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, V} <: AbstractVector{V}

A dedicated interface for sets in a state space. It is an ordered container of equally-sized points of length D, with element type T, represented by a vector of type V. Typically V is SVector{D,T} or Vector{T} and the data are always stored internally as Vector{V}. SSSet is an alias for StateSpaceSet.

The underlying Vector{V} can be obtained by vec(ssset), although this is almost never necessary because StateSpaceSet subtypes AbstractVector and extends its interface. StateSpaceSet also supports almost all sensible vector operations like append!, push!, hcat, eachrow, among others. When iterated over, it iterates over its contained points.

Construction

Constructing a StateSpaceSet is done in three ways:

1. By giving in each individual columns of the state space set as Vector{<:Real}: StateSpaceSet(x, y, z, ...).
2. By giving in a matrix whose rows are the state space points: StateSpaceSet(m).
3. By giving in directly a vector of vectors (state space points): StateSpaceSet(v_of_v).

All constructors allow for the keyword container which sets the type of V (the type of inner vectors). At the moment options are only SVector, MVector, or Vector, and by default SVector is used.

Description of indexing

When indexed with 1 index, StateSpaceSet behaves exactly like its encapsulated vector. i.e., a vector of vectors (state space points). When indexed with 2 indices it behaves like a matrix where each row is a point.

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.