Modeling Emotions Associated With Novelty at Variable Uncertainty Levels: A Bayesian Approach - Yanagisawa, Hideyoshi; Kawamata, Oto; Ueda, Kazutaka (Frontiers in Computational Neuroscience, 2019)
Acceptance of novelty depends on the emotional state of the receiver. However, a mathematical formulation to predict emotions elicited by novelty under different conditions, such as uncertainty, has not been established yet. This paper proposes a mathematical model of two emotion dimensions, arousal and valence, elicited by the novelty of an event under different uncertainties. A state transition before and after experiencing an event is assumed. Bayesian model estimates a posterior as proportional to a product of prior and likelihood function. Kullback-Leibler divergence of posterior from prior, termed information gain, is used as arousal level because it corresponds to surprise, a high arousal emotion, when one experiences a novel event. Based on Berlyne’s hedonic function, we formalized valence as a summation of reward and aversion systems that are sigmoid functions of information gain. We mathematically derived information gain as a function of three parameters: prediction error (difference between mean of posterior and peak likelihood), uncertainty (variance of prior that is proportional to prior entropy), and noise (variance of likelihood function). Using the functional model, we found an interaction effect of prediction error and uncertainty on information gain, termed as the arousal crossover effect. The greater the uncertainty, the greater the information gain for a small prediction error. In contrast, this relationship is reversed as prediction error increases: the greater the uncertainty, the smaller the information gain for a large prediction error. To verify this effect, we conducted an experiment with human participants using short films in which different percussion instruments were played. Uncertainty and prediction error were manipulated by familiarity in appearance and congruity of the beating sounds synthesized in the films. Event-related potential P300 amplitude and subjective responses of surprise for beating sounds, used as measures of arousal level, supported the hypothesis of arousal crossover effect. The correspondence of mathematical analysis and experimental results suggests that Bayesian information gain can be decomposed into uncertainty and prediction error, and is appropriate as a measure of emotional arousal. The proposed model allows accurate predictions of arousal that may help identify positively accepted novelty.