We consider the problem of estimating differences in two Gaussian graphical
models (GGMs) which are known to have similar structure. The GGM structure is
encoded in its precision (inverse covariance) matrix. In many applications one
is interested in estimating the difference in two precision matrices to
characterize underlying changes in conditional dependencies of two sets of
data. Existing methods for differential graph estimation are based on
single-attribute (SA) models where one associates a scalar random variable with
each node. In multi-attribute (MA) graphical models, each node represents a
random vector. In this paper, we analyze a group lasso penalized D-trace loss
function approach for differential graph learning from multi-attribute data. An
alternating direction method of multipliers (ADMM) algorithm is presented to
optimize the objective function. Theoretical analysis establishing consistency
in support recovery and estimation in high-dimensional settings is provided.
Numerical results based on synthetic as well as real data are presented.

通过多属性数据分析，提出了一种基于组套索罚函数和交替方向乘子法的差分图学习方法，给出了在高维环境下对支持恢复和估计的一致性理论分析，并展示了基于合成数据和真实数据的数值结果。

从多属性数据中学习高维微分图

Learning High-Dimensional Differential Graphs From Multi-Attribute Data

We study the problem of learning causal representations from unknown, latent
interventions in a general setting, where the latent distribution is Gaussian
but the mixing function is completely general. We prove strong identifiability
results given unknown single-node interventions, i.e., without having access to
the intervention targets. This generalizes prior works which have focused on
weaker classes, such as linear maps or paired counterfactual data. This is also
the first instance of causal identifiability from non-paired interventions for
deep neural network embeddings. Our proof relies on carefully uncovering the
high-dimensional geometric structure present in the data distribution after a
non-linear density transformation, which we capture by analyzing quadratic
forms of precision matrices of the latent distributions. Finally, we propose a
contrastive algorithm to identify the latent variables in practice and evaluate
its performance on various tasks.

本文研究了从未知潜在干预中学习因果表征的问题，并且证明了在情形下强可辨识性，该情形中潜在分布是高斯分布，混合函数是完全一般化的。

从一般非线性混合干预中学习线性因果表示

Learning Linear Causal Representations from Interventions under General  Nonlinear Mixing

Banded matrices can be used as precision matrices in several models including
linear state-space models, some Gaussian processes, and Gaussian Markov random
fields. The aim of the paper is to make modern inference methods (such as
variational inference or gradient-based sampling) available for Gaussian models
with banded precision. We show that this can efficiently be achieved by
equipping an automatic differentiation framework, such as TensorFlow or
PyTorch, with some linear algebra operators dedicated to banded matrices. This
paper studies the algorithmic aspects of the required operators, details their
reverse-mode derivatives, and show that their complexity is linear in the
number of observations.

本文的主要研究领域是将带状矩阵用于高斯模型的精度矩阵中，旨在通过配备专门用于带状矩阵的线性代数算子来实现现代推理方法的运用，同时研究这些算子的算法方面，详细阐述它们的反向传播导数，并证明它们的复杂度与观测数量呈线性关系。

高斯马尔可夫模型自动微分时代中的分带矩阵算子

Banded Matrix Operators for Gaussian Markov Models in the Automatic  Differentiation Era

We introduce a general framework for estimation of inverse covariance, or
precision, matrices from heterogeneous populations. The proposed framework uses
a Laplacian shrinkage penalty to encourage similarity among estimates from
disparate, but related, subpopulations, while allowing for differences among
matrices. We propose an efficient alternating direction method of multipliers
(ADMM) algorithm for parameter estimation, as well as its extension for faster
computation in high dimensions by thresholding the empirical covariance matrix
to identify the joint block diagonal structure in the estimated precision
matrices. We establish both variable selection and norm consistency of the
proposed estimator for distributions with exponential or polynomial tails.
Further, to extend the applicability of the method to the settings with unknown
populations structure, we propose a Laplacian penalty based on hierarchical
clustering, and discuss conditions under which this data-driven choice results
in consistent estimation of precision matrices in heterogenous populations.
Extensive numerical studies and applications to gene expression data from
subtypes of cancer with distinct clinical outcomes indicate the potential
advantages of the proposed method over existing approaches.

本研究提出一种用于估计异构总体逆协方差矩阵的通用框架，该框架使用 Laplacian shrinkage penalty 来鼓励异构但相关子总体的估计值之间的相似性，同时允许矩阵之间的差异。通过使用经验协方差矩阵的阈值截断来识别所估计的精密矩阵的联合块对角线结构，提出了一种有效的交替方向乘法器（ADMM）算法以及其在高维中的快速计算扩展。研究表明，该方法具有应用价值。