We address the problem of identifiability of an arbitrary conditional causal
effect given both the causal graph and a set of any observational and/or
interventional distributions of the form $Q[S]:=P(S|do(V\setminus S))$, where
$V$ denotes the set of all observed variables and $S\subseteq V$. We call this
problem conditional generalized identifiability (c-gID in short) and prove the
completeness of Pearl's $do$-calculus for the c-gID problem by providing sound
and complete algorithm for the c-gID problem. This work revisited the c-gID
problem in Lee et al. [2020], Correa et al. [2021] by adding explicitly the
positivity assumption which is crucial for identifiability. It extends the
results of [Lee et al., 2019, Kivva et al., 2022] on general identifiability
(gID) which studied the problem for unconditional causal effects and Shpitser
and Pearl [2006b] on identifiability of conditional causal effects given merely
the observational distribution $P(\mathbf{V})$ as our algorithm generalizes the
algorithms proposed in [Kivva et al., 2022] and [Shpitser and Pearl, 2006b].

本文主要研究的问题是通过 $do$-calculus 方法推断任意条件因果效应的可识别性问题，特别将正性假设显式引入，提出了相应的 sound and complete 算法，为 Lee et al. [2020] 和 Correa et al. [2021] 的研究工作进行了扩展，并不局限于观测分布 $P (V)$。

有关条件因果效应的可识别性

On Identifiability of Conditional Causal Effects

In aggregated variables the impact of interventions is typically ill-defined
because different micro-realizations of the same macro-intervention can result
in different changes of downstream macro-variables. We show that this
ill-definedness of causality on aggregated variables can turn unconfounded
causal relations into confounded ones and vice versa, depending on the
respective micro-realization. We argue that it is practically infeasible to
only use aggregated causal systems when we are free from this ill-definedness.
Instead, we need to accept that macro causal relations are typically defined
only with reference to the micro states. On the positive side, we show that
cause-effect relations can be aggregated when the macro interventions are such
that the distribution of micro states is the same as in the observational
distribution and also discuss generalizations of this observation.

该研究讨论了聚合变量的影响，特别是针对不同微观表现会对下游宏观变量产生不同变化的问题，进而讲述了因果关系在聚合变量中的局限性，只有参考微观物态才能确定宏观因果关系，并探讨了宏观干预和微观状态分布的关系。

有意义的因果汇聚和矛盾混淆

Meaningful Causal Aggregation and Paradoxical Confounding

We study experiment design for unique identification of the causal graph of a
system where the graph may contain cycles. The presence of cycles in the
structure introduces major challenges for experiment design as, unlike acyclic
graphs, learning the skeleton of causal graphs with cycles may not be possible
from merely the observational distribution. Furthermore, intervening on a
variable in such graphs does not necessarily lead to orienting all the edges
incident to it. In this paper, we propose an experiment design approach that
can learn both cyclic and acyclic graphs and hence, unifies the task of
experiment design for both types of graphs. We provide a lower bound on the
number of experiments required to guarantee the unique identification of the
causal graph in the worst case, showing that the proposed approach is
order-optimal in terms of the number of experiments up to an additive
logarithmic term. Moreover, we extend our result to the setting where the size
of each experiment is bounded by a constant. For this case, we show that our
approach is optimal in terms of the size of the largest experiment required for
uniquely identifying the causal graph in the worst case.

本文提出了一种实验设计方法，可以学习含有循环或非循环的因果图，并且在保证最差情况下的唯一识别因果图所需实验数量最少。