BIGDATA: Mid-Scale: DA: Distribution-based machine learning for high dimensional datasets

许多应用程序要求对“分布”数据集进行表示和分析，其中每个数据点都是来自高维分布的样本集合（与典型的向量值随机变量的估值相反）。在此设置中，每个数据点都可以通过分布的集合来建模，每个分布对应一个测量属性。分布式数据的一个具体例子出现在大脑连接映射的背景下。人类大脑包含大约一千亿个神经元和几百万亿个物理连接。神经成像方法，如扩散光谱成像，试图通过创建水沿神经纤维束扩散的三维概率分布，即方向分布函数，来可视化神经通路的潜在解剖结构。该项目旨在开发新的统计和算法方法来自然概括一类标准机器学习问题（其中多维向量值数据点被分布所取代），包括测量分布数据点之间的距离和内积的技术，估计熵的变量，互信息，条件互信息，聚类分布数据，构造分布数据的低维嵌入，并从分布数据中学习分类器和函数逼近器。结果方法将在大型扩散扫描成像数据集上进行评估（其中每个患者的数据点由500,000个分布组成）。该项目产生的用于描述和预测分布数据建模的新型机器学习方法有望使其他科学领域受益，其中数据点可以通过分布集自然地建模，这是物理学，心理学，经济学，流行病学，医学和社会网络分析中的常见情况。CMU将获得新的分布式数据集，以增加南洋理工大学提供的数据，这可能使其他研究小组能够参与从分布式数据进行大数据分析的研究。开源软件的发布、视频教程、研究生的研究培训都有助于这个项目产生更广泛的影响。有关该项目的更多信息可以在http://www.autonlab.org/autonweb/20928.html上找到。

Many applications call for representation and analysis of 'distributional' data sets where each data point is a collection of samples from a high dimensional distribution (as opposed to valuations of a typically vector valued random variable). In this setting, each data point can be modeled by a collection of distributions, one for each measured attribute. A concrete example of distributional data arises in the context of brain connectivity mapping. The human brain contains around a hundred billion neurons with several hundred trillion physical connections. Neuroimaging approaches, like Diffusion Spectrum Imaging attempt to visualize the underlying anatomical architecture of neural pathways by creating 3D probability distributions of water diffusion along nerve fiber bundles, called orientation distribution functions. The project aims to develop new statistical and algorithmic approaches to natural generalizations of a class of standard machine learning problems (where multi-dimensional vector valued data points are replaced by distributions), including techniques for measuring distances and inner products between distributional data points, estimating variants of entropy, mutual information, conditional mutual information, clustering distributional data, constructing low-dimensional embeddings of distributional data, and learning classifiers and function approximators from distributional data. The resulting methods will be evaluated on large diffusion scan imaging data sets (where the data point for each patient consists of 500,000 distributions). The novel machine learning approaches for descriptive and predictive modeling of distributional data resulting from this project are expected to benefit other scientific fields where data points can be naturally modeled by sets of distributions, which is a common situation in physics, psychology, economics, epidemiology, medicine, and social network-analysis. New distributional data set to be obtained at CMU to augment the data available from NTU are likely to allow other research groups to engage in research on big data analytics from distributional data. Release of open source software, video tutorials, research-training of graduate students contribute to the broader impacts of the project. Additional information about the project can be found at: http://www.autonlab.org/autonweb/20928.html.