| Grant number: | 19/21858-0 |
| Support type: | Scholarships in Brazil - Doctorate |
| Effective date (Start): | January 01, 2021 |
| Effective date (End): | November 30, 2023 |
| Field of knowledge: | Engineering - Electrical Engineering - Telecommunications |
| Principal researcher: | Vitor Heloiz Nascimento |
| Grantee: | Carlos Augusto Prete Junior |
| Home Institution: | Escola Politécnica (EP). Universidade de São Paulo (USP). São Paulo , SP, Brazil |
Abstract Learning algorithms for nonlinear models have received much attention in the past years, especially due to the success of deep neural network architectures in several applications, as image and voice recognition. Neural networks and Volterra models are two different approaches to learn nonlinear functions, which often require a large number of parameters in practical problems. Decomposable Volterra Models (DVMs) is a recent approach that can significantly reduce the number of terms of Volterra models by constraining the Volterra kernels to rank-one tensors. Even though a DVM can only approximate a limited set of nonlinear functions exactly, its complexity is greatly reduced when compared to full Volterra models. Improving the representation capability of a single DVM by using higher rank Volterra kernels is not straightforward because the space spanned by Volterra models with rank r > 1 is usually not a closed set, and the boundary is a set with nonzero measure. Thus, the best rank-r approximation for higher rank Volterra models may not exist if r > 1. In this project, we propose to use series or parallel combinations of DVMs to approximate nonlinear functions whose Volterra kernels have rank higher than one, avoiding the problem mentioned above. We will develop not only low-complexity learning algorithms for combinations of DVMs, but also distributed and/or parallel versions of these algorithms. The developed algorithms will be compared with existing low-complexity Volterra models, neural networks and the full Volterra model. We will also test the new developed techniques to solve practical problems, in particular tropical disease spread prediction problems using data from the FAPESP/UK project CADDE. | |
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