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Found 9 papers, 2 papers with code
A New Perspective On Denoising Based On Optimal Transport
We then prove that, under appropriate identifiability assumptions on the model, our OT-based denoiser can be recovered solely from information of the marginal distribution of $Z$ and the posterior mean of the model, after solving a linear relaxation problem over a suitable space of couplings that is reminiscent of a standard multimarginal OT (MOT) problem.
A Mean Field Approach to Empirical Bayes Estimation in High-dimensional Linear Regression
We study empirical Bayes estimation in high-dimensional linear regression.
Permuted and Unlinked Monotone Regression in $\mathbb{R}^d$: an approach based on mixture modeling and optimal transport
We study permutation recovery in the permuted regression setting and develop a computationally efficient and easy-to-use algorithm for denoising based on the Kiefer-Wolfowitz [Ann.
Rates of Estimation of Optimal Transport Maps using Plug-in Estimators via Barycentric Projections
We illustrate the usefulness of this stability estimate by first providing rates of convergence for the natural discrete-discrete and semi-discrete estimators of optimal transport maps.
Convex Regression in Multidimensions: Suboptimality of Least Squares Estimators
The least squares estimator (LSE) is shown to be suboptimal in squared error loss in the usual nonparametric regression model with Gaussian errors for $d \geq 5$ for each of the following families of functions: (i) convex functions supported on a polytope (in fixed design), (ii) bounded convex functions supported on a polytope (in random design), and (iii) convex Lipschitz functions supported on any convex domain (in random design).
Multivariate Ranks and Quantiles using Optimal Transport: Consistency, Rates, and Nonparametric Testing
Under mild structural assumptions, we provide global and local rates of convergence of the empirical quantile and rank maps.
Statistics Theory Probability Statistics Theory 62G30, 62G20, 60F15, 35J96
Multivariate extensions of isotonic regression and total variation denoising via entire monotonicity and Hardy-Krause variation
We show that the finite sample risk of these LSEs is always bounded from above by $n^{-2/3}$ modulo logarithmic factors depending on $d$; thus these nonparametric LSEs avoid the curse of dimensionality to some extent.
Two-component Mixture Model in the Presence of Covariates
We propose a tuning parameter-free nonparametric maximum likelihood approach, implementable via the EM algorithm, to estimate the unknown parameters.
Methodology
Nonparametric Shape-restricted Regression
We consider the problem of nonparametric regression under shape constraints.
