Scripts simulating ideal-observer decision processes in changing environments

This repository contains, so far, four projects, whose corresponding folders are: NeuralCompCode/ ClickTask/ PerformanceSims/
sims_learning_rate/.

NeuralCompCode/

This folder contains the MATLAB scripts that were used in the article "Evidence accumulation and change rate inference in dynamic environments" by Adrian E. Radillo, Alan Veliz-Cuba, Kresimir Josic, Zachary P. Kilpatrick.

A few words on the topic

For full information and bibliography, see our article.

The problem that we study, in its simplest form, is the following: an environment Hn alternates between two values, say H+ and H-, where n is the discrete time variable and Hn is a homogeneous discrete time Markov chain. We say that the environment is symmetric when the transition probabilities H+ -> H- and H- -> H+ are the same. We call this probability epsilon. An ideal observer makes noisy observations of Hn at each time n. The noise distributions are known. The observer's main aim is to decide which state the environment is in at any present time. A subordinate aim is to learn the transition probability epsilon.

Our article deals with complexifications of the case described above, where the 2 transition probabilities are distinct, where the environment can take on N values for N >= 2, and where time becomes continuous. The code present in this repository only deals with discrete time, and with the exception of figure 4, with the 2-state symmetric case.

Short scripts description

All scripts were written for MATLAB_R2015b release.

Figure 1

Scripts: fig1B_data.m, fig1_FINAL_plotting.m

No real computation is performed by those scripts which only had an illustrative aim.

Run the script fig1B_data.m to produce a .mat file. Run subsequently fig1_FINAL_plotting.m to produce figure 1 from our article.

Figure 2

Scripts: fig2CD_data.m, fig2_FINAL_plotting.m

Panel A from figure 2 in the article was sketched manually with a drawing software. The data required to plot panels C and D is produced by the script fig2CD_data.m. Running it will produce 2 .mat files as output. These are in turn used by the final plotting script fig2_FINAL_plotting.m. Note that panel B from the figure also has a purely illustrative purpose and is therefore not simulated via the Markov chain Hn.

Figure 3

Scripts: fig3AB_data.m, fig3Ck_data.m, fig3Cu_data.m, fig3_FINAL_plotting.m

As before, all the scripts ending with data.m should be run before the fig3_FINAL_plotting.m script. Each one of the data.m script will produce its own .mat file. Both fig3Ck_data.m and fig3Cu_data.m are required for producing the data relative to panel C.

Figure 4

Scripts: enfants.m, createNodes.m, fig4AC_data.m, fig4_FINAL_plotting.m

The scripts enfants.m and createNodes.m are MATLAB functions used in fig4AC_data.m. The latter outputs a .mat file required for the final plotting script fig4_FINAL_plotting.m. Panel B from figure 4 contains the list of node counts for the 3-state case hard-coded. These numbers were computed using a combination of Shell and MATLAB. For more information, contact the corresponding author for this repository.

ClickTask/

References:

• Piet, A., Brody, C. D., and El Hady, A. (2017). Rats can optimally discount evidence for decision making in a dynamic environment. In Cosyne Abstr. 2017, Salt Lake City.
• Brunton, B. W., Botvinick, M. M., and Brody, C. D. (2013). Rats and humans can optimally accumulate evidence for decision-making. Science (80-. )., 340(6128):95-8.

We believe that with the right discretization of time, the ideal-observer model in the click-task with dynamic environment obeys the same equations as our model from the Neural Comp paper.

This model computes the joint posterior over both state and change point count at every time step, recursively.

We would like to address the following questions both theoretically and numerically:

Question 1:

How does the joint probability mass evolve in time, as a function of the type of evidence collected (00,11,10,01), and as Delta t ---> 0? In particular, are there delta jumps for the observations 01,10, and continuous variation for 00 and 11?

Question 2:

How does the variance of the posterior over the change rate decay? This corresponds to the high-level question: How well and quickly can the change rate be learned by the observer? The answer will depend at least on the SNR and on the value of the change rate.

Question 3:

The third question is more general and not specific to this task. How is performance impacted by the evidence accumulation model? A few parameters to manipulate are:

• number of observations
• mean and width of the Beta prior over the change rate
• SNR
• type of algorithm: a) ideal-obs with delta prior on rate b) ideal-obs with non-delta prior on rate c) naive observer, with no integration of history

PerformanceSims/

The aim of this project is to explore the parameter space with simulations in order to get an idea of how the performance of the ideal-observer in the interrogation paradigm depends on the following parameters: T = interrogation time SNR h = true hazard rate alpha, beta = Beta hyperparameters of the prior over h

sims_learning_rate/

Right now, I am running simulations to investigate the effect of feedback on the posterior computed by an ideal-observer.

Corresponding author for the scripts

adrian@math.uh.edu

License

See the LICENSE.txt file in this repository.