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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.

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.

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.

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.

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., Comment: 6 pages

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.

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., Comment: 17 pages, 6 figures, 3 tables

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.

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., Comment: 16 pages, 6 figures

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., Comment: 12 pages, 3 figures

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., Comment: 21 pages, 10 figures

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., Comment: 21 pages, 2 figures, 11 tables

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., Comment: 8 pages

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.

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., Comment: 22 pages, Transportation Research Part C: Emerging Technologies (Elsevier)

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., Comment: 14 pages, IEEE Transactions on Pattern Analysis and Machine Intelligence (Volume: 39 , Issue: 11 , Nov. 1 2017)

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., Comment: 10 pages, IEEE Transactions on Intelligent Transportation Systems, 2018

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., Comment: 12 pages, 9 figures

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., Comment: 14 pages

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., Comment: 20 pages, 6 figures

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., Comment: 10 pages, The Thirty-Second AAAI Conference on Artificial Intelligence (AAAI), 2018