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Temporal Influence on Reaching Strategies: Analyzing Körding & Wolpert (2004) Data Using Kalman Filter

This study delves into how recent experience and current sensory information impact reaching strategies, analyzing Körding & Wolpert's (2004) data from the ★DREAM★ database. By implementing the Kalman filter, regression analysis, and prior evolution, the research uncovers the role of temporal factors in shaping subject strategies and performance. Findings suggest that subjects' trust in past estimations and their responses to uncertainty are key determinants of reaching strategies.

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Temporal Influence on Reaching Strategies: Analyzing Körding & Wolpert (2004) Data Using Kalman Filter

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  1. Temporal Influence on Subject Reaching Strategies CoSMo 2012 Matt Balcarras Irene Tamagnone Leonie OostwoudWijdenes Andrew Brennan Deborah Barany YasharZeighami “Kalman, maybe?”

  2. Outline • How do reaching strategies depend on recent experience and current sensory information? • Analyzed Körding & Wolpert (2004) data from the ★DREAM★ database • Original paper did not consider recent trial effects on performance

  3. Outline Temporal Structure • Three approaches • Regression analysis • Prior evolution • Kalman Filter Regression Analysis Prior Evolution Kalman Filter

  4. Körding & Wolpert (2004) End point hand position End point cursor position Deviation from midpoint and endpoint positions

  5. Regression Analysis • Predictors • Mid-point hand position • Mid-point cursor position • Five-trial running mean • Cumulative mean

  6. Regression Coefficients

  7. Estimating the Prior Berniker, Voss, & Körding, 2010

  8. Prior Estimate Over Time Prior (cm) Trial Bin

  9. Likelihood Variance ∞ 0.29 0.43 0.60 σL σ∞ σ0 σM

  10. Implementation of Kalman Filter • Our state vector : Current perturbation Pt and perturbation mean μtcomputed on all the previous trials • Our observer: Midpoint Cursor Position where: • Parameter α • Weights the contributions of the previous perturbation and of the whole history of perturbations in the current prediction • Is optimized on the training data (first 1000 trials)

  11. Kalman Filter Fit Typical Subject Kalman Filter Subject Data End Hand Position (cm) α (across subjects)=0.35 R2 = 0.18 Trial

  12. Conclusions • Recent trial history and online cursor feedback play a significant role in predicting end position • The prior is learned quickly and is stable over time • Likelihood variance increases with uncertainty • The Kalman filter reveals that subjects trust the estimation of the previous trial • Under uncertain conditions, temporal factors influence subject strategy suboptimally

  13. M I L A D Y

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