Distance Shrinkage and Euclidean Embedding via Regularized Kernel Estimation
Autor: | Grace Wahba, Luwan Zhang, Ming Yuan |
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Jazyk: | angličtina |
Rok vydání: | 2014 |
Předmět: |
FOS: Computer and information sciences
Statistics and Probability Mathematical optimization Kernel density estimation Machine Learning (stat.ML) Mathematics - Statistics Theory Statistics Theory (math.ST) 010103 numerical & computational mathematics Euclidean distance matrix 01 natural sciences Methodology (stat.ME) 010104 statistics & probability Statistics - Machine Learning FOS: Mathematics Multidimensional scaling 0101 mathematics Statistics - Methodology Mathematics Estimator 3. Good health Euclidean distance Distance matrix Embedding Pairwise comparison Statistics Probability and Uncertainty Algorithm |
Popis: | Summary Although recovering a Euclidean distance matrix from noisy observations is a common problem in practice, how well this could be done remains largely unknown. To fill in this void, we study a simple distance matrix estimate based on the so-called regularized kernel estimate. We show that such an estimate can be characterized as simply applying a constant amount of shrinkage to all observed pairwise distances. This fact allows us to establish risk bounds for the estimate, implying that the true distances can be estimated consistently in an average sense as the number of objects increases. In addition, such a characterization suggests an efficient algorithm to compute the distance matrix estimator, as an alternative to the usual second-order cone programming which is known not to scale well for large problems. Numerical experiments and an application in visualizing the diversity of Vpu protein sequences from a recent study of human immunodeficiency virus type 1 further demonstrate the practical merits of the method proposed. |
Databáze: | OpenAIRE |
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