Fig 1.
Examples of possible cost functions, including a Hits model (all non-zero errors are punished equally), linear and quadratic functions, and two parametric functions: a power model and an inverted Gaussian (iG) model.
Power and iG parametric models are shown with the values Kording obtained across subjects controlling an interface with low inherent noise. The x-axis range is indicative of the maximum error experienced in this experiment, which used noisier control signals. The white region is the range of error considered by Kording’s experiment. If subjects use the same cost function for noisier signals, there should be a notable difference between the iG and power models for high levels of error: the iG model in particular should flatten out. If, however, people scale the model found in Kording’s study relative to the range of error encountered, the cost function would look like a scaled version of the white range of the figure.
Fig 2.
A trajectory moves across the screen from right to left. The subject moves the cursor up and down in the middle of the screen. The displayed cursor blinks at 1 Hz, and is drawn from a skewed distribution that is shifted by the user’s control input m. The subject is asked to, on average, keep the cursor on the waveform.
Fig 3.
Skewed probability distribution was generated by sampling from two Gaussian distributions with different means.
Given the nature of the equation, the skewed distribution had the same mean (m), regardless of skewness ρ.
Fig 4.
Surface electrodes were cuffed on the forearm. The hand grasped a fixed rod, and the forearm was held in place by two adjustable padded rods.
Fig 5.
Empirical shifts caused by a skewed noise distribution (median values shown, with inter-quartile vertical bars).
Optimal shifts according to candidate cost functions are also illustrated, including the interquartile range of the three parametric models.
Fig 6.
Accuracy of the candidate cost functions in predicting the empirical shifts.
Fig 7.
Interquartile range of parametric candidate cost functions across the range of error encountered in this study.
Note that the inverted Gaussian distribution does not flatten out for the optimum parameter set and over the range of error encountered.