Bayesian Inference of Stochastic Dynamical Networks
- URL: http://arxiv.org/abs/2206.00858v1
- Date: Thu, 2 Jun 2022 03:22:34 GMT
- Title: Bayesian Inference of Stochastic Dynamical Networks
- Authors: Yasen Wang, Junyang Jin, and Jorge Goncalves
- Abstract summary: This paper presents a novel method for learning network topology and internal dynamics.
It is compared with group sparse Bayesian learning (GSBL), BINGO, kernel-based methods, dynGENIE3, GENIE3 and ARNI.
Our method achieves state-of-the-art performance compared with group sparse Bayesian learning (GSBL), BINGO, kernel-based methods, dynGENIE3, GENIE3 and ARNI.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Network inference has been extensively studied in several fields, such as
systems biology and social sciences. Learning network topology and internal
dynamics is essential to understand mechanisms of complex systems. In
particular, sparse topologies and stable dynamics are fundamental features of
many real-world continuous-time networks. Given that usually only a partial set
of nodes are able to observe, in this paper, we consider linear continuous-time
systems to depict networks since they can model unmeasured nodes via transfer
functions. Additionally, measurements tend to be noisy and with low and varying
sampling frequencies. For this reason, we consider continuous-time models (CT)
since discrete-time approximations often require fine-grained measurements and
uniform sampling steps. The developed method applies dynamical structure
functions (DSFs) derived from linear stochastic differential equations (SDEs)
to describe networks of measured nodes. Further, a numerical sampling method,
preconditioned Crank-Nicolson (pCN), is used to refine coarse-grained
trajectories to improve inference accuracy. The simulation conducted on random
and ring networks, and a synthetic biological network illustrate that our
method achieves state-of-the-art performance compared with group sparse
Bayesian learning (GSBL), BINGO, kernel-based methods, dynGENIE3, GENIE3 and
ARNI. In particular, these are challenging networks, suggesting that the
developed method can be applied under a wide range of contexts.
Related papers
- Enhancing lattice kinetic schemes for fluid dynamics with Lattice-Equivariant Neural Networks [79.16635054977068]
We present a new class of equivariant neural networks, dubbed Lattice-Equivariant Neural Networks (LENNs)
Our approach develops within a recently introduced framework aimed at learning neural network-based surrogate models Lattice Boltzmann collision operators.
Our work opens towards practical utilization of machine learning-augmented Lattice Boltzmann CFD in real-world simulations.
arXiv Detail & Related papers (2024-05-22T17:23:15Z) - How neural networks learn to classify chaotic time series [77.34726150561087]
We study the inner workings of neural networks trained to classify regular-versus-chaotic time series.
We find that the relation between input periodicity and activation periodicity is key for the performance of LKCNN models.
arXiv Detail & Related papers (2023-06-04T08:53:27Z) - GDBN: a Graph Neural Network Approach to Dynamic Bayesian Network [7.876789380671075]
We propose a graph neural network approach with score-based method aiming at learning a sparse DAG.
We demonstrate methods with graph neural network significantly outperformed other state-of-the-art methods with dynamic bayesian networking inference.
arXiv Detail & Related papers (2023-01-28T02:49:13Z) - A scalable multi-step least squares method for network identification
with unknown disturbance topology [0.0]
We present an identification method for dynamic networks with known network topology.
We use a multi-step Sequential and Null Space Fitting method to deal with reduced rank noise.
We provide a consistency proof that includes explicit-based Box model structure informativity.
arXiv Detail & Related papers (2021-06-14T16:12:49Z) - Estimating Linear Dynamical Networks of Cyclostationary Processes [0.0]
We present a novel algorithm for guaranteed topology learning in networks excited by cyclostationary processes.
Unlike prior work, the framework applies to linear dynamic system with complex valued dependencies.
In the second part of the article, we analyze conditions for consistent topology learning for bidirected radial networks when a subset of the network is unobserved.
arXiv Detail & Related papers (2020-09-26T18:54:50Z) - Provably Efficient Neural Estimation of Structural Equation Model: An
Adversarial Approach [144.21892195917758]
We study estimation in a class of generalized Structural equation models (SEMs)
We formulate the linear operator equation as a min-max game, where both players are parameterized by neural networks (NNs), and learn the parameters of these neural networks using a gradient descent.
For the first time we provide a tractable estimation procedure for SEMs based on NNs with provable convergence and without the need for sample splitting.
arXiv Detail & Related papers (2020-07-02T17:55:47Z) - Multipole Graph Neural Operator for Parametric Partial Differential
Equations [57.90284928158383]
One of the main challenges in using deep learning-based methods for simulating physical systems is formulating physics-based data.
We propose a novel multi-level graph neural network framework that captures interaction at all ranges with only linear complexity.
Experiments confirm our multi-graph network learns discretization-invariant solution operators to PDEs and can be evaluated in linear time.
arXiv Detail & Related papers (2020-06-16T21:56:22Z) - Learning Continuous-Time Dynamics by Stochastic Differential Networks [32.63114111531396]
We propose a flexible continuous-time recurrent neural network named Variational Differential Networks (VSDN)
VSDN embeds the complicated dynamics of the sporadic time series by neural Differential Equations (SDE)
We show that VSDNs outperform state-of-the-art continuous-time deep learning models and achieve remarkable performance on prediction and tasks for sporadic time series.
arXiv Detail & Related papers (2020-06-11T01:40:34Z) - Liquid Time-constant Networks [117.57116214802504]
We introduce a new class of time-continuous recurrent neural network models.
Instead of declaring a learning system's dynamics by implicit nonlinearities, we construct networks of linear first-order dynamical systems.
These neural networks exhibit stable and bounded behavior, yield superior expressivity within the family of neural ordinary differential equations.
arXiv Detail & Related papers (2020-06-08T09:53:35Z) - Kernel and Rich Regimes in Overparametrized Models [69.40899443842443]
We show that gradient descent on overparametrized multilayer networks can induce rich implicit biases that are not RKHS norms.
We also demonstrate this transition empirically for more complex matrix factorization models and multilayer non-linear networks.
arXiv Detail & Related papers (2020-02-20T15:43:02Z)
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.