TY - GEN

T1 - Making Continuous Time Bayesian Networks More Flexible

AU - Liu, Manxia

AU - Stella, Fabio

AU - Hommersom, Arjen

AU - Lucas, Peter J.F.

PY - 2018/11/1

Y1 - 2018/11/1

N2 - The time duration in continuous time Bayesian networks, i.e., the time that a variable stays in a state until it transitions to another state, follows an exponential distribution. The exponential distribution is widely applied to describe the waiting time between events in a Poisson process, which describes the distribution of the number of events in one unit of time. This distribution is parameterized by a single rate and has mode zero, implying that the highest probability mass for events to happen is attributed to the earliest times. To describe biological processes, the exponential distribution is not always natural. For example, if the immune system has not encountered a pathogen before, it most likely responds to a viral infection after a few days, rather than immediately. In this paper, we generalize our recently proposed hypoexponential continuous time Bayesian networks, by allowing any number of hypoexponential variables, i.e., variables having a hypoexponential time duration distribution. In addition, we propose and compare two learning methods to estimate parameters for the generalized models. Finally, the practical value of the generalized models is demonstrated by means of a realistic medical problem.

AB - The time duration in continuous time Bayesian networks, i.e., the time that a variable stays in a state until it transitions to another state, follows an exponential distribution. The exponential distribution is widely applied to describe the waiting time between events in a Poisson process, which describes the distribution of the number of events in one unit of time. This distribution is parameterized by a single rate and has mode zero, implying that the highest probability mass for events to happen is attributed to the earliest times. To describe biological processes, the exponential distribution is not always natural. For example, if the immune system has not encountered a pathogen before, it most likely responds to a viral infection after a few days, rather than immediately. In this paper, we generalize our recently proposed hypoexponential continuous time Bayesian networks, by allowing any number of hypoexponential variables, i.e., variables having a hypoexponential time duration distribution. In addition, we propose and compare two learning methods to estimate parameters for the generalized models. Finally, the practical value of the generalized models is demonstrated by means of a realistic medical problem.

KW - Continuous time Bayesian networks

KW - Hypoexponential distribution

KW - Parameter estimation

M3 - Conference Article in proceeding

VL - 72

T3 - Proceedings of Machine Learning Research

SP - 237

EP - 248

BT - Proceedings of the Ninth International Conference on Probabilistic Graphical Models

A2 - Kratochvíl, Václav

A2 - Studený, Milan

PB - PMLR

CY - Prague, Czech Republic

ER -