When applying VISA to models that necessitate high-dimensional parameter spaces, several potential limitations and challenges may arise. One significant challenge is related to sampling efficiency and coverage within these high-dimensional spaces. As the dimensionality increases, maintaining an adequate representation of the posterior distribution becomes increasingly difficult due to sparsity issues and curse of dimensionality effects. This can result in suboptimal convergence rates and potentially biased estimates if not addressed appropriately.
Moreover, optimizing variational objectives in high-dimensional parameter spaces requires careful tuning of hyperparameters such as learning rates and ESS thresholds. The interplay between these hyperparameters becomes more intricate as dimensionality grows, making it challenging to strike a balance between exploration and exploitation effectively.
Furthermore, interpreting results from VISA in high-dimensional settings can be complex due to difficulties in visualizing or comprehending multi-dimensional distributions accurately. Ensuring robustness against overfitting while capturing essential features of the posterior distribution poses additional challenges when dealing with vast parameter spaces.