We study local differential privacy (LDP) protocols that estimate the statistics of a group while preserving individual data privacy. One of the challenges for LDP is dealing with high-dimensional data, which is common in the medical domain and can incur a large privacy budget that grows with dimensionality. In 2018, Zhang et al. presented a novel LDP scheme, CALM (Consistent Adaptive Local Marginal), that could estimate the joint probability distribution of high-dimensional data via a set of lower-dimensional marginals, called “views.” The process involved entropy maximization with a convex optimization algorithm. However, the entropy maximization process may fail if the original data is over-randomized. We therefore propose a simple method that addresses this estimation issue using a pseudo-inverse matrix. We evaluate the accuracy of our estimation method in terms of the size of the views and frequency predictions.