A fundamental aspect of relational data, such as from a social network, is
the possibility of dependence among the relations. In particular, the relations
between members of one pair of nodes may have an effect on the relations
between members of another pair. This article develops a type of regression
model to estimate such effects in the context of longitudinal and multivariate
relational data, or other data that can be represented in the form of a tensor.
The model is based on a general multilinear tensor regression model, a special
case of which is a tensor autoregression model in which the tensor of relations
at one time point are parsimoniously regressed on relations from previous time
points. This is done via a separable, or Kronecker-structured, regression
parameter along with a separable covariance model. In the context of an
analysis of longitudinal multivariate relational data, it is shown how the
multilinear tensor regression model can represent patterns that often appear in
relational and network data, such as reciprocity and transitivity.

本文开发了一种类型的回归模型来估计纵向和多元关系数据中成员之间的关系，该模型基于多线性张量回归模型，一种特殊情况是张量自回归模型，可以表示关系和网络数据中经常出现的模式，如互惠和传递性。

多线性张量回归对于纵向关系数据的应用

Multilinear tensor regression for longitudinal relational data

A dynamic treatment regime effectively incorporates both accrued information
and long-term effects of treatment from specially designed clinical trials. As
these become more and more popular in conjunction with longitudinal data from
clinical studies, the development of statistical inference for optimal dynamic
treatment regimes is a high priority. This is very challenging due to the
difficulties arising form non-regularities in the treatment effect parameters.
In this paper, we propose a new reinforcement learning framework called
penalized Q-learning (PQ-learning), under which the non-regularities can be
resolved and valid statistical inference established. We also propose a new
statistical procedure---individual selection---and corresponding methods for
incorporating individual selection within PQ-learning. Extensive numerical
studies are presented which compare the proposed methods with existing methods,
under a variety of non-regular scenarios, and demonstrate that the proposed
approach is both inferentially and computationally superior. The proposed
method is demonstrated with the data from a depression clinical trial study.

该论文提出一种基于惩罚的 Q 学习框架（PQ-learning）来解决治疗效应参数不规则性的统计推断问题，并提出了相应的个体选择方法来将这一框架应用于动态治疗决策制定中，结果证明其在计算和推论方面均具有优越性。该方法已经应用于抑郁症临床试验研究。