  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.
