We study the problem of robust multivariate polynomial regression: let
$p\colon\mathbb{R}^n\to\mathbb{R}$ be an unknown $n$-variate polynomial of
degree at most $d$ in each variable. We are given as input a set of random
samples $(\mathbf{x}_i,y_i) \in [-1,1]^n \times \mathbb{R}$ that are noisy
versions of $(\mathbf{x}_i,p(\mathbf{x}_i))$. More precisely, each
$\mathbf{x}_i$ is sampled independently from some distribution $\chi$ on
$[-1,1]^n$, and for each $i$ independently, $y_i$ is arbitrary (i.e., an
outlier) with probability at most $\rho < 1/2$, and otherwise satisfies
$|y_i-p(\mathbf{x}_i)|\leq\sigma$. The goal is to output a polynomial
$\hat{p}$, of degree at most $d$ in each variable, within an
$\ell_\infty$-distance of at most $O(\sigma)$ from $p$.
Kane, Karmalkar, and Price [FOCS'17] solved this problem for $n=1$. We
generalize their results to the $n$-variate setting, showing an algorithm that
achieves a sample complexity of $O_n(d^n\log d)$, where the hidden constant
depends on $n$, if $\chi$ is the $n$-dimensional Chebyshev distribution. The
sample complexity is $O_n(d^{2n}\log d)$, if the samples are drawn from the
uniform distribution instead. The approximation error is guaranteed to be at
most $O(\sigma)$, and the run-time depends on $\log(1/\sigma)$. In the setting
where each $\mathbf{x}_i$ and $y_i$ are known up to $N$ bits of precision, the
run-time's dependence on $N$ is linear. We also show that our sample
complexities are optimal in terms of $d^n$. Furthermore, we show that it is
possible to have the run-time be independent of $1/\sigma$, at the cost of a
higher sample complexity.

鲍里斯全程鉴定弦扫，变身全员该事宜同异常低精度是样本。

异常值鲁棒的多元多项式回归

Outlier Robust Multivariate Polynomial Regression

Graph Neural Networks (GNNs) are gaining extensive attention for their
application in graph data. However, the black-box nature of GNNs prevents users
from understanding and trusting the models, thus hampering their applicability.
Whereas explaining GNNs remains a challenge, most existing methods fall into
approximation based and perturbation based approaches with suffer from
faithfulness problems and unnatural artifacts, respectively. To tackle these
problems, we propose DEGREE \degree to provide a faithful explanation for GNN
predictions. By decomposing the information generation and aggregation
mechanism of GNNs, DEGREE allows tracking the contributions of specific
components of the input graph to the final prediction. Based on this, we
further design a subgraph level interpretation algorithm to reveal complex
interactions between graph nodes that are overlooked by previous methods. The
efficiency of our algorithm can be further improved by utilizing GNN
characteristics. Finally, we conduct quantitative and qualitative experiments
on synthetic and real-world datasets to demonstrate the effectiveness of DEGREE
on node classification and graph classification tasks.

本文提出 DEGREE 方法，通过分解 GNN 信息生成和聚合机制，实现对输入图中特定组件对最终预测的贡献的跟踪，并设计了子图级别解释算法来揭示先前方法忽略的图节点之间的复杂交互，实现了节点分类任务上的有效性。

DEGREE: 基于分解的图神经网络解释方法

DEGREE: Decomposition Based Explanation For Graph Neural Networks

Event extraction requires high-quality expert human annotations, which are
usually expensive. Therefore, learning a data-efficient event extraction model
that can be trained with only a few labeled examples has become a crucial
challenge. In this paper, we focus on low-resource end-to-end event extraction
and propose DEGREE, a data-efficient model that formulates event extraction as
a conditional generation problem. Given a passage and a manually designed
prompt, DEGREE learns to summarize the events mentioned in the passage into a
natural sentence that follows a predefined pattern. The final event predictions
are then extracted from the generated sentence with a deterministic algorithm.
DEGREE has three advantages to learn well with less training data. First, our
designed prompts provide semantic guidance for DEGREE to leverage DEGREE and
thus better capture the event arguments. Moreover, DEGREE is capable of using
additional weakly-supervised information, such as the description of events
encoded in the prompts. Finally, DEGREE learns triggers and arguments jointly
in an end-to-end manner, which encourages the model to better utilize the
shared knowledge and dependencies among them. Our experimental results
demonstrate the strong performance of DEGREE for low-resource event extraction.

文章提出了一种数据有效性事件提取模型 DEGREE，通过联合学习触发器和参数，利用设计的提示语义指导模型，能够在少量有标注数据的情况下进行低资源端到端的事件提取，并从生成的自然语言摘要中提取最终事件预测结果。

DEGREE: 一种数据高效的基于生成的事件抽取模型

DEGREE: A Data-Efficient Generation-Based Event Extraction Model

Causality is typically treated an all-or-nothing concept; either A is a cause
of B or it is not. We extend the definition of causality introduced by Halpern
and Pearl [2001] to take into account the degree of responsibility of A for B.
For example, if someone wins an election 11--0, then each person who votes for
him is less responsible for the victory than if he had won 6--5. We then define
a notion of degree of blame, which takes into account an agent's epistemic
state. Roughly speaking, the degree of blame of A for B is the expected degree
of responsibility of A for B, taken over the epistemic state of an agent.

本文提出新的因果关系定义，以考虑 A 对 B 的责任程度与 A 的认知状态相关联的程度，并定义了一种责任程度的概念，用于衡量 A 对 B 的责任程度，从而得出预期的 A 对 B 的责任程度。