Sometimes we might find that the states "do not mix well", that is, the state assignment is dominated by between-subject differences and fails to capture the within-session dynamics. For example, when looking at fMRI data, this might happen when the static functional connectivity is too distinct between subjects.
In order to measure this, the function corrStaticFC computes the subjects by subjects matrix of static FC similarities measured in terms of correlation between each pair of subjects. If this value is too high too close to 1. An important option when dealing with large data sets is pca , which can be used to reduce dimensionality. Although these are outputs of the hmmmar function, they can also be estimated separately, once we have the HMM-MAR structure, using the function hmmdecode. Importantly, you can use this function to track the estimated states in a different data set that is, data and T do not need to be the same than in training.
Further details about the format of the inputs were provided in the Format of the inputs section. If we are dealing with task data, we can obtain the evoked state probabilities given certain task.
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For example, in Vidaurre et al. Given some vector stimulus time points by one containing when the subject pressed the button 1 indicating the data points when that happened and 0 otherwise , we can obtain task-locked state time courses by. To get around this issue, one possibility is to work in a low-dimensional space that represents the data as faithfully as possible. In the toolbox, the possibility of working in PCA space is implemented. The parameter options. There are various options to specify it. If options. It can also accept the option of specifying both, in a two elements vector where the first element is the amount of variance and the second is the number of components.
In this case, it will use the minimum of the two. Finally, if options. The state spectra can be computed using either a parametric MAR or a non-parametric approach. For more information about these, check the Theory Section, or, for even more detail, refer to Vidaurre et al. Note that for the parametric approach PDC is estimated by default, whereas for the non-parametric approach PDC is not estimated by default for computational reasons see below.
If the struct hmm is specified using the output of hmmmar , then the MAR spectra will be computed from the parameters within hmm ; in this case, X , T and Gamma can be left empty. If hmm is left empty or unspecified, the MAR parameters will be recomputed using maximum likelihood, in which case X , T and Gamma are mandatory. The rest of the arguments of options e. The variable fit contains a struct array struct with K elements, each of which contains:. The part related to the multitaper calculation is inspired by the code in the Chronux toolbox. Once all the spectra is computed either way, we use the evoked state probabilities given certain task see above to build a HMM-based time-frequency representation.
The same can be done on resting-state data for a any given fragment of the state time courses. This is done by. Once we have run the inference process on the entire data, we have state time courses for each subject and group-level states i. In some cases, we may be also interested on the specific manifestation of the states for each subject, in terms of their state distribution representation e. MAR or in terms of their spectral properties. To obtain subject-specific states we just need to use the state time courses for a particular subject and re-infer the states given such state time courses.
From there we can estimate subject-specific spectral information. The basic state distribution is the Gaussian model, of which the MAR model can be considered an extension. Some basic intuition about when to use what is given in the General Guidelines above. One possibility to alleviate these issues is to model only the within-channel AR coefficients, such that we do not model the cross-channel interactions and focus on the spectral properties of the individual channels see section Targeting specific connections.
The idea is that we model the main principal components eigenvectors of a Gaussian distribution defined not only over space but also over a window of time around the point of interest.
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This approach, inspired by and related to the theory of Gaussian processes, can capture both spatial and spectral properties without overfitting. The limitation is that the use of dimensionality reduction over this space x time by space x time matrices that represent the states makes the approach to be relatively blind to the high frequencies. In order to use this approach, we would need to specify:. The states are thus defined in time and space and contain spectral information.
To retrieve this spectral information, we can use hmmspectramt , described in section Computing the state spectra. Intuitively, using a larger window options. On the contrary, reducing this window will help to identify high frequencies. Likewise, having mode PCA components will include more information about the high frequencies. Temporal unconstrained decoding analysis, or TUDA, can be used to track trial-specific neural dynamics of stimulus processing and decision making with high temporal precision, addressing a major limitation of the traditional decoding approach: that it relies on consistent timing of these processes over trials.
Here, unlike the standard HMM, each state is a decoding model, which predicts the stimulus as a function of brain activity. The main function to perform this analysis is invoked as. Many of the options that can be specified in the options struct match those of the HMM explained above, although stochastic inference is not yet implemented for TUDA. Apart from the preprocessing options go here for details , the main options for TUDA specified as fields in options are:. Here, beta is a no.
Also, it is possible to recompute the state time courses or apply the TUDA decoding models to a different data set , using a precomputed tuda model obtained with tudatrain :. Importantly, each state corresponds to a standard Bayesian regression model. That is, the response is treated as a continuous variable i. In practice, this means that the model is not optimally suited to decode a categorical variable. Exceptionally, given the correspondence between linear regression and linear discriminant analyses, a binary variable e.
If the stimulus is categorical and has more than two values, then the best option currently is to codify it using dummy variables; that is, using a time by no. The implementation of a logistic regression observational model in order to deal more naturally with categorical data is work in progress at the moment. In modelling fMRI, we might be mainly interested in functional connectivity.
Although the assessment of functional connectivity is never free from amplitude modulations, we can place more emphasis on the former by using an appropriate observation model. More specifically, the time series to be HMM-segmented correspond to the first eigenvector main trend of these functional connectivity matrices, which are estimated using the Hilbert transformation time point by time point. In order to use LEiDA, we need to specify:. In Cabral et al. That opens the possibility of using either options.
The use of LEiDA is not compatible with options. S , and state-specific covariance matrices are not recommended. We next introduce some advanced topics. These basically are some specific options and features that you might not need in all cases. Most importantly, the options to use stochastic inference are described for those cases when training the HMM is too computationally costly either memory or computation time. Assuming the data is divided into different conditions e. The function receives a no. In either case, permutations are done at the subject level, and the statistic used to evaluate the surrogates and unpermuted data is the squared error.
The HMM variational inference iteratively estimates the state distributions and the state time courses from data. When the data set is very large, estimating the state time courses which can be parallelizable across trials but requires sequential computations within each trial can take a significant amount of time. Likewise, the estimation of the state distributions needs to have the entire data set in memory, which in turn can take a significant amount of space in memory and can potentially lead to time-consuming memory swapping.
For this case, an alternative stochastic inference scheme is included in the toolbox. Details apart, this is based on taking subsets or batches of subjects at each iteration instead of the entire data set. Stochastic inference will be run when the parameter options. BIGNbatch is specified. This parameter indicates the amount of subject in each batch.
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A very small number e. A higher number approaching the total number of subjects will resemble the non-stochastic inference. In practice, a small but not too small number will provide good solutions at a cheap cost. For example, for the HCP resting-state fMRI data set, which has up to subjects, we found 50 to be a good trade-off. More details about the algorithm and the experiments are provided in the NeuroImage paper.
Another relevant aspect is the initialisation. The initialisation for the stochastic inference method is implemented by running the standard inference on subsets of subjects, and combine all runs see the paper for more details. Importantly, when stochastic inference is used, the parameters cyc , tol , inittype , initrep and initcyc refer only to this initialisation step.
The size of these subsets of subjects on which we build the initial model is specified by the parameter BIGNinitbatch. Although options. BIGNbatch and secondarily BIGNinitbatch are the most relevant parameters, there are other parameters which have a modest impact in the inference. Importantly, if stochastic inference is to be used, the inputs both data and T ; see above must be specified as a cell, with one element per subject.
Semisupervised prediction is also done using the hmmmar function, but the first argument data is instead specified as a struct, with fields X time series; with dimension no. Some rows of C will be vectors with values between 0 and 1, and summing up to 1.
These will be interpreted as fixed values of the state time courses and will remain unmodified. The rest of the elements of C must be specified as NaN, indicating that the state time courses must be estimated at these time points. Note that if the MAR order is higher than 0, the first order rows of each trial of C will be ignored. This is implemented using the option options. If the position i,j is -1 then the autoregression coefficients that predict channel j from channel i are not modelled for example, if all off-diagonal elements of S are -1, then the model would be an ensemble of unrelated AR models.
If the position i,j is 1, the corresponding coefficients are modelled normally, i. If the position i,j is 0, the corresponding coefficients are modelled globally, i. In the current version, this is implemented only for diag or uniquediag error covariance matrices parameter covtype. The main hmmmar function provides the history of the free energy throughout the variational inference process. We can recompute the free energy using hmmfe. The value obtained may be slightly lower than the final free energy calculation during training.
This is because unless supplied the state time courses are recomputed once more within hmmfe , as they are necessary for the free energy calculation. Therefore, that could be considered as an additional iteration of the inference process, and, thus, will reduce the free energy a little extra amount. Cross-validation is an alternative to the free energy for model selection of the MAR parameters yet not of K , more principled but computationally more demanding. In order to manipulate the configuration of the MAR lags, there are two functions that can be useful.
The first provides the set of lags and the maximum lag for the configuration specified by the input parameters see the hmmmar function for more information about those. The second, provided with the slowest frequency we want to cover minHz , the sampling rate of the data Fs , the number of desired lags L and the offset orderoffset , check the HMM-MAR parameters above for more details , returns the corresponding order and exptimelag parameters that we need to specify using an exponential lapse.
In general, based on our latest experience it is preferable to work with a low order and avoid using exptimelag or orderoffset if possible. This step is however not necessary if working with the power time series by setting options. Skip to content. Dismiss Join GitHub today GitHub is home to over 40 million developers working together to host and review code, manage projects, and build software together. Sign up. User Guide Jump to bottom. This is explained in the section Temporal unconstrained decoding analysis Another consideration somewhat related to the choice of model and the data modality is the use of bandpass filtering.
Gamma : a no. Note that if the MAR order is higher than 0, Gamma has less rows than data because the first order time points of each trial do not have an associated state time course estimation. Xi has one row less per trial than Gamma. GammaInit : the state time courses used after initialisation. The structure options has, or can have, the following fields: K : maximum number of HMM states mandatory, with no default. Fs : Sampling frequency default to 1.
To check which past samples will be used, use the function formorders ; for finding out which value of exptimelag is needed to cover until certain frequency using a given number of lags, use higherorder. If a value for exptimelag higher than 1 is specified, then timelag is ignored. This parameter becomes particularly useful in situations of strong autocorrelations, as for example in MEG default to 0. DirichletDiag : value of the diagonal of the prior of the transition probability matrix; the higher, the more persistent the states will be default to Note that this value is relative; the prior competes with the data, in such a way that if we have very long time series, DirichletDiag will have an irrelevant effect unless is set to a very big value.
If hpc is 0, it will only apply a lowpass filter; if lpc is Inf , it will only apply a highpass filter. Examples: options. The default is .
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See section Targeting specific connections below. The algorithm with stop earlier if tol is reached. Default to Gamma : initial estimate for the states probabilities; if provided the initialisation procedure will not be run optional hmm : initial estimate for the HMM-MAR structure; this is typically used as a warm restart using the output of a previous run as a starting point.
DirStats : if supplied with a directory name, information about the computation time of the run will be saved therein. Format of the inputs The input data comes in two variables: data and T. The time series data can be supplied in the following formats: A no. The file can be either a text file. Structure of the HMM-MAR object The states are described by i the distribution of the MAR autoregressive coefficients and mean if modelled , which expected value for state k is provided in hmm.
The HMM-MAR structure hmm has the following fields: state : a struct array with the posterior and prior distributions of each state see below. K : the number of inferred states note that this number can be lower than the specified K , because some states were dropped.
Pi : the K X 1 initial state probabilities. Omega : the parameters of the distribution of the covariance matrix, if modelled globally. Omega : the parameters of the distribution of the covariance matrix that models the error, if this is modelled statewise. Preprocessing The toolbox offers a few basic preprocessing options: Filtering: the toolbox offers to possibility of filtering the data using a Butterworth lowpass, highpass or bandpass filter, by specifying options. Analysis of the results The HMM inference provides the state time courses Gamma indicating the probability of each state to be active at each time point, and the description of the probability distribution of each state.
Estimation of the state time courses and Viterbi path Although these are outputs of the hmmmar function, they can also be estimated separately, once we have the HMM-MAR structure, using the function hmmdecode. Output arguments Gamma : a no. Evoked State Probabilities If we are dealing with task data, we can obtain the evoked state probabilities given certain task. Computing the state spectra The state spectra can be computed using either a parametric MAR or a non-parametric approach.
Input arguments X : a no. Nf : no. Using this option is only possible when the MAR models are to be recomputed, i. Output arguments The variable fit contains a struct array struct with K elements, each of which contains: psd : Nf x no. GS continues: My point was that maybe what is needed is a direct experimental investigation of relevant variables instead of an elaborate theory.
Why guess when you can just determine something directly through experiment? The whole paper seems to me to have been based on a shot-in-the-dark approach to science, where the investigators combined weak theory, sloppy experimentation, and noisy data in the vague hope that something interesting would come up.
The above paragraph expresses no allegiance to the hypothetico-deductive method or whatever. It just expresses a distrust for a certain approach to scientific inquiry which unfortunately has become all too common in psychology research. The actual post to which I am responding is contained in my post:. GS: Right. His immediate response was to delve into creating a complex-sounding model and testing it. The description would have been at home — except for the technical language — in the early chapters of a Psych text…you know, the parts where they tell the student what science is and why psychology is a science.
My point was merely that the phenomena described however rich or faulty , if real, might be investigated directly by manipulation of relevant independent-variables. If I had to take their side as I see it after translating but traduttore traditore from ordinary language into the language of known behavioral processes, I would say that what they say is reasonable ordinary-language wise.
What is very likely, in that circumstance, is escape in possibly subtle forms e. Things that you have said elsewhere on this blog also point in that direction. The whole series of posts started with my contrasting one way of doing science with another. I made a mistake in my comment above. The paper under discussion was not actually published in Psychological Science.
Do faculty at Harvard University actually let their students run studies with such supposedly planned small sample sizes? Also, if you are going to hang your hand on the NHST framework you should probably used a one-tailed t-test for the replication study study 3 that is based on the results from Study 2. Of course, then your supposed replication would really show a failure to replicate. Remember: Amy Cuddy taught at Harvard! Well, we should be thankful for small mercies. They could have used a post hoc justification for a one-tailed t test to cut their p values of. Instead, they just continued as if those were statistically significant.
Presumably I missed the point where they stated they were using an alpha level of. To be fair and critical at the same time. This study has a serious logical problem.
The statement was false; the joystick did not actually measure galvanic skin response. The researchers assumed that the subjects would take this time to reflect on their bias or not. This would probably distract me for the remainder of the study and influence my responses. There is a big difference between the two. The subjects may have been reacting to the idea that their galvanic skin response had being measured without their knowledge.
There are several questions in their questionnaire that measure the same or similar outcomes, and almost none of them show a significant difference. The authors did a handful of uncorrected t-tests, picked the single barely significant result, and then claim that they had predicted it all along. Later on, the third study actually fails to replicate study 2, but the authors claim that it does anyway. A terrible paper all around.
Most experiments described in a paper that starts with an excerpt of a poem, or novel, will fail to replicate. Does it make the paper look all fancy and intellectual or something? Also, all three tables contain a couple granularity errors, Table 1 is straight up just missing a couple statistics that copyediting value , and the degrees in Table 2 should be F 3, 73 instead of F 1, Mail will not be published.
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