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Related Experiment Video

Updated: Jun 16, 2026

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

Lattice point sets for deterministic learning and approximate optimization problems.

Cristiano Cervellera¹

¹Istituto di Studi sui Sistemi Intelligenti per l'Automazione,Consiglio Nazionale delle Ricerche, Genova, Italy. cervellera@ge.issia.cnr.it

IEEE Transactions on Neural Networks

|February 23, 2010

Summary

Lattice point sets (LPSs) guarantee convergence for empirical risk minimization (ERM) in machine learning. Using LPSs as training data can achieve superlinear convergence rates for function estimation and optimization problems.

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Last Updated: Jun 16, 2026

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

Area of Science:

Machine Learning
Optimization Theory
Numerical Analysis

Background:

Empirical Risk Minimization (ERM) is a standard principle in statistical learning.
The choice of sampling points significantly impacts the convergence of learning algorithms.
General learning problems include function estimation and dynamic optimization.

Purpose of the Study:

To investigate the efficacy of lattice point sets (LPSs) as training data for ERM.
To analyze the convergence properties of ERM when using LPSs.
To explore potential improvements in convergence rates for learning procedures.

Main Methods:

Theoretical analysis of ERM convergence with LPSs.
Mathematical proofs demonstrating convergence guarantees.
Exploration of convergence rates under specific function regularity conditions.
Preliminary simulation studies to validate theoretical findings.

Main Results:

Convergence of the ERM principle is guaranteed when LPSs are used as training sets.
Superlinear convergence rates are achievable with LPSs under certain regularity hypotheses.
LPSs offer a structured approach to sampling input spaces for learning.

Conclusions:

Lattice point sets provide a robust method for enhancing the convergence of empirical risk minimization.
The findings suggest LPSs are a valuable tool for improving the efficiency of machine learning algorithms.
Further research can explore the application of LPSs in more complex learning scenarios.