Traditionally, the sensitivity analysis of a Bayesian network studies the
impact of individually modifying the entries of its conditional probability
tables in a one-at-a-time (OAT) fashion. However, this approach fails to give a
comprehensive account of each inputs' relevance, since simultaneous
perturbations in two or more parameters often entail higher-order effects that
cannot be captured by an OAT analysis. We propose to conduct global
variance-based sensitivity analysis instead, whereby $n$ parameters are viewed
as uncertain at once and their importance is assessed jointly. Our method works
by encoding the uncertainties as $n$ additional variables of the network. To
prevent the curse of dimensionality while adding these dimensions, we use
low-rank tensor decomposition to break down the new potentials into smaller
factors. Last, we apply the method of Sobol to the resulting network to obtain
$n$ global sensitivity indices. Using a benchmark array of both expert-elicited
and learned Bayesian networks, we demonstrate that the Sobol indices can
significantly differ from the OAT indices, thus revealing the true influence of
uncertain parameters and their interactions.

传统上，贝叶斯网络的敏感性分析研究了以逐个修改其条件概率表的方式对其影响，我们提出进行全局基于方差的敏感性分析，使用低秩张量分解来降低维度，并通过 Sobol 法得出全局敏感性指标，从而展示不确定参数及其交互作用的真实影响。

贝叶斯网络中不确定参数的全局敏感性分析

Global Sensitivity Analysis of Uncertain Parameters in Bayesian Networks

Tensor data represents a multidimensional array. Regression methods based on
low-rank tensor decomposition leverage structural information to reduce the
parameter count. Multilinear logistic regression serves as a powerful tool for
the analysis of multidimensional data. To improve its efficacy and
interpretability, we present a Multilinear Sparse Logistic Regression model
with $\ell_0$-constraints ($\ell_0$-MLSR). In contrast to the $\ell_1$-norm and
$\ell_2$-norm, the $\ell_0$-norm constraint is better suited for feature
selection. However, due to its nonconvex and nonsmooth properties, solving it
is challenging and convergence guarantees are lacking. Additionally, the
multilinear operation in $\ell_0$-MLSR also brings non-convexity. To tackle
these challenges, we propose an Accelerated Proximal Alternating Linearized
Minimization with Adaptive Momentum (APALM$^+$) method to solve the
$\ell_0$-MLSR model. We provide a proof that APALM$^+$ can ensure the
convergence of the objective function of $\ell_0$-MLSR. We also demonstrate
that APALM$^+$ is globally convergent to a first-order critical point as well
as establish convergence rate by using the Kurdyka-Lojasiewicz property.
Empirical results obtained from synthetic and real-world datasets validate the
superior performance of our algorithm in terms of both accuracy and speed
compared to other state-of-the-art methods.

提出了一种基于稀疏多线性逻辑回归（Multilinear Sparse Logistic Regression）模型的加速近端交替线性化最小化（APALM$^+$）方法，用于解决多维数据分析中的特征选择问题，该方法在准确性和速度方面优于其他最先进方法。

全局收敛加速算法在多线性稀疏逻辑回归中的应用

Globally Convergent Accelerated Algorithms for Multilinear Sparse  Logistic Regression with $\ell_0$-constraints

Low-rank tensor decomposition and completion have attracted significant
interest from academia given the ubiquity of tensor data. However, the low-rank
structure is a global property, which will not be fulfilled when the data
presents complex and weak dependencies given specific graph structures. One
particular application that motivates this study is the spatiotemporal data
analysis. As shown in the preliminary study, weakly dependencies can worsen the
low-rank tensor completion performance. In this paper, we propose a novel
low-rank CANDECOMP / PARAFAC (CP) tensor decomposition and completion framework
by introducing the $L_{1}$-norm penalty and Graph Laplacian penalty to model
the weakly dependency on graph. We further propose an efficient optimization
algorithm based on the Block Coordinate Descent for efficient estimation. A
case study based on the metro passenger flow data in Hong Kong is conducted to
demonstrate improved performance over the regular tensor completion methods.

本文提出一种基于 $ L_ {1} $ -norm 和图拉普拉斯惩罚的低秩 CANDECOMP/PARAFAC（CP）张量分解和完成框架，以对图中的弱依赖性进行建模。并基于块坐标下降提出有效的优化算法，利用香港地铁乘客流量数据进行低秩张量完成任务，与传统完成方法相比，取得较好的结果。