Filipe Rodrigues

Filipe Rodrigues

Over the last years, the transportation community has witnessed a tremendous amount of research contributions on new deep learning approaches for spatio-temporal forecasting. These contributions tend to emphasize the modeling of spatial correlations, while neglecting the fairly stable and recurrent nature of human mobility patterns. In this short paper, we show that a naive baseline method based on the average weekly pattern and linear regression can achieve comparable results to many state-of-the-art deep learning approaches for spatio-temporal forecasting in transportation, or even outperform them on several datasets, thus contrasting the importance of stationarity and recurrent patterns in the data with the importance of spatial correlations. Furthermore, we establish 9 different reference benchmarks that can be used to compare new approaches for spatio-temporal forecasting, and provide a discussion on best practices and the direction that the field is taking.

Frederik Boe Hüttel, Filipe Rodrigues, Francisco Câmara Pereira

It is desirable to have accurate uncertainty estimation from a single deterministic forward-pass model, as traditional methods for uncertainty quantification are computationally expensive. However, this is difficult because single forward-pass models do not sample weights during inference and often make assumptions about the target distribution, such as assuming it is Gaussian. This can be restrictive in regression tasks, where the mean and standard deviation are inadequate to model the target distribution accurately. This paper proposes a deep Bayesian quantile regression model that can estimate the quantiles of a continuous target distribution without the Gaussian assumption. The proposed method is based on evidential learning, which allows the model to capture aleatoric and epistemic uncertainty with a single deterministic forward-pass model. This makes the method efficient and scalable to large models and datasets. We demonstrate that the proposed method achieves calibrated uncertainties on non-Gaussian distributions, disentanglement of aleatoric and epistemic uncertainty, and robustness to out-of-distribution samples.

Carolin Schmidt, Daniele Gammelli, Francisco Camara Pereira et al.

Autonomous Mobility-on-Demand (AMoD) systems are an evolving mode of transportation in which a centrally coordinated fleet of self-driving vehicles dynamically serves travel requests. The control of these systems is typically formulated as a large network optimization problem, and reinforcement learning (RL) has recently emerged as a promising approach to solve the open challenges in this space. Recent centralized RL approaches focus on learning from online data, ignoring the per-sample-cost of interactions within real-world transportation systems. To address these limitations, we propose to formalize the control of AMoD systems through the lens of offline reinforcement learning and learn effective control strategies using solely offline data, which is readily available to current mobility operators. We further investigate design decisions and provide empirical evidence based on data from real-world mobility systems showing how offline learning allows to recover AMoD control policies that (i) exhibit performance on par with online methods, (ii) allow for sample-efficient online fine-tuning and (iii) eliminate the need for complex simulation environments. Crucially, this paper demonstrates that offline RL is a promising paradigm for the application of RL-based solutions within economically-critical systems, such as mobility systems.

Zhongcan Li, Ping Huang, Chao Wen et al.

Railway operations involve different types of entities (stations, trains, etc.), making the existing graph/network models with homogenous nodes (i.e., the same kind of nodes) incapable of capturing the interactions between the entities. This paper aims to develop a heterogeneous graph neural network (HetGNN) model, which can address different types of nodes (i.e., heterogeneous nodes), to investigate the train delay evolution on railway networks. To this end, a graph architecture combining the HetGNN model and the GraphSAGE homogeneous GNN (HomoGNN), called SAGE-Het, is proposed. The aim is to capture the interactions between trains, trains and stations, and stations and other stations on delay evolution based on different edges. In contrast to the traditional methods that require the inputs to have constant dimensions (e.g., in rectangular or grid-like arrays) or only allow homogeneous nodes in the graph, SAGE-Het allows for flexible inputs and heterogeneous nodes. The data from two sub-networks of the China railway network are applied to test the performance and robustness of the proposed SAGE-Het model. The experimental results show that SAGE-Het exhibits better performance than the existing delay prediction methods and some advanced HetGNNs used for other prediction tasks; the predictive performances of SAGE-Het under different prediction time horizons (10/20/30 min ahead) all outperform other baseline methods; Specifically, the influences of train interactions on delay propagation are investigated based on the proposed model. The results show that train interactions become subtle when the train headways increase . This finding directly contributes to decision-making in the situation where conflict-resolution or train-canceling actions are needed.

Mirosława Łukawska, Anders Fjendbo Jensen, Filipe Rodrigues

The mixed multinomial logit model assumes constant preference parameters of a decision-maker throughout different choice situations, which may be considered too strong for certain choice modelling applications. This paper proposes an effective approach to model context-dependent intra-respondent heterogeneity, thereby introducing the concept of the Context-aware Bayesian mixed multinomial logit model, where a neural network maps contextual information to interpretable shifts in the preference parameters of each individual in each choice occasion. The proposed model offers several key advantages. First, it supports both continuous and discrete variables, as well as complex non-linear interactions between both types of variables. Secondly, each context specification is considered jointly as a whole by the neural network rather than each variable being considered independently. Finally, since the neural network parameters are shared across all decision-makers, it can leverage information from other decision-makers to infer the effect of a particular context on a particular decision-maker. Even though the context-aware Bayesian mixed multinomial logit model allows for flexible interactions between attributes, the increase in computational complexity is minor, compared to the mixed multinomial logit model. We illustrate the concept and interpretation of the proposed model in a simulation study. We furthermore present a real-world case study from the travel behaviour domain - a bicycle route choice model, based on a large-scale, crowdsourced dataset of GPS trajectories including 119,448 trips made by 8,555 cyclists.

Niklas Petersen, Filipe Rodrigues, Francisco Pereira

Predicting travel time under rare temporal conditions (e.g., public holidays, school vacation period, etc.) constitutes a challenge due to the limitation of historical data. If at all available, historical data often form a heterogeneous time series due to high probability of other changes over long periods of time (e.g., road works, introduced traffic calming initiatives, etc.). This is especially prominent in cities and suburban areas. We present a vector-space model for encoding rare temporal conditions, that allows coherent representation learning across different temporal conditions. We show increased performance for travel time prediction over different baselines when utilizing the vector-space encoding for representing the temporal setting.

Frederik Boe Hüttel, Filipe Rodrigues, Francisco Câmara Pereira

Electric vehicle charging demand models, with charging records as input, will inherently be biased toward the supply of available chargers. These models often fail to account for demand lost from occupied charging stations and competitors. The lost demand suggests that the actual demand is likely higher than the charging records reflect, i.e., the true demand is latent (unobserved), and the observations are censored. As a result, machine learning models that rely on these observed records for forecasting charging demand may be limited in their application in future infrastructure expansion and supply management, as they do not estimate the true demand for charging. We propose using censorship-aware models to model charging demand to address this limitation. These models incorporate censorship in their loss functions and learn the true latent demand distribution from observed charging records. We study how occupied charging stations and competing services censor demand using GPS trajectories from cars in Copenhagen, Denmark. We find that censorship occurs up to $61\%$ of the time in some areas of the city. We use the observed charging demand from our study to estimate the true demand and find that censorship-aware models provide better prediction and uncertainty estimation of actual demand than censorship-unaware models. We suggest that future charging models based on charging records should account for censoring to expand the application areas of machine learning models in supply management and infrastructure expansion.

Luigi Tresca, Carolin Schmidt, James Harrison et al.

Fleets of robo-taxis offering on-demand transportation services, commonly known as Autonomous Mobility-on-Demand (AMoD) systems, hold significant promise for societal benefits, such as reducing pollution, energy consumption, and urban congestion. However, orchestrating these systems at scale remains a critical challenge, with existing coordination algorithms often failing to exploit the systems' full potential. This work introduces a novel decision-making framework that unites mathematical modeling with data-driven techniques. In particular, we present the AMoD coordination problem through the lens of reinforcement learning and propose a graph network-based framework that exploits the main strengths of graph representation learning, reinforcement learning, and classical operations research tools. Extensive evaluations across diverse simulation fidelities and scenarios demonstrate the flexibility of our approach, achieving superior system performance, computational efficiency, and generalizability compared to prior methods. Finally, motivated by the need to democratize research efforts in this area, we release publicly available benchmarks, datasets, and simulators for network-level coordination alongside an open-source codebase designed to provide accessible simulation platforms and establish a standardized validation process for comparing methodologies. Code available at: https://github.com/StanfordASL/RL4AMOD

Dang Viet Anh Nguyen, Carlos Lima Azevedo, Tomer Toledo et al.

Reinforcement learning-based traffic signal control (RL-TSC) has emerged as a promising approach for improving urban mobility. However, its robustness under real-world disruptions such as traffic incidents remains largely underexplored. In this study, we introduce T-REX, an open-source, SUMO-based simulation framework for training and evaluating RL-TSC methods under dynamic, incident scenarios. T-REX models realistic network-level performance considering drivers' probabilistic rerouting, speed adaptation, and contextual lane-changing, enabling the simulation of congestion propagation under incidents. To assess robustness, we propose a suite of metrics that extend beyond conventional traffic efficiency measures. Through extensive experiments across synthetic and real-world networks, we showcase T-REX for the evaluation of several state-of-the-art RL-TSC methods under multiple real-world deployment paradigms. Our findings show that while independent value-based and decentralized pressure-based methods offer fast convergence and generalization in stable traffic conditions and homogeneous networks, their performance degrades sharply under incident-driven distribution shifts. In contrast, hierarchical coordination methods tend to offer more stable and adaptable performance in large-scale, irregular networks, benefiting from their structured decision-making architecture. However, this comes with the trade-off of slower convergence and higher training complexity. These findings highlight the need for robustness-aware design and evaluation in RL-TSC research. T-REX contributes to this effort by providing an open, standardized and reproducible platform for benchmarking RL methods under dynamic and disruptive traffic scenarios.

Filipe Rodrigues, Carlos Lima Azevedo

Reinforcement learning (RL) constitutes a promising solution for alleviating the problem of traffic congestion. In particular, deep RL algorithms have been shown to produce adaptive traffic signal controllers that outperform conventional systems. However, in order to be reliable in highly dynamic urban areas, such controllers need to be robust with the respect to a series of exogenous sources of uncertainty. In this paper, we develop an open-source callback-based framework for promoting the flexible evaluation of different deep RL configurations under a traffic simulation environment. With this framework, we investigate how deep RL-based adaptive traffic controllers perform under different scenarios, namely under demand surges caused by special events, capacity reductions from incidents and sensor failures. We extract several key insights for the development of robust deep RL algorithms for traffic control and propose concrete designs to mitigate the impact of the considered exogenous uncertainties.

Ekin Uğurel, Cynthia Chen, Brian H. Y. Lee et al.

Inferring sociodemographic attributes from mobility data could help transportation planners better leverage passively collected datasets, but this task remains difficult due to weak and inconsistent relationships between mobility patterns and sociodemographic traits, as well as limited generalization across contexts. We address these challenges from three angles. First, to improve predictive accuracy while retaining interpretability, we introduce a behaviorally grounded set of higher-order mobility descriptors based on directed mobility graphs. These features capture structured patterns in trip sequences, travel modes, and social co-travel, and significantly improve prediction of age, gender, income, and household structure over baselines features. Second, we introduce metrics and visual diagnostic tools that encourage evenness between model confidence and accuracy, enabling planners to quantify uncertainty. Third, to improve generalization and sample efficiency, we develop a multitask learning framework that jointly predicts multiple sociodemographic attributes from a shared representation. This approach outperforms single-task models, particularly when training data are limited or when applying models across different time periods (i.e., when the test set distribution differs from the training set).

Dang Viet Anh Nguyen, J. Victor Flensburg, Fabrizio Cerreto et al.

With the expansion of cities over time, URT (Urban Rail Transit) networks have also grown significantly. Demand prediction plays an important role in supporting planning, scheduling, fleet management, and other operational decisions. In this study, we propose an Origin-Destination (OD) demand prediction model called Multi-Graph Inductive Representation Learning (mGraphSAGE) for large-scale URT networks under operational uncertainties. Our main contributions are twofold: we enhance prediction results while ensuring scalability for large networks by relying simultaneously on multiple graphs, where each OD pair is a node on a graph and distinct OD relationships, such as temporal and spatial correlations; we show the importance of including operational uncertainties such as train delays and cancellations as inputs in demand prediction for daily operations. The model is validated on three different scales of the URT network in Copenhagen, Denmark. Experimental results show that by leveraging information from neighboring ODs and learning node representations via sampling and aggregation, mGraphSAGE is particularly suitable for OD demand prediction in large-scale URT networks, outperforming reference machine learning methods. Furthermore, during periods with train cancellations and delays, the performance gap between mGraphSAGE and other methods improves compared to normal operating conditions, demonstrating its ability to leverage system reliability information for predicting OD demand under uncertainty.

Frederik Boe Hüttel, Christoffer Riis, Filipe Rodrigues et al.

Bayesian active learning is based on information theoretical approaches that focus on maximising the information that new observations provide to the model parameters. This is commonly done by maximising the Bayesian Active Learning by Disagreement (BALD) acquisitions function. However, we highlight that it is challenging to estimate BALD when the new data points are subject to censorship, where only clipped values of the targets are observed. To address this, we derive the entropy and the mutual information for censored distributions and derive the BALD objective for active learning in censored regression ($\mathcal{C}$-BALD). We propose a novel modelling approach to estimate the $\mathcal{C}$-BALD objective and use it for active learning in the censored setting. Across a wide range of datasets and models, we demonstrate that $\mathcal{C}$-BALD outperforms other Bayesian active learning methods in censored regression.

Emil Kragh Toft, Carolin Schmidt, Daniele Gammelli et al.

Autonomous Mobility-on-Demand (AMoD) systems promise to revolutionize urban transportation by providing affordable on-demand services to meet growing travel demand. However, realistic AMoD markets will be competitive, with multiple operators competing for passengers through strategic pricing and fleet deployment. While reinforcement learning has shown promise in optimizing single-operator AMoD control, existing work fails to capture competitive market dynamics. We investigate the impact of competition on policy learning by introducing a multi-operator reinforcement learning framework where two operators simultaneously learn pricing and fleet rebalancing policies. By integrating discrete choice theory, we enable passenger allocation and demand competition to emerge endogenously from utility-maximizing decisions. Experiments using real-world data from multiple cities demonstrate that competition fundamentally alters learned behaviors, leading to lower prices and distinct fleet positioning patterns compared to monopolistic settings. Notably, we demonstrate that learning-based approaches are robust to the additional stochasticity of competition, with competitive agents successfully converging to effective policies while accounting for partially unobserved competitor strategies.

Oskar Bohn Lassen, Serio Angelo Maria Agriesti, Filipe Rodrigues et al.

Climate policy studies require models that capture the combined effects of multiple greenhouse gases on global temperature, but these models are computationally expensive and difficult to embed in reinforcement learning. We present a multi-agent reinforcement learning (MARL) framework that integrates a high-fidelity, highly efficient climate surrogate directly in the environment loop, enabling regional agents to learn climate policies under multi-gas dynamics. As a proof of concept, we introduce a recurrent neural network architecture pretrained on ($20{,}000$) multi-gas emission pathways to surrogate the climate model CICERO-SCM. The surrogate model attains near-simulator accuracy with global-mean temperature RMSE $\approx 0.0004 \mathrm{K}$ and approximately $1000\times$ faster one-step inference. When substituted for the original simulator in a climate-policy MARL setting, it accelerates end-to-end training by $>\!100\times$. We show that the surrogate and simulator converge to the same optimal policies and propose a methodology to assess this property in cases where using the simulator is intractable. Our work allows to bypass the core computational bottleneck without sacrificing policy fidelity, enabling large-scale multi-agent experiments across alternative climate-policy regimes with multi-gas dynamics and high-fidelity climate response.

Silke K. Kaiser, Filipe Rodrigues, Carlos Lima Azevedo et al.

Reliable street-level traffic volume data, covering multiple modes of transportation, helps urban planning by informing decisions on infrastructure improvements, traffic management, and public transportation. Yet, traffic sensors measuring traffic volume are typically scarcely located, due to their high deployment and maintenance costs. To address this, interpolation methods can estimate traffic volumes at unobserved locations using available data. Graph Neural Networks have shown strong performance in traffic volume forecasting, particularly on highways and major arterial networks. Applying them to urban settings, however, presents unique challenges: urban networks exhibit greater structural diversity, traffic volumes are highly overdispersed with many zeros, the best way to account for spatial dependencies remains unclear, and sensor coverage is often very sparse. We introduce the Graph Neural Network for Urban Interpolation (GNNUI), a novel urban traffic volume estimation approach. GNNUI employs a masking algorithm to learn interpolation, integrates node features to capture functional roles, and uses a loss function tailored to zero-inflated traffic distributions. In addition to the model, we introduce two new open, large-scale urban traffic volume benchmarks, covering different transportation modes: Strava cycling data from Berlin and New York City taxi data. GNNUI outperforms recent, some graph-based, interpolation methods across metrics (MAE, RMSE, true-zero rate, Kullback-Leibler divergence) and remains robust from 90% to 1% sensor coverage. On Strava, for instance, MAE rises only from 7.1 to 10.5, on Taxi from 23.0 to 40.4, demonstrating strong performance under extreme data scarcity, common in real-world urban settings. We also examine how graph connectivity choices influence model accuracy.

Xiaoyi Wu, Ravi Seshadri, Filipe Rodrigues et al.

Tradable credit schemes (TCS) are an increasingly studied alternative to congestion pricing, given their revenue neutrality and ability to address issues of equity through the initial credit allocation. Modeling TCS to aid future design and implementation is associated with challenges involving user and market behaviors, demand-supply dynamics, and control mechanisms. In this paper, we focus on the latter and address the day-to-day dynamic tolling problem under TCS, which is formulated as a discrete-time Markov Decision Process and solved using reinforcement learning (RL) algorithms. Our results indicate that RL algorithms achieve travel times and social welfare comparable to the Bayesian optimization benchmark, with generalization across varying capacities and demand levels. We further assess the robustness of RL under different hyperparameters and apply regularization techniques to mitigate action oscillation, which generates practical tolling strategies that are transferable under day-to-day demand and supply variability. Finally, we discuss potential challenges such as scaling to large networks, and show how transfer learning can be leveraged to improve computational efficiency and facilitate the practical deployment of RL-based TCS solutions.

Filipe Rodrigues

Inferring the true demand for a product or a service from aggregate data is often challenging due to the limited available supply, thus resulting in observations that are censored and correspond to the realized demand, thereby not accounting for the unsatisfied demand. Censored regression models are able to account for the effect of censoring due to the limited supply, but they don't consider the effect of substitutions, which may cause the demand for similar alternative products or services to increase. This paper proposes Diffusion-aware Censored Demand Models, which combine a Tobit likelihood with a graph diffusion process in order to model the latent process of transfer of unsatisfied demand between similar products or services. We instantiate this new class of models under the framework of GPs and, based on both simulated and real-world data for modeling sales, bike-sharing demand, and EV charging demand, demonstrate its ability to better recover the true demand and produce more accurate out-of-sample predictions.

Carolin Schmidt, Mathias Tygesen, Filipe Rodrigues

Urban mobility is on the cusp of transformation with the emergence of shared, connected, and cooperative automated vehicles. Yet, for them to be accepted by customers, trust in their punctuality is vital. Many pilot initiatives operate without a fixed schedule, thus enhancing the importance of reliable arrival time (AT) predictions. This study presents an AT prediction system for autonomous shuttles, utilizing separate models for dwell and running time predictions, validated on real-world data from five cities. Alongside established methods such as XGBoost, we explore the benefits of integrating spatial data using graph neural networks (GNN). To accurately handle the case of a shuttle bypassing a stop, we propose a hierarchical model combining a random forest classifier and a GNN. The results for the final AT prediction are promising, showing low errors even when predicting several stops ahead. Yet, no single model emerges as universally superior, and we provide insights into the characteristics of pilot sites that influence the model selection process. Finally, we identify dwell time prediction as the key determinant in overall AT prediction accuracy when autonomous shuttles are deployed in low-traffic areas or under regulatory speed limits. This research provides insights into the current state of autonomous public transport prediction models and paves the way for more data-informed decision-making as the field advances.

Daniele Gammelli, James Harrison, Kaidi Yang et al.

Optimization problems over dynamic networks have been extensively studied and widely used in the past decades to formulate numerous real-world problems. However, (1) traditional optimization-based approaches do not scale to large networks, and (2) the design of good heuristics or approximation algorithms often requires significant manual trial-and-error. In this work, we argue that data-driven strategies can automate this process and learn efficient algorithms without compromising optimality. To do so, we present network control problems through the lens of reinforcement learning and propose a graph network-based framework to handle a broad class of problems. Instead of naively computing actions over high-dimensional graph elements, e.g., edges, we propose a bi-level formulation where we (1) specify a desired next state via RL, and (2) solve a convex program to best achieve it, leading to drastically improved scalability and performance. We further highlight a collection of desirable features to system designers, investigate design decisions, and present experiments on real-world control problems showing the utility, scalability, and flexibility of our framework.

Mathias Niemann Tygesen, Francisco C. Pereira, Filipe Rodrigues

Predicting the supply and demand of transport systems is vital for efficient traffic management, control, optimization, and planning. For example, predicting where from/to and when people intend to travel by taxi can support fleet managers to distribute resources; better predicting traffic speeds/congestion allows for pro-active control measures or for users to better choose their paths. Making spatio-temporal predictions is known to be a hard task, but recently Graph Neural Networks (GNNs) have been widely applied on non-euclidean spatial data. However, most GNN models require a predefined graph, and so far, researchers rely on heuristics to generate this graph for the model to use. In this paper, we use Neural Relational Inference to learn the optimal graph for the model. Our approach has several advantages: 1) a Variational Auto Encoder structure allows for the graph to be dynamically determined by the data, potentially changing through time; 2) the encoder structure allows the use of external data in the generation of the graph; 3) it is possible to place Bayesian priors on the generated graphs to encode domain knowledge. We conduct experiments on two datasets, namely the NYC Yellow Taxi and the PEMS road traffic datasets. In both datasets, we outperform benchmarks and show performance comparable to state-of-the-art. Furthermore, we do an in-depth analysis of the learned graphs, providing insights on what kinds of connections GNNs use for spatio-temporal predictions in the transport domain.

Daniele Gammelli, Yihua Wang, Dennis Prak et al.

Bike-sharing systems are a rapidly developing mode of transportation and provide an efficient alternative to passive, motorized personal mobility. The asymmetric nature of bike demand causes the need for rebalancing bike stations, which is typically done during night time. To determine the optimal starting inventory level of a station for a given day, a User Dissatisfaction Function (UDF) models user pickups and returns as non-homogeneous Poisson processes with piece-wise linear rates. In this paper, we devise a deep generative model directly applicable in the UDF by introducing a variational Poisson recurrent neural network model (VP-RNN) to forecast future pickup and return rates. We empirically evaluate our approach against both traditional and learning-based forecasting methods on real trip travel data from the city of New York, USA, and show how our model outperforms benchmarks in terms of system efficiency and demand satisfaction. By explicitly focusing on the combination of decision-making algorithms with learning-based forecasting methods, we highlight a number of shortcomings in literature. Crucially, we show how more accurate predictions do not necessarily translate into better inventory decisions. By providing insights into the interplay between forecasts, model assumptions, and decisions, we point out that forecasts and decision models should be carefully evaluated and harmonized to optimally control shared mobility systems.

Frederik Boe Hüttel, Inon Peled, Filipe Rodrigues et al.

Electric vehicles can offer a low carbon emission solution to reverse rising emission trends. However, this requires that the energy used to meet the demand is green. To meet this requirement, accurate forecasting of the charging demand is vital. Short and long-term charging demand forecasting will allow for better optimisation of the power grid and future infrastructure expansions. In this paper, we propose to use publicly available data to forecast the electric vehicle charging demand. To model the complex spatial-temporal correlations between charging stations, we argue that Temporal Graph Convolution Models are the most suitable to capture the correlations. The proposed Temporal Graph Convolutional Networks provide the most accurate forecasts for short and long-term forecasting compared with other forecasting methods.

Daniele Gammelli, Kaidi Yang, James Harrison et al.

Autonomous mobility-on-demand (AMoD) systems represent a rapidly developing mode of transportation wherein travel requests are dynamically handled by a coordinated fleet of robotic, self-driving vehicles. Given a graph representation of the transportation network - one where, for example, nodes represent areas of the city, and edges the connectivity between them - we argue that the AMoD control problem is naturally cast as a node-wise decision-making problem. In this paper, we propose a deep reinforcement learning framework to control the rebalancing of AMoD systems through graph neural networks. Crucially, we demonstrate that graph neural networks enable reinforcement learning agents to recover behavior policies that are significantly more transferable, generalizable, and scalable than policies learned through other approaches. Empirically, we show how the learned policies exhibit promising zero-shot transfer capabilities when faced with critical portability tasks such as inter-city generalization, service area expansion, and adaptation to potentially complex urban topologies.

Niklas Christoffer Petersen, Anders Parslov, Filipe Rodrigues

This paper presents two novel approaches for uncertainty estimation adapted and extended for the multi-link bus travel time problem. The uncertainty is modeled directly as part of recurrent artificial neural networks, but using two fundamentally different approaches: one based on Deep Quantile Regression (DQR) and the other on Bayesian Recurrent Neural Networks (BRNN). Both models predict multiple time steps into the future, but handle the time-dependent uncertainty estimation differently. We present a sampling technique in order to aggregate quantile estimates for link level travel time to yield the multi-link travel time distribution needed for a vehicle to travel from its current position to a specific downstream stop point or transfer site. To motivate the relevance of uncertainty-aware models in the domain, we focus on the connection assurance application as a case study: An expert system to determine whether a bus driver should hold and wait for a connecting service, or break the connection and reduce its own delay. Our results show that the DQR-model performs overall best for the 80%, 90% and 95% prediction intervals, both for a 15 minute time horizon into the future (t + 1), but also for the 30 and 45 minutes time horizon (t + 2 and t + 3), with a constant, but very small underestimation of the uncertainty interval (1-4 pp.). However, we also show, that the BRNN model still can outperform the DQR for specific cases. Lastly, we demonstrate how a simple decision support system can take advantage of our uncertainty-aware travel time models to prioritize the difference in travel time uncertainty for bus holding at strategic points, thus reducing the introduced delay for the connection assurance application.

Frederik Boe Hüttel, Inon Peled, Filipe Rodrigues et al.

Shared mobility services require accurate demand models for effective service planning. On the one hand, modeling the full probability distribution of demand is advantageous because the entire uncertainty structure preserves valuable information for decision-making. On the other hand, demand is often observed through the usage of the service itself, so that the observations are censored, as they are inherently limited by available supply. Since the 1980s, various works on Censored Quantile Regression models have performed well under such conditions. Further, in the last two decades, several papers have proposed to implement these models flexibly through Neural Networks. However, the models in current works estimate the quantiles individually, thus incurring a computational overhead and ignoring valuable relationships between the quantiles. We address this gap by extending current Censored Quantile Regression models to learn multiple quantiles at once and apply these to synthetic baseline datasets and datasets from two shared mobility providers in the Copenhagen metropolitan area in Denmark. The results show that our extended models yield fewer quantile crossings and less computational overhead without compromising model performance.

Georges Sfeir, Filipe Rodrigues, Maya Abou-Zeid

We present a Gaussian Process - Latent Class Choice Model (GP-LCCM) to integrate a non-parametric class of probabilistic machine learning within discrete choice models (DCMs). Gaussian Processes (GPs) are kernel-based algorithms that incorporate expert knowledge by assuming priors over latent functions rather than priors over parameters, which makes them more flexible in addressing nonlinear problems. By integrating a Gaussian Process within a LCCM structure, we aim at improving discrete representations of unobserved heterogeneity. The proposed model would assign individuals probabilistically to behaviorally homogeneous clusters (latent classes) using GPs and simultaneously estimate class-specific choice models by relying on random utility models. Furthermore, we derive and implement an Expectation-Maximization (EM) algorithm to jointly estimate/infer the hyperparameters of the GP kernel function and the class-specific choice parameters by relying on a Laplace approximation and gradient-based numerical optimization methods, respectively. The model is tested on two different mode choice applications and compared against different LCCM benchmarks. Results show that GP-LCCM allows for a more complex and flexible representation of heterogeneity and improves both in-sample fit and out-of-sample predictive power. Moreover, behavioral and economic interpretability is maintained at the class-specific choice model level while local interpretation of the latent classes can still be achieved, although the non-parametric characteristic of GPs lessens the transparency of the model.

Daniele Gammelli, Kasper Pryds Rolsted, Dario Pacino et al.

When modelling censored observations, a typical approach in current regression methods is to use a censored-Gaussian (i.e. Tobit) model to describe the conditional output distribution. In this paper, as in the case of missing data, we argue that exploiting correlations between multiple outputs can enable models to better address the bias introduced by censored data. To do so, we introduce a heteroscedastic multi-output Gaussian process model which combines the non-parametric flexibility of GPs with the ability to leverage information from correlated outputs under input-dependent noise conditions. To address the resulting inference intractability, we further devise a variational bound to the marginal log-likelihood suitable for stochastic optimization. We empirically evaluate our model against other generative models for censored data on both synthetic and real world tasks and further show how it can be generalized to deal with arbitrary likelihood functions. Results show how the added flexibility allows our model to better estimate the underlying non-censored (i.e. true) process under potentially complex censoring dynamics.

Georges Sfeir, Maya Abou-Zeid, Filipe Rodrigues et al.

This study presents a semi-nonparametric Latent Class Choice Model (LCCM) with a flexible class membership component. The proposed model formulates the latent classes using mixture models as an alternative approach to the traditional random utility specification with the aim of comparing the two approaches on various measures including prediction accuracy and representation of heterogeneity in the choice process. Mixture models are parametric model-based clustering techniques that have been widely used in areas such as machine learning, data mining and patter recognition for clustering and classification problems. An Expectation-Maximization (EM) algorithm is derived for the estimation of the proposed model. Using two different case studies on travel mode choice behavior, the proposed model is compared to traditional discrete choice models on the basis of parameter estimates' signs, value of time, statistical goodness-of-fit measures, and cross-validation tests. Results show that mixture models improve the overall performance of latent class choice models by providing better out-of-sample prediction accuracy in addition to better representations of heterogeneity without weakening the behavioral and economic interpretability of the choice models.

Daniele Gammelli, Filipe Rodrigues

Mobility-on-demand (MoD) systems represent a rapidly developing mode of transportation wherein travel requests are dynamically handled by a coordinated fleet of vehicles. Crucially, the efficiency of an MoD system highly depends on how well supply and demand distributions are aligned in spatio-temporal space (i.e., to satisfy user demand, cars have to be available in the correct place and at the desired time). To do so, we argue that predictive models should aim to explicitly disentangle between temporal} and spatial variability in the evolution of urban mobility demand. However, current approaches typically ignore this distinction by either treating both sources of variability jointly, or completely ignoring their presence in the first place. In this paper, we propose recurrent flow networks (RFN), where we explore the inclusion of (i) latent random variables in the hidden state of recurrent neural networks to model temporal variability, and (ii) normalizing flows to model the spatial distribution of mobility demand. We demonstrate how predictive models explicitly disentangling between spatial and temporal variability exhibit several desirable properties, and empirically show how this enables the generation of distributions matching potentially complex urban topologies.

Filipe Rodrigues

Variational inference methods have been shown to lead to significant improvements in the computational efficiency of approximate Bayesian inference in mixed multinomial logit models when compared to standard Markov-chain Monte Carlo (MCMC) methods without compromising accuracy. However, despite their demonstrated efficiency gains, existing methods still suffer from important limitations that prevent them to scale to very large datasets, while providing the flexibility to allow for rich prior distributions and to capture complex posterior distributions. In this paper, we propose an Amortized Variational Inference approach that leverages stochastic backpropagation, automatic differentiation and GPU-accelerated computation, for effectively scaling Bayesian inference in Mixed Multinomial Logit models to very large datasets. Moreover, we show how normalizing flows can be used to increase the flexibility of the variational posterior approximations. Through an extensive simulation study, we empirically show that the proposed approach is able to achieve computational speedups of multiple orders of magnitude over traditional MSLE and MCMC approaches for large datasets without compromising estimation accuracy.

Daniele Gammelli, Inon Peled, Filipe Rodrigues et al.

Transport demand is highly dependent on supply, especially for shared transport services where availability is often limited. As observed demand cannot be higher than available supply, historical transport data typically represents a biased, or censored, version of the true underlying demand pattern. Without explicitly accounting for this inherent distinction, predictive models of demand would necessarily represent a biased version of true demand, thus less effectively predicting the needs of service users. To counter this problem, we propose a general method for censorship-aware demand modeling, for which we devise a censored likelihood function. We apply this method to the task of shared mobility demand prediction by incorporating the censored likelihood within a Gaussian Process model, which can flexibly approximate arbitrary functional forms. Experiments on artificial and real-world datasets show how taking into account the limiting effect of supply on demand is essential in the process of obtaining an unbiased predictive model of user demand behavior.

Filipe Rodrigues, Nicola Ortelli, Michel Bierlaire et al.

Specifying utility functions is a key step towards applying the discrete choice framework for understanding the behaviour processes that govern user choices. However, identifying the utility function specifications that best model and explain the observed choices can be a very challenging and time-consuming task. This paper seeks to help modellers by leveraging the Bayesian framework and the concept of automatic relevance determination (ARD), in order to automatically determine an optimal utility function specification from an exponentially large set of possible specifications in a purely data-driven manner. Based on recent advances in approximate Bayesian inference, a doubly stochastic variational inference is developed, which allows the proposed DCM-ARD model to scale to very large and high-dimensional datasets. Using semi-artificial choice data, the proposed approach is shown to very accurately recover the true utility function specifications that govern the observed choices. Moreover, when applied to real choice data, DCM-ARD is shown to be able discover high quality specifications that can outperform previous ones from the literature according to multiple criteria, thereby demonstrating its practical applicability.

Niklas Christoffer Petersen, Filipe Rodrigues, Francisco Camara Pereira

Accurate and reliable travel time predictions in public transport networks are essential for delivering an attractive service that is able to compete with other modes of transport in urban areas. The traditional application of this information, where arrival and departure predictions are displayed on digital boards, is highly visible in the city landscape of most modern metropolises. More recently, the same information has become critical as input for smart-phone trip planners in order to alert passengers about unreachable connections, alternative route choices and prolonged travel times. More sophisticated Intelligent Transport Systems (ITS) include the predictions of connection assurance, i.e. to hold back services in case a connecting service is delayed. In order to operate such systems, and to ensure the confidence of passengers in the systems, the information provided must be accurate and reliable. Traditional methods have trouble with this as congestion, and thus travel time variability, increases in cities, consequently making travel time predictions in urban areas a non-trivial task. This paper presents a system for bus travel time prediction that leverages the non-static spatio-temporal correlations present in urban bus networks, allowing the discovery of complex patterns not captured by traditional methods. The underlying model is a multi-output, multi-time-step, deep neural network that uses a combination of convolutional and long short-term memory (LSTM) layers. The method is empirically evaluated and compared to other popular approaches for link travel time prediction and currently available services, including the currently deployed model in Copenhagen, Denmark. We find that the proposed model significantly outperforms all the other methods we compare with, and is able to detect small irregular peaks in bus travel times very quickly.

Filipe Rodrigues, Stanislav S. Borysov, Bernardete Ribeiro et al.

Public special events, like sports games, concerts and festivals are well known to create disruptions in transportation systems, often catching the operators by surprise. Although these are usually planned well in advance, their impact is difficult to predict, even when organisers and transportation operators coordinate. The problem highly increases when several events happen concurrently. To solve these problems, costly processes, heavily reliant on manual search and personal experience, are usual practice in large cities like Singapore, London or Tokyo. This paper presents a Bayesian additive model with Gaussian process components that combines smart card records from public transport with context information about events that is continuously mined from the Web. We develop an efficient approximate inference algorithm using expectation propagation, which allows us to predict the total number of public transportation trips to the special event areas, thereby contributing to a more adaptive transportation system. Furthermore, for multiple concurrent event scenarios, the proposed algorithm is able to disaggregate gross trip counts into their most likely components related to specific events and routine behavior. Using real data from Singapore, we show that the presented model outperforms the best baseline model by up to 26% in R2 and also has explanatory power for its individual components.

Filipe Rodrigues, Kristian Henrickson, Francisco C. Pereira

Traffic speed data imputation is a fundamental challenge for data-driven transport analysis. In recent years, with the ubiquity of GPS-enabled devices and the widespread use of crowdsourcing alternatives for the collection of traffic data, transportation professionals increasingly look to such user-generated data for many analysis, planning, and decision support applications. However, due to the mechanics of the data collection process, crowdsourced traffic data such as probe-vehicle data is highly prone to missing observations, making accurate imputation crucial for the success of any application that makes use of that type of data. In this article, we propose the use of multi-output Gaussian processes (GPs) to model the complex spatial and temporal patterns in crowdsourced traffic data. While the Bayesian nonparametric formalism of GPs allows us to model observation uncertainty, the multi-output extension based on convolution processes effectively enables us to capture complex spatial dependencies between nearby road segments. Using 6 months of crowdsourced traffic speed data or "probe vehicle data" for several locations in Copenhagen, the proposed approach is empirically shown to significantly outperform popular state-of-the-art imputation methods.

Filipe Rodrigues, Francisco C. Pereira

Accurately modeling traffic speeds is a fundamental part of efficient intelligent transportation systems. Nowadays, with the widespread deployment of GPS-enabled devices, it has become possible to crowdsource the collection of speed information to road users (e.g. through mobile applications or dedicated in-vehicle devices). Despite its rather wide spatial coverage, crowdsourced speed data also brings very important challenges, such as the highly variable measurement noise in the data due to a variety of driving behaviors and sample sizes. When not properly accounted for, this noise can severely compromise any application that relies on accurate traffic data. In this article, we propose the use of heteroscedastic Gaussian processes (HGP) to model the time-varying uncertainty in large-scale crowdsourced traffic data. Furthermore, we develop a HGP conditioned on sample size and traffic regime (SRC-HGP), which makes use of sample size information (probe vehicles per minute) as well as previous observed speeds, in order to more accurately model the uncertainty in observed speeds. Using 6 months of crowdsourced traffic data from Copenhagen, we empirically show that the proposed heteroscedastic models produce significantly better predictive distributions when compared to current state-of-the-art methods for both speed imputation and short-term forecasting tasks.

Filipe Rodrigues, Francisco C. Pereira

Spatio-temporal problems are ubiquitous and of vital importance in many research fields. Despite the potential already demonstrated by deep learning methods in modeling spatio-temporal data, typical approaches tend to focus solely on conditional expectations of the output variables being modeled. In this paper, we propose a multi-output multi-quantile deep learning approach for jointly modeling several conditional quantiles together with the conditional expectation as a way to provide a more complete "picture" of the predictive density in spatio-temporal problems. Using two large-scale datasets from the transportation domain, we empirically demonstrate that, by approaching the quantile regression problem from a multi-task learning perspective, it is possible to solve the embarrassing quantile crossings problem, while simultaneously significantly outperforming state-of-the-art quantile regression methods. Moreover, we show that jointly modeling the mean and several conditional quantiles not only provides a rich description about the predictive density that can capture heteroscedastic properties at a neglectable computational overhead, but also leads to improved predictions of the conditional expectation due to the extra information and a regularization effect induced by the added quantiles.

Filipe Rodrigues, Mariana Lourenço, Bernardete Ribeiro et al.

The growing need to analyze large collections of documents has led to great developments in topic modeling. Since documents are frequently associated with other related variables, such as labels or ratings, much interest has been placed on supervised topic models. However, the nature of most annotation tasks, prone to ambiguity and noise, often with high volumes of documents, deem learning under a single-annotator assumption unrealistic or unpractical for most real-world applications. In this article, we propose two supervised topic models, one for classification and another for regression problems, which account for the heterogeneity and biases among different annotators that are encountered in practice when learning from crowds. We develop an efficient stochastic variational inference algorithm that is able to scale to very large datasets, and we empirically demonstrate the advantages of the proposed model over state-of-the-art approaches.

Filipe Rodrigues, Ioulia Markou, Francisco Pereira

Accurate time-series forecasting is vital for numerous areas of application such as transportation, energy, finance, economics, etc. However, while modern techniques are able to explore large sets of temporal data to build forecasting models, they typically neglect valuable information that is often available under the form of unstructured text. Although this data is in a radically different format, it often contains contextual explanations for many of the patterns that are observed in the temporal data. In this paper, we propose two deep learning architectures that leverage word embeddings, convolutional layers and attention mechanisms for combining text information with time-series data. We apply these approaches for the problem of taxi demand forecasting in event areas. Using publicly available taxi data from New York, we empirically show that by fusing these two complementary cross-modal sources of information, the proposed models are able to significantly reduce the error in the forecasts.

Filipe Rodrigues, Francisco Pereira

Over the last few years, deep learning has revolutionized the field of machine learning by dramatically improving the state-of-the-art in various domains. However, as the size of supervised artificial neural networks grows, typically so does the need for larger labeled datasets. Recently, crowdsourcing has established itself as an efficient and cost-effective solution for labeling large sets of data in a scalable manner, but it often requires aggregating labels from multiple noisy contributors with different levels of expertise. In this paper, we address the problem of learning deep neural networks from crowds. We begin by describing an EM algorithm for jointly learning the parameters of the network and the reliabilities of the annotators. Then, a novel general-purpose crowd layer is proposed, which allows us to train deep neural networks end-to-end, directly from the noisy labels of multiple annotators, using only backpropagation. We empirically show that the proposed approach is able to internally capture the reliability and biases of different annotators and achieve new state-of-the-art results for various crowdsourced datasets across different settings, namely classification, regression and sequence labeling.