A Constraint-Based Algorithm for the Structural Learning of Continuous-Time Bayesian Networks

• URL: http://arxiv.org/abs/2007.03248v3
• Date: Wed, 2 Jun 2021 19:27:44 GMT
• Title: A Constraint-Based Algorithm for the Structural Learning of Continuous-Time Bayesian Networks
• Authors: Alessandro Bregoli, Marco Scutari, Fabio Stella
• Abstract summary: We propose the first constraint-based algorithm for learning the structure of continuous-time Bayesian networks. We discuss the different statistical tests and the underlying hypotheses used by our proposal to establish conditional independence.
• Score: 70.88503833248159
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Dynamic Bayesian networks have been well explored in the literature as discrete-time models: however, their continuous-time extensions have seen comparatively little attention. In this paper, we propose the first constraint-based algorithm for learning the structure of continuous-time Bayesian networks. We discuss the different statistical tests and the underlying hypotheses used by our proposal to establish conditional independence. Furthermore, we analyze and discuss the computational complexity of the best and worst cases for the proposed algorithm. Finally, we validate its performance using synthetic data, and we discuss its strengths and limitations comparing it with the score-based structure learning algorithm from Nodelman et al. (2003). We find the latter to be more accurate in learning networks with binary variables, while our constraint-based approach is more accurate with variables assuming more than two values. Numerical experiments confirm that score-based and constraint-based algorithms are comparable in terms of computation time.

Related papers

• A Full DAG Score-Based Algorithm for Learning Causal Bayesian Networks with Latent Confounders [0.0]
  Causal Bayesian networks (CBN) are popular graphical probabilistic models that encode causal relations among variables. This paper introduces the first fully score-based structure learning algorithm searching the space of DAGs that is capable of identifying the presence of some latent confounders.
  arXiv  Detail & Related papers  (2024-08-20T20:25:56Z)
• Discrete Neural Algorithmic Reasoning [18.497863598167257]
  We propose to force neural reasoners to maintain the execution trajectory as a combination of finite predefined states. trained with supervision on the algorithm's state transitions, such models are able to perfectly align with the original algorithm.
  arXiv  Detail & Related papers  (2024-02-18T16:03:04Z)
• A Stable, Fast, and Fully Automatic Learning Algorithm for Predictive Coding Networks [65.34977803841007]
  Predictive coding networks are neuroscience-inspired models with roots in both Bayesian statistics and neuroscience. We show how by simply changing the temporal scheduling of the update rule for the synaptic weights leads to an algorithm that is much more efficient and stable than the original one.
  arXiv  Detail & Related papers  (2022-11-16T00:11:04Z)
• Structured Optimal Variational Inference for Dynamic Latent Space Models [16.531262817315696]
  We consider a latent space model for dynamic networks, where our objective is to estimate the pairwise inner products plus the intercept of the latent positions. To balance posterior inference and computational scalability, we consider a structured mean-field variational inference framework.
  arXiv  Detail & Related papers  (2022-09-29T22:10:42Z)
• On the Convergence of Distributed Stochastic Bilevel Optimization Algorithms over a Network [55.56019538079826]
  Bilevel optimization has been applied to a wide variety of machine learning models. Most existing algorithms restrict their single-machine setting so that they are incapable of handling distributed data. We develop novel decentralized bilevel optimization algorithms based on a gradient tracking communication mechanism and two different gradients.
  arXiv  Detail & Related papers  (2022-06-30T05:29:52Z)
• Scalable computation of prediction intervals for neural networks via matrix sketching [79.44177623781043]
  Existing algorithms for uncertainty estimation require modifying the model architecture and training procedure. This work proposes a new algorithm that can be applied to a given trained neural network and produces approximate prediction intervals.
  arXiv  Detail & Related papers  (2022-05-06T13:18:31Z)
• Adaptive Discretization for Model-Based Reinforcement Learning [10.21634042036049]
  We introduce the technique of adaptive discretization to design an efficient model-based episodic reinforcement learning algorithm. Our algorithm is based on optimistic one-step value iteration extended to maintain an adaptive discretization of the space.
  arXiv  Detail & Related papers  (2020-07-01T19:36:46Z)
• Fast Objective & Duality Gap Convergence for Non-Convex Strongly-Concave Min-Max Problems with PL Condition [52.08417569774822]
  This paper focuses on methods for solving smooth non-concave min-max problems, which have received increasing attention due to deep learning (e.g., deep AUC)
  arXiv  Detail & Related papers  (2020-06-12T00:32:21Z)
• Beyond Worst-Case Analysis in Stochastic Approximation: Moment Estimation Improves Instance Complexity [58.70807593332932]
  We study oracle complexity of gradient based methods for approximation problems. We focus on instance-dependent complexity instead of worst case complexity. Our proposed algorithm and its analysis provide a theoretical justification for the success of moment estimation.
  arXiv  Detail & Related papers  (2020-06-08T09:25:47Z)
• DYNOTEARS: Structure Learning from Time-Series Data [6.7638850283606855]
  We propose a method that simultaneously estimates contemporaneous (intra-slice) and time-lagged (inter-slice) relationships between variables in a time-series. Compared to state-of-the-art methods for learning dynamic Bayesian networks, our method is both scalable and accurate on real data.
  arXiv  Detail & Related papers  (2020-02-02T21:47:48Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.