UniPC TU

The UniPC TU sampler is an unadjusted Langevin algorithm used for sampling from probability distributions in machine learning. Here are some key details:

• UniPC stands for Unadjusted Preconditioned Cauchy. TU stands for Times Updater.
• It is a variant of the Langevin Monte Carlo algorithm that performs Markov Chain Monte Carlo (MCMC) sampling.
• Used to draw samples from multimodal distributions where the probability density has multiple peaks.
• Works by adding Gaussian noise to the parameters during the sampling process to help explore complex distributions.
• The magnitude of noise is controlled by a friction term that is adapted during sampling. Helps convergence.
• Uses Cauchy distributions instead of Gaussian noise in the parameter updates. Makes it more robust.
• Can handle high dimensional and ill-conditioned probability distributions.
• The "Times Updater" refers to scaling the gradient in the update equation by a factor related to the Fisher information matrix. Improves conditioning.
• Overall, UniPC TU sampler extends Langevin dynamics to sample efficiently from complex, non-convex densities in machine learning problems like Bayesian neural nets.
• Allows training deep learning models with fewer assumptions about distributions and gets better uncertainty estimates.

In summary, the UniPC TU sampler is an enhanced MCMC algorithm that can explore multimodal distributions for deep learning using carefully calibrated noise injection in parameter space.