Summary of Efficient Prior Calibration From Indirect Data, by O. Deniz Akyildiz et al.
Efficient Prior Calibration From Indirect Data
by O. Deniz Akyildiz, Mark Girolami, Andrew M. Stuart, Arnaud Vadeboncoeur
First submitted to arxiv on: 28 May 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Computation (stat.CO)
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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 The proposed approach leverages Bayesian inversion to quantify uncertainty in various scientific and engineering applications, requiring four core ingredients: a forward model, observation operator, noise model, and prior model. The paper focuses on learning the prior model from indirect data obtained through noisy observations. A generative model represents the prior as the pushforward of a Gaussian distribution in a latent space, which is learned by minimizing an appropriate loss function. To make this methodology implementable, an efficient neural operator approximation of the forward model is proposed, allowing concurrent learning with the pushforward map using bilevel optimization. This approach has potential to improve computational efficiency when dealing with expensive or non-smooth observation processes. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper uses Bayesian inversion to figure out uncertainty in different scientific and engineering problems. It needs four main things: a way to predict what we don’t know, a way to get data from what we do know, an idea of how noisy the data is, and an understanding of what we already know about what we’re trying to figure out. The paper focuses on learning what we already know by looking at indirect data that’s been affected by noise. It uses a special kind of model to represent this prior knowledge as a pushforward of a Gaussian distribution in a hidden space. The model is learned by finding the right combination of things that makes sense. This approach could make it faster and easier to learn from noisy data. |
Keywords
» Artificial intelligence » Generative model » Latent space » Loss function » Optimization
