Paired single-cell sequencing technologies enable the simultaneous
measurement of complementary modalities of molecular data at single-cell
resolution. Along with the advances in these technologies, many methods based
on variational autoencoders have been developed to integrate these data.
However, these methods do not explicitly incorporate prior biological
relationships between the data modalities, which could significantly enhance
modeling and interpretation. We propose a novel probabilistic learning
framework that explicitly incorporates conditional independence relationships
between multi-modal data as a directed acyclic graph using a generalized
hierarchical variational autoencoder. We demonstrate the versatility of our
framework across various applications pertinent to single-cell multi-omics data
integration. These include the isolation of common and distinct information
from different modalities, modality-specific differential analysis, and
integrated cell clustering. We anticipate that the proposed framework can
facilitate the construction of highly flexible graphical models that can
capture the complexities of biological hypotheses and unravel the connections
between different biological data types, such as different modalities of paired
single-cell multi-omics data. The implementation of the proposed framework can
be found in the repository this https URL

提出了一种新颖的概率学习框架，该框架明确地将多模态数据之间的条件独立关系作为一个有向无环图来考虑，用于集成单细胞多组学数据。

CAVACHON：一种用于整合多模态单细胞数据的分层变分自编码器

CAVACHON: a hierarchical variational autoencoder to integrate  multi-modal single-cell data

Several causal discovery algorithms have been proposed. However, when the
sample size is small relative to the number of variables, the accuracy of
estimating causal graphs using existing methods decreases. And some methods are
not feasible when the sample size is smaller than the number of variables. To
circumvent these problems, some researchers proposed causal structure learning
algorithms using divide-and-conquer approaches. For learning the entire causal
graph, the approaches first split variables into several subsets according to
the conditional independence relationships among the variables, then apply a
conventional causal discovery algorithm to each subset and merge the estimated
results. Since the divide-and-conquer approach reduces the number of variables
to which a causal structure learning algorithm is applied, it is expected to
improve the estimation accuracy of causal graphs, especially when the sample
size is small relative to the number of variables and the model is sparse.
However, existing methods are either computationally expensive or do not
provide sufficient accuracy when the sample size is small. This paper proposes
a new algorithm for grouping variables based the ancestral relationships among
the variables, under the LiNGAM assumption, where the causal relationships are
linear, and the mutually independent noise are distributed as continuous
non-Gaussian distributions. We call the proposed algorithm CAG. The time
complexity of the ancestor finding in CAG is shown to be cubic to the number of
variables. Extensive computer experiments confirm that the proposed method
outperforms the original DirectLiNGAM without grouping variables and other
divide-and-conquer approaches not only in estimation accuracy but also in
computation time when the sample size is small relative to the number of
variables and the model is sparse.

该论文提出了一种基于变量的祖先关系分组的新算法 CAG，通过分组变量减少计算量和提高估计准确性，特别是在样本量相对较小且模型稀疏的情况下，在计算时间和估计准确性方面优于原始的直接 LiNGAM 方法和其他分治算法。