For causal discovery in the presence of latent confounders, constraints
beyond conditional independences exist that can enable causal discovery
algorithms to distinguish more pairs of graphs. Such constraints are not
well-understood yet. In the setting of linear structural equation models
without bows, we study algebraic constraints and argue that these provide the
most fine-grained resolution achievable. We propose efficient algorithms that
decide whether two graphs impose the same algebraic constraints, or whether the
constraints imposed by one graph are a subset of those imposed by another
graph.

对于包含潜在混淆因素的因果发现问题，存在超越条件独立性的约束条件，可以使因果发现算法能够区分更多的图对。在没有圆弓的线性结构方程模型的设置下，我们研究了代数约束，并认为这些约束提供了最精细的解析度。我们提出了有效的算法，判断两个图是否施加相同的代数约束，或者一个图所施加的约束是否是另一个图所施加约束的子集。

高效决定无弓型无环路径图的代数等价性

Efficiently Deciding Algebraic Equivalence of Bow-Free Acyclic Path  Diagrams

If $X,Y,Z$ denote sets of random variables, two different data sources may
contain samples from $P_{X,Y}$ and $P_{Y,Z}$, respectively. We argue that
causal discovery can help inferring properties of the `unobserved joint
distributions' $P_{X,Y,Z}$ or $P_{X,Z}$. The properties may be conditional
independences (as in `integrative causal inference') or also quantitative
statements about dependences.
More generally, we define a learning scenario where the input is a subset of
variables and the label is some statistical property of that subset. Sets of
jointly observed variables define the training points, while unobserved sets
are possible test points. To solve this learning task, we infer, as an
intermediate step, a causal model from the observations that then entails
properties of unobserved sets. Accordingly, we can define the VC dimension of a
class of causal models and derive generalization bounds for the predictions.
Here, causal discovery becomes more modest and better accessible to empirical
tests than usual: rather than trying to find a causal hypothesis that is `true'
a causal hypothesis is {\it useful} whenever it correctly predicts statistical
properties of unobserved joint distributions. This way, a sparse causal graph
that omits weak influences may be more useful than a dense one (despite being
less accurate) because it is able to reconstruct the full joint distribution
from marginal distributions of smaller subsets.
Within such a `pragmatic' application of causal discovery, some popular
heuristic approaches become justified in retrospect. It is, for instance,
allowed to infer DAGs from partial correlations instead of conditional
independences if the DAGs are only used to predict partial correlations.

通过因果推断方法可以推断未被观察到的联合分布的性质，进一步定义了一种从已观察到的变量中引入因果模型来推断未观察到变量的统计性质的学习场景，并且通过推导因果模型的 VC 维，得出了预测的泛化界限。