Network Diffusions via Neural Mean-Field Dynamics
- URL: http://arxiv.org/abs/2006.09449v3
- Date: Tue, 19 Jan 2021 16:15:10 GMT
- Title: Network Diffusions via Neural Mean-Field Dynamics
- Authors: Shushan He, Hongyuan Zha, Xiaojing Ye
- Abstract summary: We propose a novel learning framework for inference and estimation problems of diffusion on networks.
Our framework is derived from the Mori-Zwanzig formalism to obtain an exact evolution of the node infection probabilities.
Our approach is versatile and robust to variations of the underlying diffusion network models.
- Score: 52.091487866968286
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We propose a novel learning framework based on neural mean-field dynamics for
inference and estimation problems of diffusion on networks. Our new framework
is derived from the Mori-Zwanzig formalism to obtain an exact evolution of the
node infection probabilities, which renders a delay differential equation with
memory integral approximated by learnable time convolution operators, resulting
in a highly structured and interpretable RNN. Directly using cascade data, our
framework can jointly learn the structure of the diffusion network and the
evolution of infection probabilities, which are cornerstone to important
downstream applications such as influence maximization. Connections between
parameter learning and optimal control are also established. Empirical study
shows that our approach is versatile and robust to variations of the underlying
diffusion network models, and significantly outperform existing approaches in
accuracy and efficiency on both synthetic and real-world data.
Related papers
- Neural Networks Decoded: Targeted and Robust Analysis of Neural Network Decisions via Causal Explanations and Reasoning [9.947555560412397]
We introduce TRACER, a novel method grounded in causal inference theory to estimate the causal dynamics underpinning DNN decisions.
Our approach systematically intervenes on input features to observe how specific changes propagate through the network, affecting internal activations and final outputs.
TRACER further enhances explainability by generating counterfactuals that reveal possible model biases and offer contrastive explanations for misclassifications.
arXiv Detail & Related papers (2024-10-07T20:44:53Z) - Predicting Cascading Failures with a Hyperparametric Diffusion Model [66.89499978864741]
We study cascading failures in power grids through the lens of diffusion models.
Our model integrates viral diffusion principles with physics-based concepts.
We show that this diffusion model can be learned from traces of cascading failures.
arXiv Detail & Related papers (2024-06-12T02:34:24Z) - Statistical Physics of Deep Neural Networks: Initialization toward
Optimal Channels [6.144858413112823]
In deep learning, neural networks serve as noisy channels between input data and its representation.
We study a frequently overlooked possibility that neural networks can be intrinsic toward optimal channels.
arXiv Detail & Related papers (2022-12-04T05:13:01Z) - Data-driven emergence of convolutional structure in neural networks [83.4920717252233]
We show how fully-connected neural networks solving a discrimination task can learn a convolutional structure directly from their inputs.
By carefully designing data models, we show that the emergence of this pattern is triggered by the non-Gaussian, higher-order local structure of the inputs.
arXiv Detail & Related papers (2022-02-01T17:11:13Z) - Robust Learning via Ensemble Density Propagation in Deep Neural Networks [6.0122901245834015]
We formulate the problem of density propagation through layers of a deep neural network (DNN) and solve it using an Ensemble Density propagation scheme.
Experiments using MNIST and CIFAR-10 datasets show a significant improvement in the robustness of the trained models to random noise and adversarial attacks.
arXiv Detail & Related papers (2021-11-10T21:26:08Z) - Learning Neural Causal Models with Active Interventions [83.44636110899742]
We introduce an active intervention-targeting mechanism which enables a quick identification of the underlying causal structure of the data-generating process.
Our method significantly reduces the required number of interactions compared with random intervention targeting.
We demonstrate superior performance on multiple benchmarks from simulated to real-world data.
arXiv Detail & Related papers (2021-09-06T13:10:37Z) - Influence Estimation and Maximization via Neural Mean-Field Dynamics [60.91291234832546]
We propose a novel learning framework using neural mean-field (NMF) dynamics for inference and estimation problems.
Our framework can simultaneously learn the structure of the diffusion network and the evolution of node infection probabilities.
arXiv Detail & Related papers (2021-06-03T00:02:05Z) - Diffusion Mechanism in Residual Neural Network: Theory and Applications [12.573746641284849]
In many learning tasks with limited training samples, the diffusion connects the labeled and unlabeled data points.
We propose a novel diffusion residual network (Diff-ResNet) internally introduces diffusion into the architectures of neural networks.
Under the structured data assumption, it is proved that the proposed diffusion block can increase the distance-diameter ratio that improves the separability of inter-class points.
arXiv Detail & Related papers (2021-05-07T10:42:59Z) - An Ode to an ODE [78.97367880223254]
We present a new paradigm for Neural ODE algorithms, called ODEtoODE, where time-dependent parameters of the main flow evolve according to a matrix flow on the group O(d)
This nested system of two flows provides stability and effectiveness of training and provably solves the gradient vanishing-explosion problem.
arXiv Detail & Related papers (2020-06-19T22:05:19Z)
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.