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Reid, Nancy (Ed.)Manifold learning (ML), also known as nonlinear dimension reduction, is a set of methods to find the low-dimensional structure of data. Dimension reduction for large, high-dimensional data is not merely a way to reduce the data; the new representations and descriptors obtained by ML reveal the geometric shape of high-dimensional point clouds and allow one to visualize, denoise, and interpret them. This review presents the underlying principles of ML, its representative methods, and their statistical foundations, all from a practicing statistician's perspective. It describes the trade-offs and what theory tells us about the parameter and algorithmic choices we make in order to obtain reliable conclusions. Expected final online publication date for the Annual Review of Statistics and Its Application, Volume 11 is March 2024. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.more » « less
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Zhang, Susu; Liu, Jingchen; Ying, Zhiliang (, Annual review of statistics and its application)Reid, Nancy (Ed.)Diagnostic classification tests are designed to assess examinees’ discrete mastery status on a set of skills or attributes. Such tests have gained increas- ing attention in educational and psychological measurement. We review diagnostic classification models and their applications to testing and learning, discuss their statistical and machine learning connections and related challenges, and introduce some contemporary and future extensions.more » « less
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