Titulo Estágio
Structure Identification of Networked Dynamical Systems under Partial Observability via Machine Learning Techniques: Application to Brain Functional Connectivity
Áreas de especialidade
Sistemas Inteligentes
Sistemas de Informação
Local do Estágio
DEI-FCTUC
Enquadramento
In this internship, we explore the paradigm of structure identification of large-scale Networked Dynamical Systems via Machine Learning Techniques. Identifying the underlying network of interactions among agents/nodes in a complex Networked Dynamical System from its time-series (reflecting the state-evolution of the system over time) is a research field of critical importance as, in general, the connectivity pattern plays an important role in the long-term evolution of these systems, while being a latent object concealed in the underlying time-series. Examples are: i) [Pandemics] The underlying profile of interactions among communities critically impacts the overall lifetime of a strain of virus; ii) [Brain Connectivity] Recent evidence shows that the structure of the underlying Functional Connectivity matrix conveys relevant signatures about cognitive disorders; iii) [Social Networks.] The emergence of inconsistent beliefs or fake news is fostered by certain connectivity patterns among the involved communities.
Recently, the advisors (jointly with other collaborators, including a current master student) of this proposal have developed a machine learning method for consistent causal inference over linear networked dynamical systems and that outperforms state-of-the-art counterparts. The method consists in devising certain feature-vectors based on the observed time-series (reflecting the state-evolution of the observed nodes). We proved that these special features were consistently linearly separable, i.e., there exists a hyperplane (or an affine map) that separates the features associated with connected pairs from the features associated with disconnected pairs – thus, conducive to consistent structure identification provided that we have the proper separating hyperplane. By resorting to nonlinear classifiers, we obtained a causal inference method that outperforms other state-of-the-art algorithms in terms of sample-complexity (i.e., reaching a certain level of accuracy with a minimal number of samples).
We are on the fringe of the problem and there is much ado to continue with the efforts. Are there other features that exhibit a better separability property yielding a more efficient causal inference method for linear systems? What happens when the underlying dynamical law is not linear? Can we devise proper features exhibiting a separability pattern that can be learned by neural networks? What happens under coloured noise? Missing samples? We plan to apply the methods and tools developed for causal inference to the ‘Functional connectivity’ problem in the Brain, i.e., in characterizing as faithfully as possible the functional connectivity in the Brain.
Objetivo
The goal of this internship is to continue the study of structure identification via machine learning techniques:
1) [Linear Networked Dynamical Systems]. Given the time-series of the nodes in the networked dynamical system, we will design other feature-vectors that exhibit better separability properties under white and colored noise (two distinct important paradigms). We attempt to devise features that are robust to missing samples, as well.
2) [Nonlinear Networked Dynamical Systems]. We attempt to devise features that exhibit a separability pattern that can be learned by nonlinear classifiers (e.g., neural networks).
3) [Functional Connectivity]. We apply the machine learning methods developed based on the design of the features and their good separability properties to the problem of functional connectivity (identifying the connectivity pattern among distinct regions of the Brain).
For the validation in point 3), we resort to data available online across distinct platforms, e.g.,
http://preprocessed-connectomes-project.org/abide/
CRCNS.org
https://search.kg.ebrains.eu/ (Brain Project)
https://www.fil.ion.ucl.ac.uk/spm/data/
https://www.oasis-brains.org/
In this internship, the student will be exposed to four hot topics/fields of current research: Artificial Intelligence, Deep learning, Brain Functional Connectivity (Neuroscience), Model Identification (especially, causal inference).
Plano de Trabalhos - Semestre 1
[Some tasks might overlap; M=Month]
T1 (M1-M2): Knowledge transfer and State of the art analysis: Study the paradigm of structure identification of networked dynamical systems.
T2 (M3): Study machine learning techniques applied to the problem of structure identification.
T3 (M4-M5): Devise feature-vectors based on the observed time-series for network identification (or causal inference).
T4 (M6): Writing the Intermediate Report.
Plano de Trabalhos - Semestre 2
[Some tasks might overlap; M=Month]
T5 (M7-M8): Implementation of the proposed methods for network structure identification (via deep learning tools) and test them across synthetic/real datasets for linear/nonlinear systems.
T6 (M9-M10): Data mining and application of the methods on the functional connectivity problem.
T7 (M11): Writing the thesis.
Condições
Note: there is a possibility of having a 6-month scholarship.
Type of scholarship: Bolsa de Investigação para Licenciado.
Value of the scholarship: 752,38€.
Observações
Please, contact the advisors for any questions or clarifications needed.
Advisors: Augusto Santos (augustosantos@dei.uc.pt), Paulo Gil (pgil@dei.uc.pt), Jorge Henriques (jh@dei.uc.pt).
Orientador
Augusto Santos / Paulo Gil / Jorge Henriques
augustosantos@dei.uc.pt 📩