Glossary of Terms
The glossary provides short definitions of vocabulary specific to pyspi and general statistical concepts. If you think a term is missing, please consider opening a pull request to add it.
Multivariate Time Series (MTS)
Multivariate time-series. As the name suggests, a MTS dataset comprises multiple variables (processes), each consisting of a fixed number of observations (samples). Each variable in the dataset is a time series itself, and these variables may or may not be related to one another.
Keywords
For each SPI, we associate a small number of keywords to help users understand the key assumptions of the interactions they measure. If you would like to filter SPIs based on their corresponding keywords, see here. The following table summarises the keywords and provides a short description of each:
| Keyword | Description |
|---|---|
| Measures that do not specify a direction of influence or flow between time series. They assess the strength or presence of a relationship without indicating which series is influencing the other. |
| Measures that identify the direction of influence or causal relationship between time series. They determine not only the presence, but also the direction of interaction from one time-series to the other. |
| Measures that assume a linear relationship between time series. These methods are most effective when changes in one series proportionally affect the other series in a consistent manner. |
| Measures that do not assume a linear relationship between time series. These measures are used when the relationship between series is complex and cannot be adequately described by linear models. |
| Some SPIs can take a positive or negative value. For example, correlation coefficients are signed as they can take a value within [-1, 1]. Other SPIs, such as distance correlation (defined in the range [0,1]) are unsigned. This keyword refers to whether the sign of the SPI indicates how fluctuations in time series A correspond to that of time series B. |
| Refers to a single time series measurement. |
| Refers to measures that involve two time series (i.e., pairs of time-series). |
| Refers to measures that involve more than two time series. |
| Measures that focus on relationships or interactions occurring at the same point across time series. |
| Measures that analyse how relationships between time series evolve over time. |
| Measures that analyse relationships in the frequency domains. |
| Measures that analyse relationships in both the time and frequency domain. |
Directed SPIs
Some of the SPIs are directed, meaning that the value from process A to process B will be computed separately to the value from process B to process A. This generally results in asymmetric matrices, which can be useful for analysing the directionality of interactions.
As an example, consider the SPI di_gaussian which measures the directed information from process A to process B using a Gaussian density estimator, and an MTS consisting of three processes (e.g., three brain regions). The table returned by computing this SPI will be a 3x3 matrix, where entry calc.table['di_gaussian'][0,1] will be the directed information from process 0 to process 1. The rows in this table reflect the sources while the columns reflect the targets, as schematically depicted below:
Modifiers
Many of the algorithms we implement include a number of free parameters that we set either using optimisation procedures or fix to a small number of sensible predefined settings. The combination of both the parameter configuration and the different summary statistics gives each SPI in the library a unique identifier (as a string).
As an example, consider the SPI identifier xcorr_mean_sig-True. Here, xcorr refers to the method of cross-correlation between x and y, which itself does not provide a single statistic, but rather a correlogram. However, the two additional modifiers that are separated by underscores in the identifier, mean and sig-True, collectively return a scalar value. The first modifier, mean indicates that we are taking the average across lags of the cross-correlation function. The second modifier, sig-True indicates that we will only take the mean over statistically significant lags.
By using different parameters and modifiers of distinct methodologies, we obtain hundreds of SPIs.
Matrix of Pairwise Interactions (MPI)
An M-by-M square matrix of pairwise interactions for M-variate time-series that is obtained by computing a single SPI. For undirected SPIs, this matrix will be symmetric about the diagonal, that is, entry [i, j] will be equal to entry [j, i]. On the other hand, for directed SPIs, the MPI will generally be asymmetric.
Last updated
