Complexity of zigzag sampling algorithm for strongly log-concave distributions
This provides theoretical guarantees for an efficient MCMC method in high-dimensional Bayesian inference, though it is incremental as it builds on existing zigzag sampling.
The paper tackled the computational complexity of the zigzag sampling algorithm for strongly log-concave distributions, proving it achieves ε error in chi-square divergence with a cost of O(κ² d^(1/2) (log(1/ε))^(3/2)) gradient evaluations under specific conditions.
We study the computational complexity of zigzag sampling algorithm for strongly log-concave distributions. The zigzag process has the advantage of not requiring time discretization for implementation, and that each proposed bouncing event requires only one evaluation of partial derivative of the potential, while its convergence rate is dimension independent. Using these properties, we prove that the zigzag sampling algorithm achieves $\varepsilon$ error in chi-square divergence with a computational cost equivalent to $O\bigl(κ^2 d^\frac{1}{2}(\log\frac{1}{\varepsilon})^{\frac{3}{2}}\bigr)$ gradient evaluations in the regime $κ\ll \frac{d}{\log d}$ under a warm start assumption, where $κ$ is the condition number and $d$ is the dimension.