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bsfit_stats.m
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bsfit_stats.m
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% Test significance of the fitted source cross-bispectrum within
% subjects based on the following steps:
%
% 1. Estimate the (true) sensor cross-bispectrum B_true.
% 2. Run the decomposition method on B_true to estimate A_hat (true mixing
% matrix) and D_hat (true source cross-bispectrum)
% 3. Fit surrogate source cross-bispectra by holding the mixing matrix A_hat fix (i.e., only fit D_shuf).
% 4. Unmix the estimated pattern A_hat and cross-bispectrum D_hat using MOCA to get the demixed pattern
% A_demixed and demixed cross-bispectrum D_demixed.
% 5. Perform source localization using significant demixed pattern A_demixed.
% 6. Compute p-values based on the absolute values of the estimate source cross-bispectra.
% The result will be a (n x n x n) tensor of p-values.
%
% Notations:
% n_chans - number of EEG channels (sensors)
% n - model order (number of estimated sources)
% epleng - length of a single epoch/trial
% n_epochs - number of epochs/trials
%
% Inputs:
% data - (n_chans x epleng x n_epochs) time series used to estimate the sensor cross-bispectrum
% f1 - single frequency in Hz or frequency band, e.g., [9 11](low frequency)
% f2 - single frequency in Hz or frequency band, e.g., [22 24] (high frequency)
% n - number of estimated sources
% nshuf - number of shuffles
% frqs - (n_frq x 1) array of frequencies
% segleng - segment length (see METH toolbox documentation)
% segshift - overlap of segments (see METH toolbox documentation)
% epleng - epoch length (see METH toolbox documentation)
% alpha - significance level, default is 0.05.
% L_3D - (n_chans x n_voxels x n_dum) leadfield tensor, dipole directions are typically 3
%
% Optional inputs:
% antisymm - [idx, idx, idx] array containing indices to permute, will not perform antisymmetrization if [1, 2, 3]. Default is [1, 2, 3].
% total_antisymm - ['on' | 'off'] whether TACB should be compuuted. Default is 'off'.
% train_test - ['on' | 'off'] whether A should be fitted on train data and D on test data. If yes, the train-test split is 80-20. Default is 'off'.
% bs_orig - (n_chans x n_chans x n_chans) original sensor cross-bispectrum. Default is empty.
% bs_all - (n_chans x n_chans x n_chans x nshuf) surrogate sensor cross-bispectrum. Default is empty.
% Outputs:
% P_fdr - (1 x n) cell array with (n x n x n) tensors of fdr-corrected p-values
% P - (1 x n) cell array with (n x n x n) tensors of p-values (before fdr correction)
% F - (1 x n) cell array with (n_voxels x n_dum x n) mixed sources
% F_moca - (1 x n) cell array with (n_voxels x n_dum x n) demixed sources after MOCA
% A_hat - (1 x n) cell array with (n_chan x n) estimated spatial patterns (mixing matrix)
% A_demixed - (1 x n) cell array with (n_chan x n) demixed spatial patterns
% D_hat - (1 x n) cell array with (n x n x n) estimated source cross-bispectra
% D_demixed - (1 x n) cell array with (n x n x n) demixed source cross-bispectra
% err - (1 x n) cell array with (n_freqcombs x n) errors over iterations
% bs_orig - (n_chans x n_chans x n_chans) original sensor cross-bispectrum
% bs_all - (n_chans x n_chans x n_chans x nshuf) surrogate sensor cross-bispectrum
function [P_fdr, P, F, F_moca, A_hat, A_demixed, D_hat, D_demixed, err, bs_orig, bs_all] = bsfit_stats(data, f1, f2, n, nshuf, frqs, segleng, segshift, epleng, alpha, L_3D, varargin)
g = finputcheck(varargin, { ...
'antisymm' 'integer' { } [1 2 3];
'total_antisymm' 'string' { 'on' 'off' } 'off';
'train_test' 'string' { 'on' 'off' } 'off';
'bs_orig' 'float' { } [];
'bs_all' 'float' { } [];
});
if ischar(g), error(g); end
% get frequency pairs (in bins)
freqpairs = get_freqindices(round_to_05(f1), round_to_05(f2), frqs);
if isempty(g.bs_orig) && isempty(g.bs_all)
% estimate sensor cross-bispectrum, either on full dataset or on train-test splots
clear para
disp('Start calculating surrogate sensor cross-bispectra...')
if strcmpi(g.train_test, 'off')
para.nrun = nshuf;
[bs_all, bs_orig] = data2bs_event_surro_final(data(:, :)', segleng, segshift, epleng, freqpairs, para);
else
% fit A_hat and D_hat on bs_orig that is computed using training data, later fit D_shuf on bs_all that is computed using test data
cut = round(size(data, 2) * 0.8);
train = data(:, 1:cut);
test = data(:, cut+1:end);
para.nrun = 1; % original bispectrum on training data
[~, bs_orig] = data2bs_event_surro_final(train', segleng, segshift, epleng, freqpairs, para);
para.nrun = nshuf; % surrogates on test data
[bs_all, ~] = data2bs_event_surro_final(test', segleng, segshift, epleng, freqpairs, para);
end
else
bs_orig = g.bs_orig;
bs_all = g.bs_all;
end
% antisymmetrization
if strcmpi(g.total_antisymm, 'on')
disp('Perform total antisymmetrization')
bs_orig = bs_orig + permute(bs_orig, [3, 1, 2]) + permute(bs_orig, [2, 3, 1]) - permute(bs_orig, [3, 2, 1]) - permute(bs_orig, [2, 1, 3]) - permute(bs_orig, [1, 3, 2]);
bs_all = bs_all + permute(bs_all, [3, 1, 2, 4]) + permute(bs_all, [2, 3, 1, 4]) - permute(bs_all, [3, 2, 1, 4]) - permute(bs_all, [2, 1, 3, 4]) - permute(bs_all, [1, 3, 2, 4]);
elseif ~isequal(g.antisymm, [1, 2, 3])
disp('Perform partial antisymmetrization')
bs_orig = bs_orig - permute(bs_orig, g.antisymm);
bs_all = bs_all - permute(bs_all, [g.antisymm, 4]);
else
disp('No antisymmetrization')
end
% run decomposition on the original sensor cross-bispectrum
A_hat = {};
D_hat = {};
err = {};
for m_order = n
% [A_hat, D_hat] = bsfit(bs_orig, n);
[A_hat{end+1}, D_hat{end+1}, ~, ~, err{end+1}] = bsfit_freqbands(bs_orig, m_order);
end
% fit surrogate source cross-bispectra with fixed mixing matrix
disp('Start calculating surrogate source cross-bispectra...')
D_shuf = {};
for n_idx = 1:length(n)
clear para
para.a = A_hat{n_idx};
para.isfit_a = false;
m_order = n(n_idx);
disp(['Fitting for model order ' num2str(m_order) ':...'])
fprintf('Progress of %d:', nshuf);
D_shuf_n = zeros(m_order, m_order, m_order, nshuf);
for ishuf = 1:nshuf
if mod(ishuf, 10) == 0
fprintf('%d', ishuf);
elseif mod(ishuf, 2) == 0
fprintf('.');
end
% [~, D_ishuf] = bsfit(bs_all(:, :, :, ishuf), n, para);
[~, D_ishuf] = bsfit_freqbands(bs_all(:, :, :, ishuf), m_order, para);
D_shuf_n(:, :, :, ishuf) = D_ishuf;
end
D_shuf{end+1} = D_shuf_n;
fprintf('\n');
end
fprintf('\n');
% demix the source interactions using MOCA and compute p-values
P = {};
P_fdr = {};
F = {};
F_moca = {};
A_demixed = {};
D_demixed = {};
for n_idx = 1:length(n)
[A_moca, F_moca{end+1}, F{end+1}] = apply_moca(L_3D, A_hat{n_idx}, n(n_idx));
A_demixed{end+1} = A_hat{n_idx} * A_moca'; % demix sensor pattern
D_demixed{end+1} = calc_bsmodel(A_moca', D_hat{n_idx}); % demix source cross-bispectrum
% % demix shuffles
% D_shuf_demixed = zeros(n_idx, n_idx, n_idx, nshuf);
% for ishuf = 1:n_idx
% D_shuf_demixed(:, :, :, ishuf) = calc_bsmodel(A_moca', D_shuf{n_idx}(:, :, :, ishuf));
% end
% compute p-values
% [P{end+1}, P_fdr{end+1}] = compute_pvalues(abs(D_demixed{n_idx}), abs(D_shuf_demixed), nshuf, alpha, 'shuf_dim', 4);
[P{end+1}, P_fdr{end+1}] = compute_pvalues(abs(D_demixed{n_idx}), abs(D_shuf{n_idx}), nshuf, alpha, 'shuf_dim', 4);
end
end