Although many real-world applications, such as disease prediction, and fault
detection suffer from class imbalance, most existing graph-based classification
methods ignore the skewness of the distribution of classes; therefore, tend to
be biased towards the majority class(es). Conventional methods typically tackle
this problem through the assignment of weights to each one of the class samples
based on a function of their loss, which can lead to over-fitting on outliers.
In this paper, we propose a meta-learning algorithm, named Meta-GCN, for
adaptively learning the example weights by simultaneously minimizing the
unbiased meta-data set loss and optimizing the model weights through the use of
a small unbiased meta-data set. Through experiments, we have shown that
Meta-GCN outperforms state-of-the-art frameworks and other baselines in terms
of accuracy, the area under the receiver operating characteristic (AUC-ROC)
curve, and macro F1-Score for classification tasks on two different datasets.

本论文提出了一种名为 Meta-GCN 的元学习算法，通过同时最小化无偏元数据集损失和优化模型权重来自适应地学习样本权重，实验证明 Meta-GCN 在两个不同数据集上的分类任务中在准确性、接收器操作特性下的曲线下面积（AUC-ROC 曲线）和宏 F1 分数等方面优于现有最先进框架和其他基线模型。

元图卷积网络：处理图神经网络中的数据不平衡的动态加权损失最小化方法

Meta-GCN: A Dynamically Weighted Loss Minimization Method for Dealing  with the Data Imbalance in Graph Neural Networks

Automatic Differentiation Variational Inference (ADVI) is efficient in
learning probabilistic models. Classic ADVI relies on the parametric approach
to approximate the posterior. In this paper, we develop a spline-based
nonparametric approximation approach that enables flexible posterior
approximation for distributions with complicated structures, such as skewness,
multimodality, and bounded support. Compared with widely-used nonparametric
variational inference methods, the proposed method is easy to implement and
adaptive to various data structures. By adopting the spline approximation, we
derive a lower bound of the importance weighted autoencoder and establish the
asymptotic consistency. Experiments demonstrate the efficiency of the proposed
method in approximating complex posterior distributions and improving the
performance of generative models with incomplete data.

我们提出了一种基于样条的非参数逼近方法，可以灵活逼近具有复杂结构的后验分布，如偏度、多峰性和有界支持。通过采用样条逼近，我们得到了重要性加权自编码器的下界，并建立了渐近一致性。实验证明了该方法在逼近复杂的后验分布和提高具有不完整数据的生成模型性能方面的高效性。

非参数自动微分变分推断与样条逼近

Nonparametric Automatic Differentiation Variational Inference with  Spline Approximation

We calculate the cosmological evolution of the 1-point probability
distribution function (PDF), using an analytic approximation that combines
gravitational perturbation theory with the Edgeworth expansion of the PDF. Our
method applies directly to a smoothed mass density field or to the divergence
of a smoothed peculiar velocity field, provided that rms fluctuations are small
compared to unity on the smoothing scale, and that the primordial fluctuations
that seed the growth of structure are Gaussian. We use this `Edgeworth
approximation' to compute the evolution of $<\delta|\delta|>$ and $<|delta|>$;
these measures are similar to the skewness and kurtosis of the density field,
but they are less sensitive to tails of the probability distribution, so they
may be more accurately estimated from surveys of limited volume. We compare our
analytic calculations to cosmological N-body simulations in order to assess
their range of validity. When $\sigma \ll 1$, the numerical simulations and
perturbation theory agree precisely, demonstrating that the N-body method can
yield accurate results in the regime of weakly non-linear clustering. We show
analytically that `biased' galaxy formation preserves the relation $<\delta^3>
\propto <\delta^2>^2$ predicted by second-order perturbation theory, provided
that the galaxy density is a local function of the underlying mass density.

本研究尝试通过结合重力扰动理论和 PDF 的 Edgeworth 扩展的分析逼近方法，计算 1 点概率分布函数的宇宙演化，并使用类似于密度场偏斜和峭度的措辞计算其演化情况，同时将分析计算与 N - 体模拟进行比较以验证其准确性。