Instrumental variable (IV) regression is a standard strategy for learning
causal relationships between confounded treatment and outcome variables from
observational data by utilizing an instrumental variable, which affects the
outcome only through the treatment. In classical IV regression, learning
proceeds in two stages: stage 1 performs linear regression from the instrument
to the treatment; and stage 2 performs linear regression from the treatment to
the outcome, conditioned on the instrument. We propose a novel method, deep
feature instrumental variable regression (DFIV), to address the case where
relations between instruments, treatments, and outcomes may be nonlinear. In
this case, deep neural nets are trained to define informative nonlinear
features on the instruments and treatments. We propose an alternating training
regime for these features to ensure good end-to-end performance when composing
stages 1 and 2, thus obtaining highly flexible feature maps in a
computationally efficient manner. DFIV outperforms recent state-of-the-art
methods on challenging IV benchmarks, including settings involving high
dimensional image data. DFIV also exhibits competitive performance in
off-policy policy evaluation for reinforcement learning, which can be
understood as an IV regression task.

本研究提出了一种新的方法，即深度特征工具变量回归（DFIV），用于解决仪器、处理和结果之间可能是非线性关系的情况。通过训练深度神经网络，定义仪器和处理的信息非线性特征。采用交替训练模式确保优良的端到端性能，解决了应用传统仪器变量回归可能存在的局限性，可有效提高其应用范围和性能。

工具变量回归中学习深度特征

Learning Deep Features in Instrumental Variable Regression

In an age of increasingly large data sets, investigators in many different
disciplines have turned to clustering as a tool for data analysis and
exploration. Existing clustering methods, however, typically depend on several
nontrivial assumptions about the structure of data. Here we reformulate the
clustering problem from an information theoretic perspective which avoids many
of these assumptions. In particular, our formulation obviates the need for
defining a cluster "prototype", does not require an a priori similarity metric,
is invariant to changes in the representation of the data, and naturally
captures non-linear relations. We apply this approach to different domains and
find that it consistently produces clusters that are more coherent than those
extracted by existing algorithms. Finally, our approach provides a way of
clustering based on collective notions of similarity rather than the
traditional pairwise measures.

该研究采用信息理论的视角来重新构造聚类问题，避免了许多现有聚类方法所依赖的非常规结构的假设，且捕捉了非线性关系。基于集体相似度而非传统的成对度量，该方法在不同领域内都表现出比现有算法更高的聚类一致性。