Sparse adaptive pre-conditioning for MCMC

我们将探索使用稀疏预条件和自适应MCMC方法来提高马尔可夫链蒙特卡罗(MCMC)算法的效率和精度的方法。ADAP VE预条件是一种非常有效的策略，它通过学习“预条件矩阵”来使用马尔科夫链蒙特卡罗算法来加速对分布的探索。然而，这可能是计算昂贵的，因为对于d维问题需要学习O(d^2)个矩阵条目，如果完成得很幼稚，还可能需要O(d^3)次计算。我们将探索在预条件矩阵上施加稀疏性的策略，以便需要学习的矩阵条目更少，并且可以更有效地执行矩阵运算。我们将为MCMC发展新的理论和方法，并将新的方法应用到不同的应用领域。

We will explore ways to improve the efficiency and accuracy of Markov Chain Monte Carlo (MCMC) algorithms using sparse pre-conditioning and adap ve MCMC methods. Adap ve pre-conditioning is a very effective strategy to speed up the exploration of a distribution using a Markov chain Monte Carlo algorithm, by learning a 'pre-conditioning matrix'. It can, however, be computationally expensive, as O(d^2) matrix entries need to be learned for a d-dimensional problem, and O(d^3) computations may also be needed if done naively. We will explore strategies for imposing sparsity on the pre-conditioning matrix, so that fewer matrix entries need to be learned and that matrix operations can be performed more efficiently. We will develop new theory and methodology for MCMC and also apply the new methods to various application areas.