Analyzing large volumes of high-dimensional data is an issue of fundamental importance in data science, molecular simulations and beyond. Several approaches work on the assumption that the important content of a dataset belongs to a manifold whose Intrinsic Dimension (ID) is much lower than the crude large number of coordinates. Such manifold is generally twisted and curved, in addition points on it will be non-uniformly distributed: two factors that make the identification of the ID and its exploitation really hard. Here we propose a new ID estimator using only the distance of the first and the second nearest neighbor of each point in the sample. This extreme minimality enables us to reduce the effects of curvature, of density variation, and the resulting computational cost. The ID estimator is theoretically exact in uniformly distributed datasets, and provides consistent measures in general. When used in combination with block analysis, it allows discriminating the relevant dimensions as a function of the block size. This allows estimating the ID even when the data lie on a manifold perturbed by a high-dimensional noise, a situation often encountered in real world data sets. We demonstrate the usefulness of the approach on molecular simulations and image analysis.
Joint Estimation of Edge Probabilities for Multi-layer Networks via Neighborhood Smoothing
Institute for Financial Studies, Shandong University（山东大学金融研究院）；Southern University of Science and Technology（南方科技大学）；School of Statistics and Data Science, Zhejiang Gongshang University（浙江工商大学统计与数据科学学院）
Estimating Bicycle Route Attractivity from Image Data
Czech Technical University in Prague（捷克技术大学（布拉格））
本硕士论文的重点是卷积神经网络模型在自行车吸引力评分道路标记任务中的实际应用。我们首先将真实世界的位置抽象为部分注释数据集中的节点和得分边。我们通过Google街景服务中的照片数据和Open Street Map数据库中的其他邻里信息增强了每个边缘的可用信息。我们在这个增强的数据集上教授一个模型，并在ImageNet大规模视觉识别竞赛中进行实验。我们尝试不同的数据集增强技术以及各种模型架构，以提高道路评分。我们还利用迁移学习将ImageNet数据集丰富的任务中的特征用于图像数量较少的任务中，以防止模型过拟合。
Subspace Determination through Local Intrinsic Dimensional Decomposition: Theory and Experimentation
Gran Sasso Science Institute（格兰萨索科学研究所）；Ecole Polytechnique de Montréal（蒙特利尔理工学院）；National Institute of Informatics（国立信息学研究所）；Saarland University（萨尔大学）；University of Southern Denmark（南丹麦大学）
Geometry-Aware Maximum Likelihood Estimation of Intrinsic Dimension
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究所）；Higher School of Economics（高等经济学院）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Institute for Information Transmission Problems（信息传输问题研究所）
LIDL: Local Intrinsic Dimension Estimation Using Approximate Likelihood
University of Warsaw（华沙大学）；Polish National Institute for Machine Learning（波兰国家机器学习研究所）；Applica；Jagiellonian University（雅盖隆大学）；University of Oxford（牛津大学）
