The Paper Feed
A feed of Bayesian network related papers, articles, books and research that we happen across and find of interest
Exploring the utility of Bayesian Networks for modelling cultural ecosystem services: A canoeing case study
Modelling cultural ecosystem services is challenging as they often involve subjective and intangible concepts. As a consequence they have been neglected in ecosystem service studies, something that needs remedying if environmental decision making is to be truly holistic. We suggest Bayesian Networks (BNs) have a number of qualities that may make them well-suited for dealing with cultural services. For example, they define relationships between variables probabilistically, enabling conceptual and physical variables to be linked, and therefore the numerical representation of stakeholder opinions. We assess whether BNs are a good method for modelling cultural services by building one collaboratively with canoeists to predict how the subjective concepts of fun and danger are impacted on by weir modification. The BN successfully captured the relationships between the variables, with model output being broadly consistent with verbal descriptions by the canoeists. There were however a number of discrepancies indicating imperfect knowledge capture. This is likely due to the structure of the network and the abstract and laborious nature of the probability elicitation stage. New techniques should be developed to increase the intuitiveness and efficiency of probability elicitation. The limitations we identified with BNs are avoided if their structure can be kept simple, and it is in such circumstances that BNs can offer a good method for modelling cultural ecosystem services.
A comparison between discrete and continuous time Bayesian networks in learning from clinical time series data with irregularity
Background Recently, mobile devices, such as smartphones, have been introduced into healthcare research to substitute paper diaries as data-collection tools in the home environment. Such devices support collecting patient data at different time points over a long period, resulting in clinical time-series data with high temporal complexity, such as time irregularities. Analysis of such time series poses new challenges for machine-learning techniques. The clinical context for the research discussed in this paper is home monitoring in chronic obstructive pulmonary disease (COPD). Objective The goal of the present research is to find out which properties of temporal Bayesian network models allow to cope best with irregularly spaced multivariate clinical time-series data. Methods Two mainstream temporal Bayesian network models of multivariate clinical time series are studied: dynamic Bayesian networks, where the system is described as a snapshot at discrete time points, and continuous time Bayesian networks, where transitions between states are modeled in continuous time. Their capability of learning from clinical time series that vary in nature are extensively studied. In order to compare the two temporal Bayesian network types for regularly and irregularly spaced time-series data, three typical ways of observing time-series data were investigated: (1) regularly spaced in time with a fixed rate; (2) irregularly spaced and missing completely at random at discrete time points; (3) irregularly spaced and missing at random at discrete time points. In addition, similar experiments were carried out using real-world COPD patient data where observations are unevenly spaced. Results For regularly spaced time series, the dynamic Bayesian network models outperform the continuous time Bayesian networks. Similarly, if the data is missing completely at random, discrete-time models outperform continuous time models in most situations. For more realistic settings where data is not missing completely at random, the situation is more complicated. In simulation experiments, both models perform similarly if there is strong prior knowledge available about the missing data distribution. Otherwise, continuous time Bayesian networks perform better. In experiments with unevenly spaced real-world data, we surprisingly found that a dynamic Bayesian network where time is ignored performs similar to a continuous time Bayesian network. Conclusion The results confirm conventional wisdom that discrete-time Bayesian networks are appropriate when learning from regularly spaced clinical time series. Similarly, we found that time series where the missingness occurs completely at random, dynamic Bayesian networks are an appropriate choice. However, for complex clinical time-series data that motivated this research, the continuous-time models are at least competitive and sometimes better than their discrete-time counterparts. Furthermore, continuous-time models provide additional benefits of being able to provide more fine-grained predictions than discrete-time models, which will be of practical relevance in clinical applications.
Bayesian networks with a logistic regression model for the conditional probabilities
Logistic regression techniques can be used to restrict the conditional probabilities of a Bayesian network for discrete variables. More specifically, each variable of the network can be modeled through a logistic regression model, in which the parents of the variable define the covariates. When all main effects and interactions between the parent variables are incorporated as covariates, the conditional probabilities are estimated without restrictions, as in a traditional Bayesian network. By incorporating interaction terms up to a specific order only, the number of parameters can be drastically reduced. Furthermore, ordered logistic regression can be used when the categories of a variable are ordered, resulting in even more parsimonious models. Parameters are estimated by a modified junction tree algorithm. The approach is illustrated with the Alarm network.