本文研究了主题模型中高维，离散，可能稀疏的混合模型的估计。数据包括在$ n $独立文档中观察到的$ p $单词的多项式计数。在主题模型中，$ p \ times n $预期的单词频率矩阵被认为被分解为$ p \ times k $ word-top-topic矩阵$ a $ a $和a $ k \ times n $ topic-document $ t $ t $ 。由于两个矩阵的列代表属于概率简单的条件概率，因此$ a $的列被视为$ p $ - 二维混合组件，这些混合组件是所有文档共有的，而$ t $的列被视为$ k $二维的混合物特定文档并允许稀疏的权重。主要的兴趣是提供鲜明的，有限的样本，$ \ ell_1 $ norm收敛速率，用于混合物重量$ t $的估计量，当$ a $是已知或未知时。对于已知的$ a $，我们建议MLE估计为$ t $。我们对MLE的非标准分析不仅建立了其$ \ ell_1 $收敛率，而且揭示了一个非凡的属性：MLE，没有额外的正则化，可能完全稀疏，并且包含$ t $的真实零模式。我们进一步表明，MLE既是最佳的最佳选择，又适应了一大批稀疏主题分布中未知的稀疏性。当$ a $未知时，我们通过优化与$ a $ a $的插件的可能性功能来估计$ t $。对于任何满足与$ a $ $ a $的详细条件的估计器$ \ hat {a} $，显示出$ t $的估计器可保留为MLE建立的属性。环境尺寸$ k $和$ p $可以随着样本量而增长。我们的应用是对文档生成分布之间1-Wasserstein距离的估计。我们建议，估计和分析两个概率文档表示之间的新1-Wasserstein距离。

In this book chapter, we briefly describe the main components that constitute the gradient descent method and its accelerated and stochastic variants. We aim at explaining these components from a mathematical point of view, including theoretical and practical aspects, but at an elementary level. We will focus on basic variants of the gradient descent method and then extend our view to recent variants, especially variance-reduced stochastic gradient schemes (SGD). Our approach relies on revealing the structures presented inside the problem and the assumptions imposed on the objective function. Our convergence analysis unifies several known results and relies on a general, but elementary recursive expression. We have illustrated this analysis on several common schemes.

Classical differential private DP-SGD implements individual clipping with random subsampling, which forces a mini-batch SGD approach. We provide a general differential private algorithmic framework that goes beyond DP-SGD and allows any possible first order optimizers (e.g., classical SGD and momentum based SGD approaches) in combination with batch clipping, which clips an aggregate of computed gradients rather than summing clipped gradients (as is done in individual clipping). The framework also admits sampling techniques beyond random subsampling such as shuffling. Our DP analysis follows the $f$-DP approach and introduces a new proof technique which allows us to also analyse group privacy. In particular, for $E$ epochs work and groups of size $g$, we show a $\sqrt{g E}$ DP dependency for batch clipping with shuffling. This is much better than the previously anticipated linear dependency in $g$ and is much better than the previously expected square root dependency on the total number of rounds within $E$ epochs which is generally much more than $\sqrt{E}$.

背景：在信息提取和自然语言处理域中，可访问的数据集对于复制和比较结果至关重要。公开可用的实施和工具可以用作基准，并促进更复杂的应用程序的开发。但是，在临床文本处理的背景下，可访问数据集的数量很少 - 现有工具的数量也很少。主要原因之一是数据的敏感性。对于非英语语言，这个问题更为明显。方法：为了解决这种情况，我们介绍了一个工作台：德国临床文本处理模型的集合。这些模型接受了德国肾脏病报告的识别语料库的培训。结果：提出的模型为内域数据提供了有希望的结果。此外，我们表明我们的模型也可以成功应用于德语的其他生物医学文本。我们的工作台公开可用，因此可以开箱即用，或转移到相关问题上。

The potential for complex systems to exhibit tipping points in which an equilibrium state undergoes a sudden and often irreversible shift is well established, but prediction of these events using standard forecast modeling techniques is quite difficult. This has led to the development of an alternative suite of methods that seek to identify signatures of critical phenomena in data, which are expected to occur in advance of many classes of dynamical bifurcation. Crucially, the manifestations of these critical phenomena are generic across a variety of systems, meaning that data-intensive deep learning methods can be trained on (abundant) synthetic data and plausibly prove effective when transferred to (more limited) empirical data sets. This paper provides a proof of concept for this approach as applied to lattice phase transitions: a deep neural network trained exclusively on 2D Ising model phase transitions is tested on a number of real and simulated climate systems with considerable success. Its accuracy frequently surpasses that of conventional statistical indicators, with performance shown to be consistently improved by the inclusion of spatial indicators. Tools such as this may offer valuable insight into climate tipping events, as remote sensing measurements provide increasingly abundant data on complex geospatially-resolved Earth systems.

人类在感知幻觉纲要方面非常出色。我们随时能够在提供包含连接外观的破碎碎片的图像时完成轮廓，形状，场景，甚至不均匀的对象。在视觉科学中，这种能力在很大程度上通过感知分组解释：人类视觉中的基础集进程，描述了如何分组分离的元素。在本文中，我们重新审视了一种称为随机完成领域（SCFS）的算法，该算法机械化一套这样的工艺 - 良好的连续性，闭合和接近 - 通过轮廓完成。本文实现了SCF算法的现代化模型，并在图像编辑框架中使用它提出了新的方法来完成碎片的轮廓。我们展示了SCF算法如何合理地模仿人类感知。我们使用SCF完成的轮廓作为染色的指南，并表明我们的指南提高了最先进的模型的性能。此外，我们表明SCF有助于在高噪声环境中找到边缘。总体而言，我们所描述的算法类似于人类视觉系统中的一个重要机制，并提供了一种新颖的计算机视觉模型可以从中受益的新框架。

Array programming provides a powerful, compact, expressive syntax for accessing, manipulating, and operating on data in vectors, matrices, and higher-dimensional arrays [1]. NumPy is the primary array programming library for the Python language [2,3,4,5]. It plays an essential role in research analysis pipelines in fields as diverse as physics, chemistry, astronomy, geoscience, biology, psychology, material science, engineering, finance, and economics. For example, in astronomy, NumPy was an important part of the software stack used in the discovery of gravitational waves [6] and the first imaging of a black hole [7].Here we show how a few fundamental array concepts lead to a simple and powerful programming paradigm for organizing, exploring, and analyzing scientific data. NumPy is the foundation upon which the entire scientific Python universe is constructed. It is so pervasive that several projects, targeting audiences with specialized needs, have developed their own NumPy-like interfaces and array objects. Because of its central position in the ecosystem, NumPy increasingly plays the role of an interoperability layer between these new array computation libraries.