Daily Arxiv

This page organizes papers related to artificial intelligence published around the world.
This page is summarized using Google Gemini and is operated on a non-profit basis.
The copyright of the paper belongs to the author and the relevant institution. When sharing, simply cite the source.

Efficient Approximate Posterior Sampling with Annealed Langevin Monte Carlo

Created by
  • Haebom

Author

Advait Parulekar, Litu Rout, Karthikeyan Shanmugam, Sanjay Shakkottai

Outline

This paper studies the problem of posterior probability distribution sampling for score-based generative models. Sampling is performed using the prior probability $p(x)$, the measurement model $p(y|x)$, and the posterior probability $p(x|y)$. Exact posterior probability sampling from the KL divergence perspective is known to be computationally challenging. Rather than exploring the possibility of exact sampling, this paper approaches the problem of "tilting" the distribution toward the measurements. With minimal assumptions, we show that it is possible to simultaneously sample from a distribution that approximates the posterior probability of a noisy prior under KL divergence and the true posterior probability under Fisher divergence. This ensures that the resulting sample matches both the measurements and the prior probability. This paper presents the first formal result for (approximate) posterior probability sampling in polynomial time.

Takeaways, Limitations

Takeaways:
We present a novel approach to the posterior probability sampling problem in score-based generative models.
Combining KL divergence and Fisher divergence allows sampling that takes into account both measurement and prior probabilities.
(Approximate) Presents the first polynomial-time algorithm for posterior probability sampling.
It has the potential to be applied to real-world applications such as image super-resolution, style transfer, and reconstruction.
Limitations:
Since it is an approximate sampling method, there may be differences from the actual posterior probability.
Further experimental verification of the algorithm's accuracy and performance is required.
There is room for optimization and efficiency improvements for specific applications.
Comparative analysis with other sampling techniques is needed in terms of computational complexity.
👍