The growing interest for high dimensional and functional data analysis led in
the last decade to an important research developing a consequent amount of
techniques. Parallelized algorithms, which consist in distributing and treat
the data into different machines, for example, are a good answer to deal with
large samples taking values in high dimensional spaces. We introduce here a
parallelized averaged stochastic gradient algorithm, which enables to treat
efficiently and recursively the data, and so, without taking care if the
distribution of the data into the machines is uniform. The rate of convergence
in quadratic mean as well as the asymptotic normality of the parallelized
estimates are given, for strongly and locally strongly convex objectives.

介绍了一种并行的平均随机梯度算法，能够高效地递归处理高维空间中的大样本数据，并给出了强凸目标和局部强凸目标的平均收敛速度和渐近正态性。

并行平均随机梯度算法收敛率

On the rates of convergence of Parallelized Averaged Stochastic Gradient  Algorithms

We propose a likelihood ratio based inferential framework for high
dimensional semiparametric generalized linear models. This framework addresses
a variety of challenging problems in high dimensional data analysis, including
incomplete data, selection bias, and heterogeneous multitask learning. Our work
has three main contributions. (i) We develop a regularized statistical
chromatography approach to infer the parameter of interest under the proposed
semiparametric generalized linear model without the need of estimating the
unknown base measure function. (ii) We propose a new framework to construct
post-regularization confidence regions and tests for the low dimensional
components of high dimensional parameters. Unlike existing post-regularization
inferential methods, our approach is based on a novel directional likelihood.
In particular, the framework naturally handles generic regularized estimators
with nonconvex penalty functions and it can be used to infer least false
parameters under misspecified models. (iii) We develop new concentration
inequalities and normal approximation results for U-statistics with unbounded
kernels, which are of independent interest. We demonstrate the consequences of
the general theory by using an example of missing data problem. Extensive
simulation studies and real data analysis are provided to illustrate our
proposed approach.

提出一种基于似然比的高维半参数广义线性模型的推理框架，包括使用规则化统计制备模型、构建后规则化的置信区间和测试、发展新的浓缩不等式和正态逼近结果，以及应用于缺失数据问题的示例。