close
Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2017 Jan 30;12(1):e0169795.
doi: 10.1371/journal.pone.0169795. eCollection 2017.

A Bayesian Account of Vocal Adaptation to Pitch-Shifted Auditory Feedback

Richard H R Hahnloser  1 , Gagan Narula  1
Affiliations

A Bayesian Account of Vocal Adaptation to Pitch-Shifted Auditory Feedback

Richard H R Hahnloser et al. PLoS One. .

Abstract

Motor systems are highly adaptive. Both birds and humans compensate for synthetically induced shifts in the pitch (fundamental frequency) of auditory feedback stemming from their vocalizations. Pitch-shift compensation is partial in the sense that large shifts lead to smaller relative compensatory adjustments of vocal pitch than small shifts. Also, compensation is larger in subjects with high motor variability. To formulate a mechanistic description of these findings, we adapt a Bayesian model of error relevance. We assume that vocal-auditory feedback loops in the brain cope optimally with known sensory and motor variability. Based on measurements of motor variability, optimal compensatory responses in our model provide accurate fits to published experimental data. Optimal compensation correctly predicts sensory acuity, which has been estimated in psychophysical experiments as just-noticeable pitch differences. Our model extends the utility of Bayesian approaches to adaptive vocal behaviors.

PubMed Disclaimer

Conflict of interest statement

The authors have declared that no competing interests exist.

Figures

Fig 1
Fig 1. Model of optimal pitch adaptation.
Motor areas in the brain generate a motor plan μm by integrating a desired pitch μ* and pitch adaptation ϵ. The produced pitch suffers from motor noise. Auditory areas optimally combine the motor plan with corrupted feedback pf, then reweight the estimate by the probability of feedback being self-caused P(s|pf) to produce a final pitch deviation Δp relative to the desired pitch μ*. The two free parameters highlighted in red are estimated by fitting pitch compensation data from Bengalese finches and humans (Fig 2).
Fig 2
Fig 2. Model fits (black lines) to Bengalese finch data (crosses) digitized from [14].
Best fits to compensation data (a) and to overlap-fraction data (b) are achieved for σf = 23, k = 1.5 * 10−4. For comparison, the dashed line in (b) is the fit to the data provided by the overlap model in [14]. (c) The learning time constant (in days) was estimated as τ = q〈P(e|pf)〉/〈P(s|pf)〉, i.e. as the ratio of the self-versus external-source posterior probabilities (learning occurs mainly during inferred self-produced syllable renditions), q is a parameter estimated using a least-squared error fit.
Fig 3
Fig 3. Model fits (lines) to human pitch compensation data (black crosses) digitized from [11].
(a) The model fit (black line) reveals only qualitative agreement but no precise match; k = 5.2 * 10−4, σf = 0 cents, σm = 32 cents. After introducing an additional offset parameter ϵ0 to account for a read-out bias, the model fit (red line) becomes excellent; k = 1.4 * 10−3, σf = 0 cents, σm = 14 cents, ϵo = 31 cents. (b) Fits (black line) through data points (crosses) extracted from the linear regression in [23]. k = 10−320 (essentially k = 0), σf = 7.5 cents. The same fit results (red dashed line) when enforcing a self-source interpretation, P(s|pf) 1. σf = 7.5. cents.
Fig 4
Fig 4. Non-monotonic dependence of percent compensation as a function of sensory noise.
For both small and large pitch shifts pΔ (superimposed full and dashed lines), the percent pitch compensation is a non-monotonic function that peaks at an intermediate level of sensory noise. Model simulations were performed with best-fit parameters for the human data in Fig 3: σm = 32 cents, k = 0. The red line marks the upper limit of our inferred pitch variability in humans (σf = 7.5 cents).
See this image and copyright information in PMC

References

    1. Körding KP, Beierholm U, Ma WJ, Quartz S, Tenenbaum JB, Shams L. Causal inference in multisensory perception. PLoS One. 2007;2. - PMC - PubMed
    1. Ernst MO, Banks MS. Humans integrate visual and haptic information in a statistically optimal fashion. Nature. 2002;415: 429–33. 10.1038/415429a - DOI - PubMed
    1. Körding KP, Wolpert DM. Bayesian integration in sensorimotor learning. Nature. 2004;427: 244–247. 10.1038/nature02169 - DOI - PubMed
    1. Marko MK, Haith AM, Harran MD, Shadmehr R. Sensitivity to prediction error in reach adaptation. J Neurophysiol. 2012;108: 1752–1763. 10.1152/jn.00177.2012 - DOI - PMC - PubMed
    1. Shadmehr R, Mussa-Ivaldi FA. Adaptive representation of dynamics during learning of a motor task. J Neurosci. 1994;14: 3208–3224. - PMC - PubMed

LinkOut - more resources