高维非独立同分布数据的分布式推断

分布式推断是统计学热门研究问题，分布式算法不仅具有计算高效性，而且与经典方法具有渐近一致的统计效率，因此可以有效应对海量数据带来的技术挑战。现有的分布式研究主要基于数据的独立同分布假设，然而在实际应用中，不同局部机器收集得到的数据可能存在机器差异性，即来自不同的子总体和环境。非独立同分布数据会导致经典的分布式算法及对应理论推断失效，给当前的分布式研究带来很大的挑战。本项目拟针对高维非独立同分布数据，研究分布参数估计问题。通过引入局部机器特有参数，建立分布调整机制，并构造通信高效的分布式算法。进一步探索稀疏回归和支持向量机模型下的分布式算法构造，根据非独立同分布数据结构结合正则化方法研究高维模型下的参数估计和统计推断问题。所得算法将达到近似最优统计误差率，并被应用于生物、医学、工程学等领域解决实际问题。

Distributed inference is a popular topic in statistics. Distributed algorithms not only are computationally efficient but also achieve the optimal statistical efficiency, hence they can effectively overcome the challenges brought by the growing size of modern data. Most existing distributed methods focus on independent and identically distributed (i.i.d.) data, while in practice, data collected from different local machines may be machine-specific, i.e., coming from various sub-populations and environments. Non-i.i.d. data make the classical distributed methodologies and theories invalid, which brings huge challenges to existing distributed studies. In this project, we propose to study the parameter estimation of distributions for high-dimensional non-i.i.d. data. Through introducing machine-specific parameters, we establish an adjustment mechanism for distributions and construct communication-efficient distributed algorithms. We further explore distributed algorithms for sparse regression and support vector machine, conduct parameter estimation and statistical inference based on non-i.i.d. data with regularization methods for high-dimensional models. The resulting methods will attain near-optimal statistical error rates and be evaluated by practice applications in biology, medicine, engineering and other fields.