Putting perception into action with inverse optimal control for continuous psychophysics
- Centre for Cognitive Science, Technical University of Darmstadt, Germany
- Institute of Psychology, Technical University of Darmstadt, Germany
- Frankfurt Institute for Advanced Studies, Goethe University Frankfurt, Germany
Figures
Figure 1
Conceptual frameworks for classical and continuous psychophysics.
(A) In a classical psychophysics task, the subject receives stimuli xt on independent trials, generates sensory observations yt, forms beliefs about the stimulus , and (B) makes a single decision u…
Figure 2 with 1 supplement
Computational models for continuous psychophysics.
(A) In the Kalman filter (KF) model, the subject makes an observation with Gaussian variability at each time step. They combine their prediction with their observation to compute an optimal …
Figure 2—figure supplement 1
Pareto efficiency plot.
The Pareto efficiency plot visualizes the trade-off between two costs contributing to the cost function. The cost function is composed of two terms: state costs and action costs , whose …
Figure 3 with 1 supplement
Inference on simulated data.
(A) Pairwise joint posterior distributions (0.5, 0.9, and 0.99 highest density intervals) inferred from simulated data from the subjective actor with parameters representative of real tracking data …
Figure 3—figure supplement 1
Model comparison for simulations.
Model comparison using widely applicable information criterion (WAIC) between different models fit to data simulated from the bounded actor or subjective actor model. Error bars indicate 95% CIs …
Figure 4
Continuous psychophysics.
(A) Perceptual uncertainty (σ) parameter estimates (posterior means) for the two-interval forced-choice (2IFC) task and the tracking task (Kalman filter [KF] and linear quadratic Gaussian [LQG] …
Figure 5 with 2 supplements
Model comparison on motion-tracking data.
(A) Average cross-correlograms (CCGs) for S1 from Bonnen et al., 2017 and three models in different target random walk conditions. For the other two subjects, see Figure 3. (B) Difference in widely …
Figure 5—figure supplement 1
Cross-correlograms (CCGs) for all subjects.
(A) CCGs as in Figure 5 for all three subjects separately based on the data in experiment 2 from Bonnen et al., 2017.
Figure 5—figure supplement 2
Posterior distributions of model parameters of the subjective model in experiment 2 (Bonnen et al., 2017).
(A) Posterior distributions for action cost (c) and action variability (). (B) Posterior distributions for subjective stimulus dynamics parameters (position: , velocity: ).
Appendix 5—figure 1
Cross-validation of estimated parameters.
(A) Difference in log-posterior relative to the best model per left-out condition from the experiment by Bonnen et al., 2017. Each model was fitted on the remaining four conditions as described in …
Appendix 5—figure 2
Model comparison on eye-tracking data.
Widely applicable information criterion (WAIC) on our four models for the eye-tracking data, fit separately to the X and Y dimension.
Tables
Appendix 2—table 1
Model overview.
| Model | State space | Dynamical systemmatrices | Cost function | Free parameters |
|---|---|---|---|---|
| Ideal observer | - | σ | ||
| Optimal actor | ||||
| Bounded actor | as above as above | as above as above | as above, as above | |
| Subjective actor |
