We propose an adaptive importance sampling scheme for Gaussian approximations of intractable posteriors. Optimization-based approximations like variational inference can be too inaccurate while existing Monte Carlo methods can be too slow. Therefore, we propose a hybrid where, at each iteration, the Monte Carlo effective sample size can be guaranteed at a fixed computational cost by interpolating between natural-gradient variational inference and importance sampling. The amount of damping in the updates adapts to the posterior and guarantees the effective sample size. Gaussianity enables the use of Stein's lemma to obtain gradient-based optimization in the highly damped variational inference regime and a reduction of Monte Carlo error for undamped adaptive importance sampling. The result is a generic, embarrassingly parallel and adaptive posterior approximation method. Numerical studies on simulated and real data show its competitiveness with other, less general methods.

翻译：我们提出一种用于难以计算后验分布的高斯近似的自适应重要性采样方案。基于优化的近似方法（如变分推断）可能精度不足，而现有蒙特卡洛方法可能过于缓慢。因此，我们提出一种混合方法，在每次迭代中通过插值自然梯度变分推断与重要性采样，以固定计算成本保证蒙特卡洛有效样本量。更新中的阻尼量自适应于后验分布，并确保有效样本量。高斯性允许利用斯坦引理在高阻尼变分推断区域实现基于梯度的优化，同时降低无阻尼自适应重要性采样的蒙特卡洛误差。最终得到一种通用、可完美并行化且自适应的后验近似方法。在模拟数据和真实数据上的数值研究表明，该方法相比其他通用性较弱的方案具有竞争力。