Associations.jl

Associations

Associations.jl is a package for quantifying associations, independence testing and causal inference.

All further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.

Key features

• Association API: includes measures and their estimators for pairwise, conditional and other forms of association from conventional statistics, from dynamical systems theory, and from information theory: partial correlation, distance correlation, (conditional) mutual information, transfer entropy, convergent cross mapping and a lot more!
• Independence testing API, which is automatically compatible with every association measure estimator implemented in the package.
• Causal (network) inference API integrating the association measures and independence testing framework.

Addititional features

Extending on features from ComplexityMeasures.jl, we also offer

• Discretization API for multiple (multivariate) input datasets.
• Multivariate counting and probability estimation API.
• Multivariate information measure API

Installation

To install the package, run import Pkg; Pkg.add("Associations").

Previously, this package was called CausalityTools.jl.

StateSpaceSet{D, T} <: AbstractStateSpaceSet{D,T}

A dedicated interface for sets in a state space. It is an ordered container of equally-sized points of length D. Each point is represented by SVector{D, T}. The data are a standard Julia Vector{SVector}, and can be obtained with vec(ssset::StateSpaceSet). Typically the order of points in the set is the time direction, but it doesn't have to be.

When indexed with 1 index, StateSpaceSet is like a vector of points. When indexed with 2 indices it behaves like a matrix that has each of the columns be the timeseries of each of the variables. When iterated over, it iterates over its contained points. See description of indexing below for more.

StateSpaceSet also supports almost all sensible vector operations like append!, push!, hcat, eachrow, among others.

Description of indexing

In the following let i, j be integers, typeof(X) <: AbstractStateSpaceSet and v1, v2 be <: AbstractVector{Int} (v1, v2 could also be ranges, and for performance benefits make v2 an SVector{Int}).

• X[i] == X[i, :] gives the ith point (returns an SVector)
• X[v1] == X[v1, :], returns a StateSpaceSet with the points in those indices.
• X[:, j] gives the jth variable timeseries (or collection), as Vector
• X[v1, v2], X[:, v2] returns a StateSpaceSet with the appropriate entries (first indices being "time"/point index, while second being variables)
• X[i, j] value of the jth variable, at the ith timepoint

Use Matrix(ssset) or StateSpaceSet(matrix) to convert. It is assumed that each column of the matrix is one variable. If you have various timeseries vectors x, y, z, ... pass them like StateSpaceSet(x, y, z, ...). You can use columns(dataset) to obtain the reverse, i.e. all columns of the dataset in a tuple.