Ergodic Averaging
A technique that applies time averaging along the trajectory of a stochastic process to reduce variance and improve the stability of estimation.
Timeline (last 90 days)
The paper "Averaged Annealed Markov Chains Achieve the Algorithmic Threshold for Tensor PCA, Part II: Langevin Dynamics" proves that spherical Langevin dynamics with annealing and ergodic averaging can, starting from a uniform random initialization, reach the algorithmic threshold in polynomial time and achieve strong recovery.
Annealing refers to gradually lowering the temperature (increasing β) so that the distribution gradually concentrates from uniform to high-probability regions; ergodic averaging refers to the time average of the trajectory (1/T)∫_0^T X_t dt, whose variance is far smaller than that of a single-point estimate.
Annealing and averaging are classic techniques in MCMC, and this paper shows that they can significantly improve the performance of local algorithms on complex high-dimensional problems.
All Facts (3)
The paper "Averaged Annealed Markov Chains Achieve the Algorithmic Threshold for Tensor PCA, Part II: Langevin Dynamics" proves that spherical Langevin dynamics with annealing and ergodic averaging can, starting from a uniform random initialization, reach the algorithmic threshold in polynomial time and achieve strong recovery.
50%UnverifiedAnnealing refers to gradually lowering the temperature (increasing β) so that the distribution gradually concentrates from uniform to high-probability regions; ergodic averaging refers to the time average of the trajectory (1/T)∫_0^T X_t dt, whose variance is far smaller than that of a single-point estimate.
50%UnverifiedAnnealing and averaging are classic techniques in MCMC, and this paper shows that they can significantly improve the performance of local algorithms on complex high-dimensional problems.
50%