Projected Stein Variational Gradient Descent
This work addresses the challenge of high-dimensional Bayesian inference for practitioners in fields like machine learning and statistics, offering a more scalable solution, though it appears incremental as an adaptation of SVGD.
The authors tackled the curse of dimensionality in Bayesian inference by proposing a projected Stein variational gradient descent (pSVGD) method that exploits intrinsic low-dimensional data subspaces, resulting in improved accuracy and efficiency over SVGD, with scalability demonstrated across parameter dimensions from hundreds to tens of thousands.
The curse of dimensionality is a longstanding challenge in Bayesian inference in high dimensions. In this work, we propose a projected Stein variational gradient descent (pSVGD) method to overcome this challenge by exploiting the fundamental property of intrinsic low dimensionality of the data informed subspace stemming from ill-posedness of such problems. We adaptively construct the subspace using a gradient information matrix of the log-likelihood, and apply pSVGD to the much lower-dimensional coefficients of the parameter projection. The method is demonstrated to be more accurate and efficient than SVGD. It is also shown to be more scalable with respect to the number of parameters, samples, data points, and processor cores via experiments with parameters dimensions ranging from the hundreds to the tens of thousands.