A Generative Model for Measuring Latent Timing Structure in Motor Sequences

Abstract

Motor variability often reflects a mixture of different neural and peripheral sources operating over a range of timescales. We present a statistical model of sequence timing that can be used to measure three distinct components of timing variability: global tempo changes that are spread across the sequence, such as might stem from neuromodulatory sources with widespread influence; fast, uncorrelated timing noise, stemming from noisy components within the neural system; and timing jitter that does not alter the timing of subsequent elements, such as might be caused by variation in the motor periphery or by measurement error. In addition to quantifying the variability contributed by each of these latent factors in the data, the approach assigns maximum likelihood estimates of each factor on a trial-to-trial basis. We applied the model to adult zebra finch song, a temporally complex behavior with rich structure on multiple timescales. We find that individual song vocalizations (syllables) contain roughly equal amounts of variability in each of the three components while overall song length is dominated by global tempo changes. Across our sample of syllables, both global and independent variability scale with average length while timing jitter does not, a pattern consistent with the Wing and Kristofferson (1973) model of sequence timing. We also find significant day-to-day drift in all three timing sources, but a circadian pattern in tempo only. In tests using artificially generated data, the model successfully separates out the different components with small error. The approach provides a general framework for extracting distinct sources of timing variability within action sequences, and can be applied to neural and behavioral data from a wide array of systems.

Development of temporal structure in zebra finch song

“…The main thrust of our analysis used our previously published timing variability model (Glaze and Troyer 2012) to separate distinct components of temporal variability and track these over development. The required input to the model is a series of repeated renditions of a single stereotyped sequence of syllables.…”

“…To determine if the sound in these clips matched syllables in the bird's song, templates were formed by aligning and averaging four to five manually chosen clips corresponding to each syllable in the repertoire for that bird-byage sample; exemplars were time aligned by finding the peaks in a standard cross-correlation of syllable spectrograms. All recorded clips were then matched against each syllable template using a sliding algorithm (Glaze and Troyer 2007). For each template and each time point (t) in the clip, a match score [c(t)] was computed as the reciprocal of the mean squared difference between template and song log amplitudes at matched time-frequency points, as follows:…”

“…Fine-grained spectrograms were recalculated for all syllables using FFTs with a 128-point window slid forward in 4-point steps, yielding 0.16-ms time bins. Although previous research (Glaze andTroyer 2006, 2007) used log amplitudes, here we used raw amplitudes, which we have found to be more reliable. The resulting spectrograms were then smoothed in time with a 64-point window formed by truncating a Gaussian with a 25.6-point (ϳ5 ms) SD.…”

“…We also quantified an "independent" component of timing variability that was uncorrelated across syllables and gaps and may be linked with synaptic or neural noise in the pattern generator for song. We have recently developed a statistical "timing variability model" that allows us to separate out these variability components in a principled way (Glaze and Troyer 2012).To probe the development of the motor code for song timing, we applied the timing variability model to analyze changes in the temporal structure of zebra finch song from 65 dph through 1 yr of age. We found that between 65 and 85 dph, silent gaps decreased in both average duration and their sen-…”

“…We also quantified an "independent" component of timing variability that was uncorrelated across syllables and gaps and may be linked with synaptic or neural noise in the pattern generator for song. We have recently developed a statistical "timing variability model" that allows us to separate out these variability components in a principled way (Glaze and Troyer 2012).…”