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We consider a family of problems that are concerned about making predictions for the majority of unlabeled, graph-structured data samples based on a small proportion of labeled samples. Relational information among the data samples, often encoded in the graph/network structure, is shown to be helpful for these semi-supervised learning tasks. However, conventional graph-based regularization methods and recent graph neural networks do not fully leverage the interrelations between the features, the graph, and the labels. In this work, we propose a flexible generative framework for graph-based semi-supervised learning, which approaches the joint distribution of the node features, labels, and the graph structure. Borrowing insights from random graph models in network science literature, this joint distribution can be instantiated using various distribution families. For the inference of missing labels, we exploit recent advances of scalable variational inference techniques to approximate the Bayesian posterior. We conduct thorough experiments on benchmark datasets for graph-based semi-supervised learning. Results show that the proposed methods outperform the state-of-the-art models in most settings.
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α-deep Probabilistic Inference (α-DPI): Efficient Uncertainty Quantification from Exoplanet Astrometry to Black Hole Feature Extraction
Abstract Inference is crucial in modern astronomical research, where hidden astrophysical features and patterns are often estimated from indirect and noisy measurements. Inferring the posterior of hidden features, conditioned on the observed measurements, is essential for understanding the uncertainty of results and downstream scientific interpretations. Traditional approaches for posterior estimation include sampling-based methods and variational inference (VI). However, sampling-based methods are typically slow for high-dimensional inverse problems, while VI often lacks estimation accuracy. In this paper, we proposeα-deep probabilistic inference, a deep learning framework that first learns an approximate posterior usingα-divergence VI paired with a generative neural network, and then produces more accurate posterior samples through importance reweighting of the network samples. It inherits strengths from both sampling and VI methods: it is fast, accurate, and more scalable to high-dimensional problems than conventional sampling-based approaches. We apply our approach to two high-impact astronomical inference problems using real data: exoplanet astrometry and black hole feature extraction.
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- PAR ID:
- 10368101
- Publisher / Repository:
- DOI PREFIX: 10.3847
- Date Published:
- Journal Name:
- The Astrophysical Journal
- Volume:
- 932
- Issue:
- 2
- ISSN:
- 0004-637X
- Format(s):
- Medium: X Size: Article No. 99
- Size(s):
- Article No. 99
- Sponsoring Org:
- National Science Foundation
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