Nonparametric Functional Approximation with Delaunay Triangulation

by   Yehong Liu, et al.
The University of Hong Kong

We propose a differentiable nonparametric algorithm, the Delaunay triangulation learner (DTL), to solve the functional approximation problem on the basis of a p-dimensional feature space. By conducting the Delaunay triangulation algorithm on the data points, the DTL partitions the feature space into a series of p-dimensional simplices in a geometrically optimal way, and fits a linear model within each simplex. We study its theoretical properties by exploring the geometric properties of the Delaunay triangulation, and compare its performance with other statistical learners in numerical studies.


Optimal prediction for kernel-based semi-functional linear regression

In this paper, we establish minimax optimal rates of convergence for pre...

Nonparametric Iterative Machine Teaching

In this paper, we consider the problem of Iterative Machine Teaching (IM...

Bayesian Nonparametric Space Partitions: A Survey

Bayesian nonparametric space partition (BNSP) models provide a variety o...

Active Linear Regression

We consider the problem of active linear regression where a decision mak...

ParK: Sound and Efficient Kernel Ridge Regression by Feature Space Partitions

We introduce ParK, a new large-scale solver for kernel ridge regression....

Hilbert Space Embeddings of POMDPs

A nonparametric approach for policy learning for POMDPs is proposed. The...

Learning Extremal Representations with Deep Archetypal Analysis

Archetypes are typical population representatives in an extremal sense, ...

Please sign up or login with your details

Forgot password? Click here to reset