TY - GEN

T1 - Manifold learning regression with non-stationary kernels

AU - Kuleshov, Alexander

AU - Bernstein, Alexander

AU - Burnaev, Evgeny

PY - 2018

Y1 - 2018

N2 - Nonlinear multi-output regression problem is to construct a predictive function which estimates an unknown smooth mapping from q-dimensional inputs to m-dimensional outputs based on a training data set consisting of given “input-output” pairs. In order to solve this problem, regression models based on stationary kernels are often used. However, such approaches are not efficient for functions with strongly varying gradients. There exist some attempts to introduce non-stationary kernels to account for possible non-regularities, although even the most efficient one called Manifold Learning Regression (MLR), which estimates the unknown function as well its Jacobian matrix, is too computationally expensive. The main problem is that the MLR is based on a computationally intensive manifold learning technique. In this paper we propose a modified version of the MLR with significantly less computational complexity while preserving its accuracy.

AB - Nonlinear multi-output regression problem is to construct a predictive function which estimates an unknown smooth mapping from q-dimensional inputs to m-dimensional outputs based on a training data set consisting of given “input-output” pairs. In order to solve this problem, regression models based on stationary kernels are often used. However, such approaches are not efficient for functions with strongly varying gradients. There exist some attempts to introduce non-stationary kernels to account for possible non-regularities, although even the most efficient one called Manifold Learning Regression (MLR), which estimates the unknown function as well its Jacobian matrix, is too computationally expensive. The main problem is that the MLR is based on a computationally intensive manifold learning technique. In this paper we propose a modified version of the MLR with significantly less computational complexity while preserving its accuracy.

KW - Manifold learning regression

KW - Non-stationary kernel

KW - Nonlinear multi-output regression

UR - http://www.scopus.com/inward/record.url?scp=85053601953&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-99978-4_12

DO - 10.1007/978-3-319-99978-4_12

M3 - Conference contribution

AN - SCOPUS:85053601953

SN - 9783319999777

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 152

EP - 164

BT - Artificial Neural Networks in Pattern Recognition - 8th IAPR TC3 Workshop, ANNPR 2018, Proceedings

A2 - Pancioni, Luca

A2 - Trentin, Edmondo

A2 - Schwenker, Friedhelm

PB - Springer Verlag

T2 - 8th IAPR TC3 workshop on Artificial Neural Networks for Pattern Recognition, ANNPR 2018

Y2 - 19 September 2018 through 21 September 2018

ER -