel demand, we are able to reasonably suggest strategic locations for public transport services such as paratransit and taxi stands, as well as new transit routes. The outcome of this study can be useful for the development of policies that can potentially help fulfill the mobility needs of city inhabitants.