Conformal prediction for interacting neuronal systems with variable-length memory

• Grant number: 25/13627-9
• Support Opportunities: Scholarships abroad - Research
• Start date: August 01, 2026
• End date: July 31, 2027
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Applied Probability and Statistics
• Principal Investigator: Ricardo Felipe Ferreira
• Grantee: Ricardo Felipe Ferreira
• Host Investigator: Gabor Lugosi
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Institution abroad: Universitat Pompeu Fabra (UPF), Spain

Abstract

Statistical learning refers to the vast set of tools whose main objective is to learn patterns from data. These tools have excelled in creating accurate predictions across various domains. However, most models and/or algorithms generate either point predictions that do not incorporate any notion of uncertainty, or prediction regions without finite-sample statistical guarantees. In neuroscience, the uncertainty associated with spike train predictions has largely been overlooked in the literature. This work aims to fill this gap by quantifying such uncertainty using conformal prediction. Conformal prediction has been a popular method for uncertainty quantification because it is distribution-free, model-agnostic, and theoretically sound. For forecasting problems in supervised learning, most conformal prediction methods focus on the assumption of exchangeability (e.g., i.i.d. data). However, this assumption generally does not hold for biological time series data. In this work, the neural network's activity is modeled as a countable system of interacting chains with memory of variable length. In this sense, we intend to generalize conformal prediction to interacting systems where the assumption of exchangeability is not valid, temporal dependencies are not fixed, and the underlying time series is multivariate. In order to validate the underlying theory, we intend to demonstrate the effectiveness of the conformal method with extensive simulation and real-data analyses, compared with non-conformal methods. We also address the question of non-parametric statistical model selection for a class of interacting biological systems, which could enhance the model's predictive accuracy when the conformal method is applied to spike train predictions.