Machine learning via learning spaces, from theory to practice: how the lack of data may be mitigated by high computational power

• Grant number: 22/06211-2
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: August 01, 2022
• End date: January 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Computer Science
• Principal Investigator: Junior Barrera
• Grantee: Diego Ribeiro Marcondes
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 14/50937-1 - INCT 2014: on the Internet of the Future, AP.TEM
• Associated scholarship(s): 23/00256-7 - Prior information in neural networks, BE.EP.PD

Abstract

The classical framework of Machine Learning is composed by a hypotheses space $\mathcal{H}$, a sample $\mathcal{D}_{N}$ and an algorithm $\mathbb{A}$, which processes $\mathcal{D}_{N}$ and returns $\hat{h}(\mathbb{A}) = \mathbb{A}(\mathcal{H},\mathcal{D}_{N})$ in $\mathcal{H}$, seeking to approximate a target hypothesis $h^{\star} \in \mathcal{H}$. In a previous study, it was proposed a new framework, in which the algorithm $\mathbb{A}$ is hierarchical, optimizing first an error measure in a structured collection of candidate hypotheses spaces $\mathbb{L}(\mathcal{H}) \in \mathcal{P}(\mathcal{H})$, called Learning Space, returning a $\hat{\mathcal{M}} \in \mathbb{L}(\mathcal{H})$, and then optimizing an error measure in $\hat{\mathcal{M}}$ to obtain $\hat{h}_{\hat{\mathcal{M}}}(\mathbb{A}) \in \hat{\mathcal{M}}$ seeking to approximate $h^{\star}$. It was proved the existence of instances in which, with a same sample $\mathcal{D}_{N}$, the error $L(\hat{h}_{\hat{\mathcal{M}}}(\mathbb{A}))$ of the hypothesis learned by the approach via Learning Space is lesser than the error $L(\hat{h}(\mathbb{A}))$. The new approach requires a combinatorial search in $\mathbb{L}(\mathcal{H})$ to compute $\hat{\mathcal{M}}$ and, although there are conditions which imply the existence of a non-exhaustive U-curve algorithm, high computational power is necessary. In this context, emerges a new paradigm, that the lack of data may be mitigated by high computational power, since, with a same sample, it is possible to better learn at the cost of performing a search of $\mathbb{L}(\mathcal{H})$. This project aims to depart from the theory about Learning Spaces in direction to the practice, converting theoretical results in methods to solve practical problems, in special those related to remote sensing in smart cities, under the paradigm of mitigating the lack of data with high computational power. To this end, it will be treated problems about learning mathematical morphology operators, developing U-curve algorithms to non-Boolean lattices, and selecting architectures of Neural Networks (Neural Architecture Search). (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

MARCONDES, DIEGO; BARRERA, JUNIOR. The Lattice Overparametrization Paradigm for the Machine Learning of Lattice Operators. DISCRETE GEOMETRY AND MATHEMATICAL MORPHOLOGY, DGMM 2024, v. 14605, p. 13-pg., 2024-01-01. (22/06211-2, 23/00256-7, 20/06950-4)

MARCONDES, DIEGO; SIMONIS, ADILSON; BARRERA, JUNIOR. Back to basics to open the black box. NATURE MACHINE INTELLIGENCE, v. 6, n. 5, p. 4-pg., 2024-05-17. (22/06211-2, 23/00256-7, 20/06950-4, 14/50937-1)

MARCONDES, DIEGO; FELDMAN, MARIANA; BARRERA, JUNIOR. An Algorithm to Train Unrestricted Sequential Discrete Morphological Neural Networks. DISCRETE GEOMETRY AND MATHEMATICAL MORPHOLOGY, DGMM 2024, v. 14605, p. 14-pg., 2024-01-01. (22/06211-2, 23/00256-7, 20/06950-4, 14/50937-1)