Abstract:
The mathematical modelling of behaviour enables the formalisation of theories
of cognition. Removed from the details of neural implementation, we can
abstractly reason about properties of the algorithms employed by the brain
which transform the presented inputs into the observed actions. However,
there are a number of complications, both in behaviour itself and the process
of modelling it, which impede a comprehensive characterisation of behaviour.
In this thesis, we present two separate modelling approaches which deal with
some of these issues. We showcase these frameworks on the International
Brain Laboratory (IBL) data of over 100 mice performing a perceptual decision-
making task. Mice learn the basic contingencies of this task over a number
of sessions and many thousands of trials. Afterwards, the task gains a biased
block structure, requiring the animals to track this hidden state to improve
their task performance.
We first build a highly flexible model which deals with the issues of non-
stationary behaviour due to learning and motivation, along with individual
differences. This is achieved using an infinite hidden Markov model (iHMM)
which provides a state based description of behaviour, with a non-parametric
Bayesian structure. The latter allows for the introduction of new states in
response to drastic changes in behaviour (such as learning through a sud-
den insight or motivational fluctuations). We fit this model to individuals
independently, exploiting automated complexity control. Dynamics in the char-
acterisation of the behavioural states additionally imbue the model with the
capacity to capture gradual learning. This allows us to identify distinct stages of
learning which are present throughout the population of IBL mice. We also find
substantial inter-individual differences in our model-based characterisations,
and quantify the limited predictability of the course of learning.
The second model we present uses neural networks to overcome the inherent
rigidities of models such as the iHMM, by progressively removing restrictions
from the class of modellable functions. This amounts to hybridising the neural
networks with a classical model of expert mouse behaviour on our task, to
maintain interpretability. We use this to find a simple extension of the classical
model which outperforms it, and thus provides a powerful but interpretable full
model of task behaviour. Amongst other insights, it shows how motivational
fluctuations represent a substantial source of behavioural variability for which
any complete model will have to account.
We thus provide tools which bring the field closer to a holistic modelling
approach of animal behaviour.
Computational Neuroscience
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