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mTRF-Toolbox is a MATLAB package for modelling multivariate stimulus-response data, suitable for neurophysiological data such as MEG, EEG, sEEG, ECoG and EMG. It can be used to model the functional relationship between neuronal populations and dynamic sensory inputs such as natural scenes and sounds, or build neural decoders for reconstructing stimulus features and developing real-time applications such as brain-computer interfaces (BCIs).


Download and unzip mTRF-Toolbox to a local directory, then in the MATLAB/GNU Octave command window enter:

addpath 'directory/mTRF-Toolbox'


For documentation and citation, please refer to the mTRF-Toolbox paper.

For usage, please see examples and example M-files.

mTRF Modelling Framework

mTRF-Toolbox provides a complementary forward/backward quantitative modelling framework. A forward model, known as a temporal response function or temporal receptive field (TRF), describes how sensory information is encoded in neuronal activity. Multivariate stimulus features such as spatio- or spectro-temporal representations, as well as categorical features such as phonetic or semantic embeddings, can be used as inputs to the model. TRFs can be subjected to conventional time-frequency/source analysis techniques or used to predict the neural responses to an independent set of stimuli. mTRF-Toolbox provides an efficient cross-validation procedure for hyperparameter optimization.

A backward model, known as a neural decoder, reverses the direction of causality between stimulus and response. Neural decoders can be used to reconstruct stimulus features from information encoded explicitly or implicitly in neuronal activity, or decode higher-order cognitive processes such as top-down attention. The mTRF modelling framework provides a basic machine learning platform for real-time BCI applications such as stimulus reconstruction/synthesis and auditory attention decoding (AAD).


Fitting encoding/decoding models

  • mTRFcrossval() - performs efficient leave-one-out cross-validation
  • mTRFtrain() - fits an encoding/decoding model (TRF/STRF estimation)
  • mTRFtransform() - transforms a decoding model into an encoding model
  • mTRFpredict() - predicts the output of an encoding/decoding model
  • mTRFevaluate() - evaluates the accuracy and error of a models prediction

Decoding attention and multisensory integration

  • mTRFattncrossval() - cross-validation for attention decoder optimization
  • mTRFattnevaluate() - evaluates the accuracy and modulation index of an attention decoder
  • mTRFmulticrossval() - cross-validation for additive multisensory model optimization
  • mTRFmultitrain() - fits an additive multisensory model (TRF/STRF estimation)

Feature engineering

  • mTRFenvelope() - computes the temporal envelope of an audio signal
  • mTRFresample() - resamples and smooths temporal features
  • lagGen() - generates time-lagged input features of multivariate data


TRF/STRF estimation

Here, we estimate a 16-channel spectro-temporal response function (STRF) from 2 minutes of EEG data recorded while a human participant listened to natural speech. To map in the forward direction (encoding model), we set the direction of causality to 1. To capture the entire STRF timecourse, the time lags are computed between -100 and 400 ms. The regularization parameter is set to 0.1 to reduce overfitting to noise.

% Load example speech dataset

% Estimate STRF model weights
model = mTRFtrain(stim,resp*factor,fs,1,-100,400,0.1);

We compute the broadband TRF by averaging the STRF model across frequency channels and the global field power (GFP) by taking the standard deviation across EEG channels, and plot them as a function of time lags. This example can also be generated using plot_speech_STRF and plot_speech_TRF.

% Plot STRF
subplot(2,2,1), mTRFplot(model,'mtrf','all',85,[-50,350]);
title('Speech STRF (Fz)'), ylabel('Frequency band'), xlabel('')

% Plot GFP
subplot(2,2,2), mTRFplot(model,'mgfp','all','all',[-50,350]);
title('Global Field Power'), xlabel('')

% Plot TRF
subplot(2,2,3), mTRFplot(model,'trf','all',85,[-50,350]);
title('Speech TRF (Fz)'), ylabel('Amplitude (a.u.)')

% Plot GFP
subplot(2,2,4), mTRFplot(model,'gfp','all','all',[-50,350]);
title('Global Field Power')

Stimulus reconstruction

Here, we build a neural decoder that can reconstruct the envelope of the speech stimulus heard by the EEG participant. First, we downsample the data and partition it into 6 equal segments for training (segments 2 to 6) and testing (segment 1).

% Load data

% Normalize and downsample data
stim = resample(sum(stim,2),64,fs);
resp = resample(resp/std(resp(:)),64,fs);
fs = 64;

% Partition data into training/test sets
nfold = 6; testTrial = 1;
[strain,rtrain,stest,rtest] = mTRFpartition(stim,resp,nfold,testTrial);

To optimize the decoders ability to predict stimulus features from new EEG data, we tune the regularization parameter using an efficient leave-one-out cross-validation (CV) procedure.

% Model hyperparameters
Dir = -1; % direction of causality
tmin = 0; % minimum time lag (ms)
tmax = 250; % maximum time lag (ms)
lambda = 10.^(-6:2:6); % regularization parameters

% Run efficient cross-validation
cv = mTRFcrossval(strain,rtrain,fs,Dir,tmin,tmax,lambda,'zeropad',0,'fast',1);

Based on the CV results, we train our model using the optimal regularization value and test it on the held-out test set. Model performance is evaluated by measuring the correlation between the original and predicted stimulus.

% Find optimal regularization value
[rmax,idx] = max(mean(cv.r));

% Train model
model = mTRFtrain(strain,rtrain,fs,Dir,tmin,tmax,lambda(idx),'zeropad',0);

% Test model
[pred,test] = mTRFpredict(stest,rtest,model,'zeropad',0);

We plot the CV metrics as a function of regularization and the test results of the final model. This example can also be generated using stimulus_reconstruction.

% Plot CV accuracy
subplot(2,2,1), errorbar(1:numel(lambda),mean(cv.r),std(cv.r)/sqrt(nfold-1),'linewidth',2)
set(gca,'xtick',1:nlambda,'xticklabel',-6:2:6), xlim([0,numel(lambda)+1]), axis square, grid on
title('CV Accuracy'), xlabel('Regularization (1\times10^\lambda)'), ylabel('Correlation')

% Plot CV error
subplot(2,2,2), errorbar(1:numel(lambda),mean(cv.err),std(cv.err)/sqrt(nfold-1),'linewidth',2)
set(gca,'xtick',1:nlambda,'xticklabel',-6:2:6), xlim([0,numel(lambda)+1]), axis square, grid on
title('CV Error'), xlabel('Regularization (1\times10^\lambda)'), ylabel('MSE')

% Plot reconstruction
subplot(2,2,3), plot((1:length(stest))/fs,stest,'linewidth',2), hold on
plot((1:length(pred))/fs,pred,'linewidth',2), hold off, xlim([0,10]), axis square, grid on
title('Reconstruction'), xlabel('Time (s)'), ylabel('Amplitude (a.u.)'), legend('Orig','Pred')

% Plot test accuracy
subplot(2,2,4), bar(1,rmax), hold on, bar(2,test.r), hold off
set(gca,'xtick',1:2,'xticklabel',{'Val.','Test'}), axis square, grid on
title('Model Performance'), xlabel('Dataset'), ylabel('Correlation')

Single-lag decoder analysis

Here, we evaluate the contribution of individual time lags towards stimulus reconstruction using a single-lag decoder analysis. First, we downsample the data and partition it into 5 equal segments.

% Load data

% Normalize and downsample data
stim = resample(sum(stim,2),64,fs);
resp = resample(resp/std(resp(:)),64,fs);
fs = 64;

% Generate training/test sets
nfold = 10;
[strain,rtrain] = mTRFpartition(stim,resp,nfold);

We run a leave-one-out cross-validation to test a series of single-lag decoders over the range 0 to 1000 ms using a pre-tuned regularization parameter.

% Run single-lag cross-validation
[stats,t] = mTRFcrossval(strain,rtrain,fs,-1,0,1e3,10.^-2,'type','single','zeropad',0);

% Compute mean and variance
macc = squeeze(mean(stats.r))'; vacc = squeeze(var(stats.r))';
merr = squeeze(mean(stats.err))'; verr = squeeze(var(stats.err))';

% Compute variance bound
xacc = [-fliplr(t),-t]; yacc = [fliplr(macc-sqrt(vacc/nfold)),macc+sqrt(vacc/nfold)];
xerr = [-fliplr(t),-t]; yerr = [fliplr(merr-sqrt(verr/nfold)),merr+sqrt(verr/nfold)];

We plot the reconstruction accuracy and error as a function of time lags. This example can also be generated using single_lag_analysis.

% Plot accuracy
subplot(1,2,1), h = fill(xacc,yacc,'b','edgecolor','none'); hold on
set(h,'facealpha',0.2), xlim([tmin,tmax]), axis square, grid on
plot(-fliplr(t),fliplr(macc),'linewidth',2), hold off
title('Reconstruction Accuracy'), xlabel('Time lag (ms)'), ylabel('Correlation')

% Plot error
h = fill(xerr,yerr,'b','edgecolor','none'); hold on
set(h,'facealpha',0.2), xlim([tmin,tmax]), axis square, grid on
plot(-fliplr(t),fliplr(merr),'linewidth',2), hold off
title('Reconstruction Error'), xlabel('Time lag (ms)'), ylabel('MSE')


BSD 3-Clause License


A MATLAB Package for Relating Neural Signals to Continuous Stimuli




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