Summary of Injective Flows For Star-like Manifolds, by Marcello Massimo Negri et al.
Injective flows for star-like manifolds
by Marcello Massimo Negri, Jonathan Aellen, Volker Roth
First submitted to arxiv on: 13 Jun 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Machine Learning (stat.ML)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary Normalizing Flows (NFs) are efficient density estimation models that can be generalized to injective flows for modeling densities on manifolds. However, current approaches either rely on bounds or approximations of the Jacobian determinant, which becomes computationally prohibitive. This paper proposes a novel approach to compute the Jacobian determinant exactly and efficiently for star-like manifolds, making it particularly relevant for variational inference settings where only unnormalized targets are available. The proposed method is showcased in two settings: Objective Bayesian penalized likelihood models and probabilistic mixing models, with implications for posterior inference on mixture weights. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper talks about a new way to model complex shapes using something called Normalizing Flows. It’s like trying to draw a picture of a star-shaped object, but instead of drawing lines, you’re working with mathematical formulas. The problem is that these formulas can get very complicated and take a long time to compute. This research shows how to simplify the formulas so they can be calculated quickly and accurately. This has important implications for understanding complex systems in fields like statistics and machine learning. |
Keywords
» Artificial intelligence » Density estimation » Inference » Likelihood » Machine learning
