Behaviour modelling has been widely explored using both statistical and machine learning techniques, primarily relying on analyzing correlations to understand passenger responses under different conditions and scenarios. However, correlation alone does not imply causation. This paper introduces a data-driven causal behaviour modelling approach, comprising two phases: causal discovery and causal inference. Causal discovery phase uses Peter-Clark (PC) algorithm to learn a directed acyclic graph that captures the causal relationships among variables. Causal inference phase estimates the corresponding model parameters and infers (conditional) causal effects of interventions designed to influence user behaviour. The method is validated by comparing the results with those from conventional modelling approaches (logistic regression and expert knowledge) using smart card data from a real-world use case on a pre-peak fare discount incentive program in the Hong Kong Mass Transit Railway system. The results highlight that the purely data-driven causal discovery method can produce reasonable causal graph. The method can also quantify the behavioural impacts of the incentive, identify key influencing factors, and estimate the corresponding causal effects. The overall causal effect of the incentive is approximately 0.7 %, with about 3 % of the population changing behaviour from previous statistical analysis. Interestingly, passengers with the highest flexibility exhibit a negative response, while those with medium-to-high flexibility demonstrate 3 times of the general level of responsiveness. The approach initiates the data-driven, causal modelling of human behaviour dynamics to support policy developments and managerial interventions.

Conventional modelling related to travel behaviours is facing challenges from rapidly changing demand dynamics, especially in a post-pandemic context with more volatile and elastic demand. In response to this challenge and to capitalize on the potential of ubiquitous travel trajectory data (such as smart card or mobile phone data), this study proposes data-driven causal behaviour modelling. The approach includes causal discovery and causal inference methods. For causal discovery, we use classic algorithms, like PC and GES, to learn a directed acyclic graph representing the causal relationships among the variables. Using this causal graph, we define a structural equation model and estimate its corresponding parameters, allowing causal inference of the (conditional) average treatment effect. The approach is validated with expert knowledge using a case study for behaviour response of passengers to a pre-peak fare discount incentive in the mass transit systems in Hong Kong. It also presents a comparative analysis of the causal inference results with those from the traditional transport model approach, e.g., logistic regression. We demonstrate the use of causal inference on a learned causal structure, which allows identification of the important factors, estimation of their causal effects, and quantification of the unique contribution of the intervention policy. Importantly, we will illustrate how to derive policy insights not only for future scenarios (what if it is…), but also from counterfactual analysis of historical actions (what if it had been…). Our approach advances data-driven modelling of casual human behaviour dynamics to support policy developments and managerial interventions.

We consider the problem of estimating the marginal independence structure of a Bayesian network from observational data, learning an undirected graph we call the unconditional dependence graph. We show that unconditional dependence graphs of Bayesian networks correspond to the graphs having equal independence and intersection numbers. Using this observation, a Gröbner basis for a toric ideal associated to unconditional dependence graphs of Bayesian networks is given and then extended by additional binomial relations to connect the space of all such graphs. An MCMC method, called GrUES (Gröbner-based unconditional equivalence search), is implemented based on the resulting moves and applied to synthetic Gaussian data. GrUES recovers the true marginal independence structure via a penalized maximum likelihood or MAP estimate at a higher rate than simple independence tests while also yielding an estimate of the posterior, for which the 20% HPD credible sets include the true structure at a high rate for data-generating graphs with density at least 0.5.

We consider the problem of causal structure learning in the setting of heterogeneous populations, i.e., populations in which a single causal structure does not adequately represent all population members, as is common in biological and social sciences. To this end, we introduce a distance covariance-based kernel designed specifically to measure the similarity between the underlying nonlinear causal structures of different samples. Indeed, we prove that the corresponding feature map is a statistically consistent estimator of nonlinear independence structure, rendering the kernel itself a statistical test for the hypothesis that sets of samples come from different generating causal structures. Even stronger, we prove that the kernel space is isometric to the space of causal ancestral graphs, so that distance between samples in the kernel space is guaranteed to correspond to distance between their generating causal structures. This kernel thus enables us to perform clustering to identify the homogeneous subpopulations, for which we can then learn causal structures using existing methods. Though we focus on the theoretical aspects of the kernel, we also evaluate its performance on synthetic data and demonstrate its use on a real gene expression data set.

We consider the problem of characterizing Bayesian networks up to unconditional equivalence, i.e., when directed acyclic graphs (DAGs) have the same set of unconditional $d$-separation statements. Each unconditional equivalence class (UEC) is uniquely represented with an undirected graph whose clique structure encodes the members of the class. Via this structure, we provide a transformational characterization of unconditional equivalence; i.e., we show that two DAGs are in the same UEC if and only if one can be transformed into the other via a finite sequence of specified moves. We also extend this characterization to the essential graphs representing the Markov equivalence classes (MECs) in the UEC. UECs form a partition coarsening of the space of MECs and are easily estimable from marginal independence tests. Thus, a characterization of unconditional equivalence has applications in methods that involve searching the space of MECs of Bayesian networks.