Training a Radial Basis Function Network Under Transformed Probability Measure

Research output: Contribution to journalArticlepeer-review


This letter deals with robust estimation of the output layer weights in a radial basis function network (RBFN) with predetermined hidden layer parameters. Specifically, we presume a RBFN regression model interfered by non-Gaussian impulsive noise. Under this framework, a new robust extension of the least-squares-estimator (LSE) is introduced. This estimator, called measure-transformed LSE (MT-LSE), operates by applying a transform to the joint probability measure associated with reshaped versions of the input-target training data pairs. The considered transform is generated by a non-negative function, called MT-function, that weights the data points. We show that proper selection of the MT-function substantially improves the estimation accuracy in the presence of impulsive noise, while maintaining the implementation simplicity of the standard LSE. The performance advantage of the MT-LSE, comparing to the LSE and other robust alternatives, is illustrated in a simulation study focusing on time-series prediction.

Original languageAmerican English
Pages (from-to)1567-1571
Number of pages5
JournalIEEE Signal Processing Letters
StatePublished - 1 Jan 2023


  • Estimation theory
  • probability measure-transform
  • radial basis function network
  • robust statistics

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Applied Mathematics
  • Electrical and Electronic Engineering


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