2-level HGF implementation

[a-yur]

Is an implementation of a 2-level version of the binary HGF available in TAPAS? From what I understand, the existing implementation of the tapas_hgf_binary in TAPAS requires to have at least three levels.

We plan to model a stimulus sequence with a 2-level HGF and then use the trial-by-trial estimates as parametric modulators, similar to Stefanics et al. (2019, NeuroImage).

[chmathys]

You can get a 2-level binary HGF by fixing the parameter kappa_2 to zero (i.e., to -Inf in logit-space). That cuts off the third level from any information, effectively removing it. You should also fix the third-level parameters mu_3^(0) and omega_3 to (arbitrary) values in order to prevent the optimization algorithm from trying to estimate them.

…

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[kwellstein]

Hi everyone,

we have a smilar issue.

We are trying to fit a 2-level eHGF binary (toolbox v7.1) but keep running into an "unstable region for the startpoint".
I tried multiple prior settings in the config file but cannot get anywhere. Maybe I am missing something fundamental though... Below the config file:

% Model name
c.model = 'ehgf_binary';

% Number of levels (minimum: 3)
c.n_levels = 2;

% Input intervals
% If input intervals are irregular, the last column of the input
% matrix u has to contain the interval between inputs k-1 and k
% in the k-th row, and this flag has to be set to true
c.irregular_intervals = false;

% Sufficient statistics of Gaussian parameter priors

% Initial mus and sigmas
% Format: row vectors of length n_levels
% For all but the first two levels, this is usually best
% kept fixed to 1 (determines origin on x_i-scale). The
% first level is NaN because it is determined by the second,
% and the second implies neutrality between outcomes when it
% is centered at 0.
c.mu_0mu = [NaN, 1]; % tried 0 too
c.mu_0sa = [NaN, 0];

c.logsa_0mu = [NaN, log(0.1)]; % tried log(1) too
c.logsa_0sa = [NaN, 0];

% Rhos
% Format: row vector of length n_levels.
% Undefined (therefore NaN) at the first level.
% Fix this to zero to turn off drift.
c.rhomu = [NaN, 0];
c.rhosa = [NaN, 0];

% Kappas
% Format: row vector of length n_levels-1.
% Fixing log(kappa1) to log(1) leads to the original HGF model.
% Higher log(kappas) should be fixed (preferably to log(1)) if the
% observation model does not use mu_i+1 (kappa then determines the
% scaling of x_i+1).
c.logkamu = [log(1)]; % also tried -Inf here
c.logkasa = [0];

% Omegas
% Format: row vector of length n_levels.
% Undefined (therefore NaN) at the first level.
c.ommu = [NaN, -3]; % also tried -6, -8, -10
c.omsa = [NaN, 4]; % also tried 4^2

thank you for your help :)

[kwellstein]

update:
We shouldnt have deleted the 3rd (or in some cases) 2nd column like the comments suggested. But still, the issue remains. This is the current config, I tried the same values as above.
The 3-level HGF fits without an issue. I also tried fitting the 2-level Hgf using random inputs, the error persists. The task has 280 trials.

c.mu_0mu = [NaN, 0, 1];
c.mu_0sa = [NaN, 0, 0];

c.logsa_0mu = [NaN, log(0.1), log(1)];
c.logsa_0sa = [NaN, 0, 0];

% Rhos
% Format: row vector of length n_levels.
% Undefined (therefore NaN) at the first level.
% Fix this to zero to turn off drift.
c.rhomu = [NaN, 0, 0];
c.rhosa = [NaN, 0, 0];

% Kappas
% Format: row vector of length n_levels-1.
% Fixing log(kappa1) to log(1) leads to the original HGF model.
% Higher log(kappas) should be fixed (preferably to log(1)) if the
% observation model does not use mu_i+1 (kappa then determines the
% scaling of x_i+1).
c.logkamu = [log(1), log(1)];
c.logkasa = [ 0, 0];

% Omegas
% Format: row vector of length n_levels.
% Undefined (therefore NaN) at the first level.
c.ommu = [NaN, -3, 2];
c.omsa = [NaN, 4, 0];