This paper proposes a general two directional simultaneous inference (TOSI) framework for high-dimensional models with a manifest variable or latent variable structure, for example, high-dimensional mean models, high-dimensional sparse regression models, and high-dimensional latent factors models. TOSI performs simultaneous inference on a set of parameters from two directions, one to test whether the assumed zero parameters indeed are zeros and one to test whether exist zeros in the parameter set of nonzeros. As a result, we can exactly identify whether the parameters are zeros, thereby keeping the data structure fully and parsimoniously expressed. We theoretically prove that the proposed TOSI method asymptotically controls the Type I error at the prespecified significance level and that the testing power converges to one. Simulations are conducted to examine the performance of the proposed method in finite sample situations and two real datasets are analyzed. The results show that the TOSI method is more predictive and has more interpretable estimators than existing methods.
Simultaneous Inference for High-dimensional Linear Models
本文提出了一种基于最近的去稀疏化Lasso估计（van de Geer et al. 2014）对高维稀疏线性模型进行同时推断的引导辅助过程。我们的程序允许感兴趣的参数向量的维度以指数方式大于样本量，并且它自动考虑去稀疏化Lasso估计器内的依赖性。此外，我们的同步测试方法可以自然地与边缘筛选（Fan and Lv 2008）相结合，以提高其在稀疏测试中的能力，同时降低计算成本，或者与步降方法（Romano and Wolf 2005）相结合，以提供对家族差错率的强有力控制。在理论上，我们证明了我们的同时测试程序渐近达到预先指定的显着性水平，并享有一定的最优性，即使在其权力的模型误差是非高斯。我们的一般理论也是有用的研究支持恢复问题。为了扩大适用范围，我们进一步将我们的主要结果推广到具有凸损失函数的广义线性模型。我们的方法的有效性通过仿真研究证明。
Efficient Inference after Directionally Stable Adaptive Experiments
University College London（伦敦大学学院）；Gatsby Computational Neuroscience Unit, University College London（伦敦大学学院计算神经科学单元）；Cornell University（康奈尔大学）；Netflix；Google DeepMind（谷歌DeepMind）；Rutgers University（罗格斯大学）
Divergence-based Robust Generalised Bayesian Inference for Directional Data via von Mises-Fisher models
School of Data Science, Meisei University（明成大学数据科学学院）；RIKEN Center for Brain Science（理化学研究所脑科学中心）；School of Business Administration, Meiji University（明治大学商学院）；Department of Information Sciences, Tokyo University of Science（东京科学技术大学信息科学系）
