Abstract-High-dimensional crowdsourced data collected from numerous users produces rich knowledge for our society. However, it also brings unprecedented privacy threats to the participants. Local privacy, a variant of differential privacy, is proposed to eliminate privacy concerns. Unfortunately, achieving local privacy on high-dimensional crowdsourced data raises great challenges in terms of both computational efficiency and effectiveness. To this end, based on Expectation Maximization (EM) algorithm and Lasso regression, we first propose efficient multi-dimensional joint distribution estimation algorithms that maintain local privacy. Then, we develop a Locally privacy-preserving high-dimensional data Publication algorithm, LoPub, by taking advantage of our distribution estimation techniques. In particular, both correlations and joint distributions among multiple attributes are identified to reduce the dimensionality of crowdsourced data, thus achieving both efficiency and effectiveness in high-dimensional data publication. To the best of our knowledge, this is the first work addressing high-dimensional crowdsourced data publication with local privacy. Extensive experiments on realworld datasets demonstrate that our multivariate distribution estimation scheme significantly outperforms existing estimation schemes in terms of both communication overhead and estimation speed, and confirm that our LoPub scheme can keep average 80% and 60% accuracy over the published approximate datasets in terms of SVM and random forest classification, respectively.