英文标题：
《A Hilbert Space of Stationary Ergodic Processes》
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作者：
Ishanu Chattopadhyay
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最新提交年份：
2018
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英文摘要：
  Identifying meaningful signal buried in noise is a problem of interest arising in diverse scenarios of data-driven modeling. We present here a theoretical framework for exploiting intrinsic geometry in data that resists noise corruption, and might be identifiable under severe obfuscation. Our approach is based on uncovering a valid complete inner product on the space of ergodic stationary finite valued processes, providing the latter with the structure of a Hilbert space on the real field. This rigorous construction, based on non-standard generalizations of the notions of sum and scalar multiplication of finite dimensional probability vectors, allows us to meaningfully talk about \"angles\" between data streams and data sources, and, make precise the notion of orthogonal stochastic processes. In particular, the relative angles appear to be preserved, and identifiable, under severe noise, and will be developed in future as the underlying principle for robust classification, clustering and unsupervised featurization algorithms.
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中文摘要：
在数据驱动建模的不同场景中，识别隐藏在噪声中的有意义信号是一个令人感兴趣的问题。我们在这里提出了一个理论框架，用于利用数据中的固有几何结构来抵抗噪声破坏，并且在严重混淆的情况下可以识别。我们的方法是基于在遍历平稳有限值过程空间上发现一个有效的完全内积，为后者提供实数域上希尔伯特空间的结构。这种严格的构造基于有限维概率向量的和和和和标量乘概念的非标准推广，使我们能够有意义地讨论数据流和数据源之间的“角度”，并使正交随机过程的概念更加精确。特别是，在严重噪声下，相对角度似乎可以被保留和识别，并将在未来发展为鲁棒分类、聚类和无监督特征化算法的基本原则。
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分类信息：

一级分类：Statistics        统计学
二级分类：Machine Learning        机器学习
分类描述：Covers machine learning papers (supervised, unsupervised, semi-supervised learning, graphical models, reinforcement learning, bandits, high dimensional inference, etc.) with a statistical or theoretical grounding
覆盖机器学习论文（监督，无监督，半监督学习，图形模型，强化学习，强盗，高维推理等）与统计或理论基础
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一级分类：Computer Science        计算机科学
二级分类：Discrete Mathematics        离散数学
分类描述：Covers combinatorics, graph theory, applications of probability. Roughly includes material in ACM Subject Classes G.2 and G.3.
涵盖组合学，图论，概率论的应用。大致包括ACM学科课程G.2和G.3中的材料。
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一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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