Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userProperties of Bethe Free Energies and Message Passing in Gaussian Models
167
0
0.0
(
0
)
Added by
Botond Cseke
Publication date
2014
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
We address the problem of computing approximate marginals in Gaussian probabilistic models by using mean field and fractional Bethe approximations. We define the Gaussian fractional Bethe free energy in terms of the moment parameters of the approximate marginals, derive a lower and an upper bound on the fractional Bethe free energy and establish a necessary condition for the lower bound to be bounded from below. It turns out that the condition is identical to the pairwise normalizability condition, which is known to be a sufficient condition for the convergence of the message passing algorithm. We show that stable fixed points of the Gaussian message passing algorithm are local minima of the Gaussian Bethe free energy. By a counterexample, we disprove the conjecture stating that the unboundedness of the free energy implies the divergence of the message passing algorithm.
rate research
Read More
Graph neural networks (GNNs) are a powerful inductive bias for modelling algorithmic reasoning procedures and data structures. Their prowess was mainly demonstrated on tasks featuring Markovian dynamics, where querying any associated data structure depends only on its latest state. For many tasks of interest, however, it may be highly beneficial to support efficient data structure queries dependent on previous states. This requires tracking the data structures evolution through time, placing significant pressure on the GNNs latent representations. We introduce Persistent Message Passing (PMP), a mechanism which endows GNNs with capability of querying past state by explicitly persisting it: rather than overwriting node representations, it creates new nodes whenever required. PMP generalises out-of-distribution to more than 2x larger test inputs on dynamic temporal range queries, significantly outperforming GNNs which overwrite states.
This paper aims to unify spatial dependency and temporal dependency in a non-Euclidean space while capturing the inner spatial-temporal dependencies for spatial-temporal graph data. For spatial-temporal attribute entities with topological structure, the space-time is consecutive and unified while each nodes current status is influenced by its neighbors past states over variant periods of each neighbor. Most spatial-temporal neural networks study spatial dependency and temporal correlation separately in processing, gravely impaired the space-time continuum, and ignore the fact that the neighbors temporal dependency period for a node can be delayed and dynamic. To model this actual condition, we propose TraverseNet, a novel spatial-temporal graph neural network, viewing space and time as an inseparable whole, to mine spatial-temporal graphs while exploiting the evolving spatial-temporal dependencies for each node via message traverse mechanisms. Experiments with ablation and parameter studies have validated the effectiveness of the proposed TraverseNets, and the detailed implementation can be found from https://github.com/nnzhan/TraverseNet.
Generative models provide a powerful framework for probabilistic reasoning. However, in many domains their use has been hampered by the practical difficulties of inference. This is particularly the case in computer vision, where models of the imaging process tend to be large, loopy and layered. For this reason bottom-up conditional models have traditionally dominated in such domains. We find that widely-used, general-purpose message passing inference algorithms such as Expectation Propagation (EP) and Variational Message Passing (VMP) fail on the simplest of vision models. With these models in mind, we introduce a modification to message passing that learns to exploit their layered structure by passing consensus messages that guide inference towards good solutions. Experiments on a variety of problems show that the proposed technique leads to significantly more accurate inference results, not only when compared to standard EP and VMP, but also when compared to competitive bottom-up conditional models.
Graph neural networks have recently achieved great successes in predicting quantum mechanical properties of molecules. These models represent a molecule as a graph using only the distance between atoms (nodes). They do not, however, consider the spatial direction from one atom to another, despite directional information playing a central role in empirical potentials for molecules, e.g. in angular potentials. To alleviate this limitation we propose directional message passing, in which we embed the messages passed between atoms instead of the atoms themselves. Each message is associated with a direction in coordinate space. These directional message embeddings are rotationally equivariant since the associated directions rotate with the molecule. We propose a message passing scheme analogous to belief propagation, which uses the directional information by transforming messages based on the angle between them. Additionally, we use spherical Bessel functions and spherical harmonics to construct theoretically well-founded, orthogonal representations that achieve better performance than the currently prevalent Gaussian radial basis representations while using fewer than 1/4 of the parameters. We leverage these innovations to construct the directional message passing neural network (DimeNet). DimeNet outperforms previous GNNs on average by 76% on MD17 and by 31% on QM9. Our implementation is available online.
Graph Neural Network (GNN) has been demonstrated its effectiveness in dealing with non-Euclidean structural data. Both spatial-based and spectral-based GNNs are relying on adjacency matrix to guide message passing among neighbors during feature aggregation. Recent works have mainly focused on powerful message passing modules, however, in this paper, we show that none of the message passing modules is necessary. Instead, we propose a pure multilayer-perceptron-based framework, Graph-MLP with the supervision signal leveraging graph structure, which is sufficient for learning discriminative node representation. In model-level, Graph-MLP only includes multi-layer perceptrons, activation function, and layer normalization. In the loss level, we design a neighboring contrastive (NContrast) loss to bridge the gap between GNNs and MLPs by utilizing the adjacency information implicitly. This design allows our model to be lighter and more robust when facing large-scale graph data and corrupted adjacency information. Extensive experiments prove that even without adjacency information in testing phase, our framework can still reach comparable and even superior performance against the state-of-the-art models in the graph node classification task.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
