96,316 research outputs found
Active Learning of Continuous-time Bayesian Networks through Interventions
We consider the problem of learning structures and parameters of
Continuous-time Bayesian Networks (CTBNs) from time-course data under minimal
experimental resources. In practice, the cost of generating experimental data
poses a bottleneck, especially in the natural and social sciences. A popular
approach to overcome this is Bayesian optimal experimental design (BOED).
However, BOED becomes infeasible in high-dimensional settings, as it involves
integration over all possible experimental outcomes. We propose a novel
criterion for experimental design based on a variational approximation of the
expected information gain. We show that for CTBNs, a semi-analytical expression
for this criterion can be calculated for structure and parameter learning. By
doing so, we can replace sampling over experimental outcomes by solving the
CTBNs master-equation, for which scalable approximations exist. This alleviates
the computational burden of sampling possible experimental outcomes in
high-dimensions. We employ this framework in order to recommend interventional
sequences. In this context, we extend the CTBN model to conditional CTBNs in
order to incorporate interventions. We demonstrate the performance of our
criterion on synthetic and real-world data.Comment: Accepted at ICML202
Fast MCMC sampling for Markov jump processes and extensions
Markov jump processes (or continuous-time Markov chains) are a simple and
important class of continuous-time dynamical systems. In this paper, we tackle
the problem of simulating from the posterior distribution over paths in these
models, given partial and noisy observations. Our approach is an auxiliary
variable Gibbs sampler, and is based on the idea of uniformization. This sets
up a Markov chain over paths by alternately sampling a finite set of virtual
jump times given the current path and then sampling a new path given the set of
extant and virtual jump times using a standard hidden Markov model forward
filtering-backward sampling algorithm. Our method is exact and does not involve
approximations like time-discretization. We demonstrate how our sampler extends
naturally to MJP-based models like Markov-modulated Poisson processes and
continuous-time Bayesian networks and show significant computational benefits
over state-of-the-art MCMC samplers for these models.Comment: Accepted at the Journal of Machine Learning Research (JMLR
Active Learning of Continuous-time Bayesian Networks through Interventions
We consider the problem of learning structures and parameters of Continuous-time Bayesian Networks (CTBNs) from time-course data under minimal experimental resources. In practice, the cost of generating experimental data poses a bottleneck, especially in the natural and social sciences. A popular approach to overcome this is Bayesian optimal experimental design (BOED). However, BOED becomes infeasible in high-dimensional settings, as it involves integration over all possible experimental outcomes. We propose a novel criterion for experimental design based on a variational approximation of the expected information gain. We show that for CTBNs, a semi-analytical expression for this criterion can be calculated for structure and parameter learning. By doing so, we can replace sampling over experimental outcomes by solving the CTBNs master-equation, for which scalable approximations exist. This alleviates the computational burden of sampling possible experimental outcomes in high-dimensions. We employ this framework to recommend interventional sequences. In this context, we extend the CTBN model to conditional CTBNs to incorporate interventions. We demonstrate the performance of our criterion on synthetic and real-world data
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