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）
The existing approaches to intrinsic dimension estimation usually are not reliable when the data are nonlinearly embedded in the high dimensional space. In this work, we show that the explicit accounting to geometric properties of unknown support leads to the polynomial correction to the standard maximum likelihood estimate of intrinsic dimension for flat manifolds. The proposed algorithm (GeoMLE) realizes the correction by regression of standard MLEs based on distances to nearest neighbors for different sizes of neighborhoods. Moreover, the proposed approach also efficiently handles the case of nonuniform sampling of the manifold. We perform numerous experiments on different synthetic and real-world datasets. The results show that our algorithm achieves state-of-the-art performance, while also being computationally efficient and robust to noise in the data.
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）
Dependency-aware Maximum Likelihood Estimation for Active Learning
Department of Electrical and Computer Engineering（电气与计算机工程系）；Northeastern University（东北大学）；Department of Computer Science（计算机科学系）；University of Massachusetts Boston（马萨诸塞大学波士顿分校）
