Math @ Duke

Publications [#322540] of David B. Dunson
search arxiv.org.Papers Published
 Yang, Y; Dunson, DB, Bayesian manifold regression,
The Annals of Statistics, vol. 44 no. 2
(April, 2016),
pp. 876905, Institute of Mathematical Statistics [doi]
(last updated on 2019/05/25)
Abstract: © Institute of Mathematical Statistics, 2016. There is increasing interest in the problem of nonparametric regression with highdimensional predictors. When the number of predictors D is large, one encounters a daunting problem in attempting to estimate aDdimensional surface based on limited data. Fortunately, in many applications, the support of the data is concentrated on a ddimensional subspace with d ≤ D. Manifold learning attempts to estimate this subspace. Our focus is on developing computationally tractable and theoretically supported Bayesian nonparametric regression methods in this context. When the subspace corresponds to a locallyEuclidean compact Riemannian manifold, we show that a Gaussian process regression approach can be applied that leads to the minimax optimal adaptive rate in estimating the regression function under some conditions. The proposed model bypasses the need to estimate the manifold, and can be implemented using standard algorithms for posterior computation in Gaussian processes. Finite sample performance is illustrated in a data analysis example.


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