Geometry-Aware Hierarchical Bayesian Learning on Manifolds
- URL: http://arxiv.org/abs/2111.00184v1
- Date: Sat, 30 Oct 2021 05:47:05 GMT
- Title: Geometry-Aware Hierarchical Bayesian Learning on Manifolds
- Authors: Yonghui Fan, Yalin Wang
- Abstract summary: We propose a hierarchical Bayesian learning model for learning on manifold-valued vision data.
We first introduce a kernel with the properties of geometry-awareness and intra- Kernel convolution.
We then use a Gaussian process regression to organize the inputs and finally implement a hierarchical Bayesian network for the feature aggregation.
- Score: 5.182379239800725
- License: http://creativecommons.org/licenses/by-nc-sa/4.0/
- Abstract: Bayesian learning with Gaussian processes demonstrates encouraging regression
and classification performances in solving computer vision tasks. However,
Bayesian methods on 3D manifold-valued vision data, such as meshes and point
clouds, are seldom studied. One of the primary challenges is how to effectively
and efficiently aggregate geometric features from the irregular inputs. In this
paper, we propose a hierarchical Bayesian learning model to address this
challenge. We initially introduce a kernel with the properties of
geometry-awareness and intra-kernel convolution. This enables geometrically
reasonable inferences on manifolds without using any specific hand-crafted
feature descriptors. Then, we use a Gaussian process regression to organize the
inputs and finally implement a hierarchical Bayesian network for the feature
aggregation. Furthermore, we incorporate the feature learning of neural
networks with the feature aggregation of Bayesian models to investigate the
feasibility of jointly learning on manifolds. Experimental results not only
show that our method outperforms existing Bayesian methods on manifolds but
also demonstrate the prospect of coupling neural networks with Bayesian
networks.
Related papers
- Automatic Discovery of Visual Circuits [66.99553804855931]
We explore scalable methods for extracting the subgraph of a vision model's computational graph that underlies recognition of a specific visual concept.
We find that our approach extracts circuits that causally affect model output, and that editing these circuits can defend large pretrained models from adversarial attacks.
arXiv Detail & Related papers (2024-04-22T17:00:57Z) - Deep Learning as Ricci Flow [38.27936710747996]
Deep neural networks (DNNs) are powerful tools for approximating the distribution of complex data.
We show that the transformations performed by DNNs during classification tasks have parallels to those expected under Hamilton's Ricci flow.
Our findings motivate the use of tools from differential and discrete geometry to the problem of explainability in deep learning.
arXiv Detail & Related papers (2024-04-22T15:12:47Z) - Inducing Gaussian Process Networks [80.40892394020797]
We propose inducing Gaussian process networks (IGN), a simple framework for simultaneously learning the feature space as well as the inducing points.
The inducing points, in particular, are learned directly in the feature space, enabling a seamless representation of complex structured domains.
We report on experimental results for real-world data sets showing that IGNs provide significant advances over state-of-the-art methods.
arXiv Detail & Related papers (2022-04-21T05:27:09Z) - Bayesian graph convolutional neural networks via tempered MCMC [0.41998444721319217]
Deep learning models, such as convolutional neural networks, have long been applied to image and multi-media tasks.
More recently, there has been more attention to unstructured data that can be represented via graphs.
These types of data are often found in health and medicine, social networks, and research data repositories.
arXiv Detail & Related papers (2021-04-17T04:03:25Z) - PointShuffleNet: Learning Non-Euclidean Features with Homotopy
Equivalence and Mutual Information [9.920649045126188]
We propose a novel point cloud analysis neural network called PointShuffleNet (PSN), which shows great promise in point cloud classification and segmentation.
Our PSN achieves state-of-the-art results on ModelNet40, ShapeNet and S3DIS with high efficiency.
arXiv Detail & Related papers (2021-03-31T03:01:16Z) - Anomaly Detection on Attributed Networks via Contrastive Self-Supervised
Learning [50.24174211654775]
We present a novel contrastive self-supervised learning framework for anomaly detection on attributed networks.
Our framework fully exploits the local information from network data by sampling a novel type of contrastive instance pair.
A graph neural network-based contrastive learning model is proposed to learn informative embedding from high-dimensional attributes and local structure.
arXiv Detail & Related papers (2021-02-27T03:17:20Z) - Deep Archimedean Copulas [98.96141706464425]
ACNet is a novel differentiable neural network architecture that enforces structural properties.
We show that ACNet is able to both approximate common Archimedean Copulas and generate new copulas which may provide better fits to data.
arXiv Detail & Related papers (2020-12-05T22:58:37Z) - Primal-Dual Mesh Convolutional Neural Networks [62.165239866312334]
We propose a primal-dual framework drawn from the graph-neural-network literature to triangle meshes.
Our method takes features for both edges and faces of a 3D mesh as input and dynamically aggregates them.
We provide theoretical insights of our approach using tools from the mesh-simplification literature.
arXiv Detail & Related papers (2020-10-23T14:49:02Z) - Learning Connectivity of Neural Networks from a Topological Perspective [80.35103711638548]
We propose a topological perspective to represent a network into a complete graph for analysis.
By assigning learnable parameters to the edges which reflect the magnitude of connections, the learning process can be performed in a differentiable manner.
This learning process is compatible with existing networks and owns adaptability to larger search spaces and different tasks.
arXiv Detail & Related papers (2020-08-19T04:53:31Z)
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.