Modelling and classification of neuronal dynamics through Generalised Linear Models

Abstract

The generalised linear models, so-called GLM, are data-driven models able to capture a wide variety nonlinear behaviours which can be difficult to simulate in classical mechanistic models. Consequently, GLMs occasionally find applications in neuron modelling, providing a flexible solution to address the complexities of neuronal dynamics. Here, this work focus on the main behaviours studied in the neuroscience research field to design relevant GLMs. Initially, the performance of the GLM is meticulously evaluated based on factors such as the length of the sequence being captured, the number of its basis functions and their designs. The parameters that remain untested are transparently highlighted. While key characteristics of those fitted filters are also discussed. In a second time, deeper investigations are conducted into the feedback filter of the fitted GLM. Although the GLMs differ according the training sequences, it exists notable similitude between them when the training sequences belongs to the same family, e.g. spiking, bursting. The extraction of features is possible thanks to the elements of the GLM. Therefore, the classification of the original sequences according the features of the GLM is addressed at the end of this these, it contributes to a comprehensive understanding of the intricate dynamics underlying neuronal behaviour. Through analysis and interpretation of GLM performance, this study offers valuable insights into the potential applications and limitations of these models in capturing and reproducing complex neuronal dynamics. By shedding light on the role of model parameters, training sequences, and extracted features, this thesis helps in the design and interpretation of GLM within the framework of neuronal representation.