A linear discriminant analysis model of imbalanced associative learning in the mushroom body compartment

To adapt to their environments, animals learn associations between sensory stimuli and unconditioned stimuli. In invertebrates, olfactory associative learning primarily occurs in the mushroom body, which is segregated into separate compartments. Within each compartment, Kenyon cells (KCs) encoding sparse odor representations project onto mushroom body output neurons (MBONs) whose outputs guide behavior. Associated with each compartment is a dopamine neuron (DAN) that modulates plasticity of the KC-MBON synapses within the compartment. Interestingly, DAN-induced plasticity of the KC-MBON synapse is imbalanced in the sense that it only weakens the synapse and is temporally sparse. We propose a normative mechanistic model of the MBON as a linear discriminant analysis (LDA) classifier that predicts the presence of an unconditioned stimulus (class identity) given a KC odor representation (feature vector). Starting from a principled LDA objective function and under the assumption of temporally sparse DAN activity, we derive an online algorithm which maps onto the mushroom body compartment. Our model accounts for the imbalanced learning at the KC-MBON synapse and makes testable predictions that provide clear contrasts with existing models.Author summary: To adapt to their environments, animals learn associations between sensory stimuli (e.g., odors) and unconditioned stimuli (e.g., sugar or heat). In flies and other insects, olfactory associative learning primarily occurs in a brain region called the mushroom body, which is partitioned into multiple compartments. Within a compartment, neurons that represent odors synapse onto neurons that guide behavior. The strength of these synapses is modulated by a dopamine neuron that responds to one type of unconditioned stimuli (e.g., sugar), which implicates these synapses as a biological substrate for associative learning in insects. Modifications of these synapses is imbalanced in the sense that dopamine-induced modifications only weaken the synapses and are temporally sparse. In this work, we propose a simple mechanistic model of learning in the mushroom body that accounts for this imbalanced learning. Our model is interpretable as implementing an algorithm for linear discriminant analysis, a classical statistical method for linearly separating feature vectors that belong to different classes. Our model makes testable predictions that provide clear contrasts with existing models.