Does Bayesian Non-linear SSM (bnlssm) actually support time-varying coefficients?

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Oleg Gredil
Oleg Gredil 2024-5-18
Accodring to its documentation, 'bnlssm' object allows any of the coefficient matrices to be time-varying and, in that case, defined as cell arrays.
However, when i modify a working example given in the documentation to feature cell-arrays for either of the matrices, i get an error message that eminates from the validation check within the 'bnlssm' object (lines 700--707) failing to recongnize that the A-cell contains a function handle instead of numeric matrivuss (and thus not being indicative of the state vector dimension):
%the fragment (lines 700--707) from bnlssm.m that calls the error msg and halts further execution :
if iscellA; At = A{1}; else; At = A; end
numStates0 = size(At,2);
if isscalar(mean0)
mean0 = mean0(ones(numStates0,1),:);
elseif ~isempty(mean0)
mean0 = mean0(:);
validateattributes(mean0,{'numeric'},{'finite','real','numel',numStates0},callerName,'Mean0');
end
The working example i considered is as follows:
rng(1,"twister") % For reproducibility
T = 100;
thetatrue = [0.8; .9; -0.75; -.9; 0.3; 0.2; 0.1];
MdlSim = varm(AR={diag(thetatrue([1 3]))},Covariance=diag(thetatrue(5:6).^2), ...
Constant=thetatrue([2 4]));
XSim = simulate(MdlSim,T);
ysim = log(sum(exp(XSim - mean(XSim)),2)) + thetatrue(7)*randn(T,1);
Mdl = bnlssm(@(params)paramMap(params, otherData), ...
@(params)priorDistribution(params, otherData));
[xhat, SmStats] = smooth(Mdl,ysim,thetatrue);
function logprior = priorDistribution(Params, otherData)
% Prior means for the parameters
prior_means = otherData.prior_means;
% Prior standard deviations for the first 4 parameters
prior_std_devs = otherData.prior_sd;
% Degrees of freedom for the chi-squared distribution (last 3 parameters)
chi2_df =otherData.chi2_df;
% Check parameter constraints
paramconstraints = [(abs(Params([1 3])) < 1) (abs(Params([2 4])) > .2) (abs(Params([1 3])) < 3) (Params(5:7) > 0)];
% keyboard
if all(paramconstraints)
% Compute log-prior for the first 4 parameters (normal distribution)
logprior_normal = sum(log(normpdf(Params(1:4), prior_means(1:4), prior_std_devs)));
% Compute log-prior for the last 3 parameters (chi-squared distribution)
logprior_chi2 = sum(log(chi2pdf(1 ./ Params(5:7), chi2_df)));
% Total log-prior is the sum of log-priors for normal and chi-squared parts
logprior = logprior_normal + logprior_chi2;
else
% If parameter constraints are violated, assign a very low log-prior
logprior = -Inf;
end
end
function [A,B,C,D,Mean0,Cov0,StateType] = paramMap(Params, otherData)
T = otherData.T;
% A = @(x)blkdiag([Params(1) Params(2); 0 1],[Params(3) Params(4); 0 1])*x;
B = [Params(5) 0; 0 0; 0 Params(6); 0 0];
D = Params(7);
C = @(x)log(exp(x(1)-Params(2)/(1-Params(1))) + ...
exp(x(3)-Params(4)/(1-Params(3))));
A = cell(T,1);
for t=1:T
A{t} = @(x)blkdiag([Params(1) Params(2); 0 1],[Params(3) Params(4); 0 1])*x;
end
Mean0 = [Params(2)/(1-Params(1)); 1; Params(4)/(1-Params(3)); 1];
Cov0 = diag([Params(5)^2/(1-Params(1)^2) 0 Params(6)^2/(1-Params(3)^2) 0]);
StateType = [0 1 0 1]; % Stationary state and constant 1 processes
end
the example works fine if 'A' is defined as constant coef. matrix, i.e.:
function [A,B,C,D,Mean0,Cov0,StateType] = paramMap(Params, otherData)
T = otherData.T;
A = @(x)blkdiag([Params(1) Params(2); 0 1],[Params(3) Params(4); 0 1])*x;
B = [Params(5) 0; 0 0; 0 Params(6); 0 0];
D = Params(7);
C = @(x)log(exp(x(1)-Params(2)/(1-Params(1))) + ...
exp(x(3)-Params(4)/(1-Params(3))));
Mean0 = [Params(2)/(1-Params(1)); 1; Params(4)/(1-Params(3)); 1];
Cov0 = diag([Params(5)^2/(1-Params(1)^2) 0 Params(6)^2/(1-Params(3)^2) 0]);
StateType = [0 1 0 1]; % Stationary state and constant 1 processes
end
The same error occurs if i feed as cell 'B' or 'D', which do not feature a function handle for x, e.g.:
function [A,B,C,D,Mean0,Cov0,StateType] = paramMap(Params, otherData)
T = otherData.T;
A = @(x)blkdiag([Params(1) Params(2); 0 1],[Params(3) Params(4); 0 1])*x;
B = [Params(5) 0; 0 0; 0 Params(6); 0 0];
D = Params(7);
C = @(x)log(exp(x(1)-Params(2)/(1-Params(1))) + ...
exp(x(3)-Params(4)/(1-Params(3))));
D = cell(T,1);
for t=1:T
D{t} = Params(7);
end
Mean0 = [Params(2)/(1-Params(1)); 1; Params(4)/(1-Params(3)); 1];
Cov0 = diag([Params(5)^2/(1-Params(1)^2) 0 Params(6)^2/(1-Params(3)^2) 0]);
StateType = [0 1 0 1]; % Stationary state and constant 1 processes
end
or if feed only only selected elements of At, as function handles.
Please advise me on a work-around that error message and/or give a working example of 'bnlssm' object's application that does feature A_t(x_{t-1}), wheby the coefficients are differnent across periods while also being a non-linear functions of the previos period's state vector elements.

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