A compact statistical model of the song syntax in Bengalese finch

TL;DR

This paper introduces a new statistical model, POMMA, that better captures Bengalese finch song syntax by incorporating adaptation and many-to-one mappings, surpassing traditional Markov models.

Contribution

The paper presents the POMMA model, a partially observable Markov model with adaptation, which more accurately describes bird song syntax than standard Markov models.

Findings

Markov models fail to capture song syntax statistics.

POMMA includes adaptation of self-transitions and many-to-one state-syllable mappings.

POMMA supports neural control hypotheses of bird song production.

Abstract

Songs of many songbird species consist of variable sequences of a finite number of syllables. A common approach for characterizing the syntax of these complex syllable sequences is to use transition probabilities between the syllables. This is equivalent to the Markov model, in which each syllable is associated with one state, and the transition probabilities between the states do not depend on the state transition history. Here we analyze the song syntax in a Bengalese finch. We show that the Markov model fails to capture the statistical properties of the syllable sequences. Instead, a state transition model that accurately describes the statistics of the syllable sequences includes adaptation of the self-transition probabilities when states are repeatedly revisited, and allows associations of more than one state to the same syllable. Such a model does not increase the model complexity significantly. Mathematically, the model is a partially observable Markov model with adaptation (POMMA). The success of the POMMA supports the branching chain network hypothesis of how syntax is controlled within the premotor song nucleus HVC, and suggests that adaptation and many-to-one mapping from neural substrates to syllables are important features of the neural control of complex song syntax.