ScientificTypesBase.jl

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A light-weight, dependency-free, Julia interface defining a collection of types (without instances) for implementing conventions about the scientific interpretation of data.

This package makes a distinction between the machine type and scientific type of a Julia object:

• The machine type refers to the Julia type being used to represent the object (for instance, Float64).

• The scientific type is one of the types defined in this package reflecting how the object should be interpreted (for instance, Continuous or Multiclass{3}).

The distinction is useful because the same machine type is often used to represent data with differing scientific interpretations - Int is used for product numbers (a factor) but also for a person's weight (a continuous variable) - while the same scientific type is frequently represented by different machine types - both Int and Float64 are used to represent weights, for example.

For implementation of a concrete convention assigning specific scientific types (interpretations) to julia objects, see instead the ScientificTypes.jl package.

Formerly "ScientificTypesBase.jl" code lived at "ScientificTypes.jl". Since version 2.0 the code at "ScientificTypes.jl" is code that formerly resided at "MLJScientificTypes.jl" (now deprecated).

Finite{N}
├─ Multiclass{N}
└─ OrderedFactor{N}

Infinite
├─ Continuous
└─ Count

Image{W,H}
├─ ColorImage{W,H}
└─ GrayImage{W,H}

ScientificTimeType
├─ ScientificDate
├─ ScientificTime
└─ ScientificDateTime

Sampleable{Ω}
└─ Density{Ω}

Annotated{S}

AnnotationFor{S}

Multiset{S}

Table{K}

Textual

ManifoldPoint{MT}

Compositional{D}

Unknown

Figure 1. The type hierarchy defined in ScientificTypesBase.jl (The Julia native Missing and Nothing type are also regarded as a scientific types).

Contents

• Who is this repository for?
• What's provided here?
• Defining a new convention

Who is this repository for?

This package should only be used by developers who intend to define their own scientific type convention. The ScientificTypes.jl package (versions 2.0 and higher) implements such a convention, first adopted in the MLJ universe, but which can be adopted by other statistical and scientific software.

The purpose of this package is to provide a mechanism for articulating conventions around the scientific interpretation of data. With such a convention in place, a numerical algorithm declares its data requirements in terms of scientific types, the user has a convenient way to check compliance of his data with that requirement, and the developer understands precisely the constraints his data specification places on the actual machine type of the data supplied.

What is provided here?

1. Scientific types

ScientificTypesBase provides the new julia types appearing in Figure 1 above, signifying "scientific type" for use in method dispatch (e.g., for trait values). Instances of the types play no role.

The types Finite{N}, Multiclass{N} and OrderedFactor{N} are all parametrised by the number of levels N, while Image{W,H}, GrayImage{W,H} and ColorImage{W,H} are all parametrised by the image width and height dimensions, (W, H). The parameter Ω in Sampleable{Ω} and Density{Ω} is the scientific type of the sample space. The type ManifoldPoint{MT}, intended for points lying on a manifold, is parameterized by the type MT of the manifold to which the points belong.

The scientific type ScientificDate is for representing dates (for example, the 23rd of April, 2029), ScientificTime represents time within a 24-hour day, while ScientificDateTime represents both a time of day and date. These types mirror the types Date, Time and DateTime from the Julia standard library Dates (and indeed, in the convention defined in ScientificTypes.jl the difference is only a formal one).

The type parameter K in Table{K} is for conveying the scientific type(s) of a table's columns. See More on the Table type.

The julia native types Missing and Nothing are also regarded as scientific types.

2. The scitype and Scitype methods

ScientificTypesBase provides a method scitype for articulating a particular convention: scitype(X, C()) is the scientific type of object X under convention C. For example, in the DefaultConvention convention, implemented by ScientificTypes, one has scitype(3.14, Defaultconvention()) = Continuous and scitype(42, Defaultconvention()) = Count.

Aside. scitype is not a mapping of types to types but from instances to types. This is because one may want to distinguish the scientific type of objects having the same machine type. For example, in the DefaultConvention implemented in ScientificTypes.jl, some CategoricalArrays.CategoricalValue objects have the scitype OrderedFactor but others are Multiclass. In CategoricalArrays.jl the ordered attribute is not a type parameter and so it can only be extracted from instances.

The developer implementing a particular scientific type convention overloads the scitype method appropriately. However, this package provides certain rudimentary fallback behaviour:

Property 0. For any convention C, scitype(missing, C()) == Missing and scitype(nothing, C()) == Nothing (regarding Missing and Nothing as native scientific types).

Property 1. For any convention C scitype(X, C()) == Unknown, unless X is a tuple, an abstract array, nothing, or missing.

Property 2. For any convention C, The scitype of a k-tuple is Tuple{S1, S2, ..., Sk} where Sj is the scitype of the jth element under convention C.

For example, in the Defaultconvention convention implemented by ScientificTypes:

julia> scitype((1, 4.5), Defaultconvention())
Tuple{Count, Continuous}

Property 3. For any given convention C, the scitype of an AbstractArray, A, is alwaysAbstractArray{U} where U is the union of the scitypes of the elements of A under convention C, with one exception: If typeof(A) <:AbstractArray{Union{Missing,T}} for some T different from Any, then the scitype of A is AbstractArray{Union{Missing, U}}, where U is the union over all non-missing elements under convention C, even if A has no missing elements.

This exception is made for performance reasons. In DefaultConvention implemented by ScientificTypes:

julia> v = [1.3, 4.5, missing]
julia> scitype(v, DefaultConvention())
AbstractArray{Union{Missing, Continuous}, 1}

julia> scitype(v[1:2], DefaultConvention())
AbstractArray{Union{Missing, Continuous},1}

Performance note. Computing type unions over large arrays is expensive and, depending on the convention's implementation and the array eltype, computing the scitype can be slow. In the common case that the scitype of an array can be determined from the machine type of the object alone, the implementer of a new connvention can speed up compututations by implementing a Scitype method. Do ?ScientificTypesBase.Scitype for details.

More on the Table type

An object of scitype Table{K} is expected to have a notion of "columns", which are AbstractVectors, and the intention of the type parameter K is to encode the scientific type(s) of its columns. Specifically, developers are requested to adhere to the following:

Tabular data convention. If scitype(X, C()) <: Table, for a given convention C then in fact

scitype(X, C()) == Table{Union{scitype(c1, C), ..., scitype(cn, C)}}

where c1, c2, ..., cn are the columns of X. With this definition, common type checks can be performed with tables. For instance, you could check that each column of X has an element scitype that is either Continuous or Finite:

scitype(X, C()) <: Table{<:Union{AbstractVector{<:Continuous}, AbstractVector{<:Finite}}}

A built-in Table constructor provides a shorthand for the right-hand side:

scitype(X, C()) <: Table(Continuous, Finite)

Note that Table(Continuous, Finite) is a type union and not a Table instance.

Defining a new convention

If you want to implement your own convention, you can consider the ScientificTypes.jl as a blueprint.

The steps below summarise the possible steps in defining such a convention:

• declare a new convention,
• add explicit scitype (and Scitype) definitions,
• optionally define coerce methods for your convention

Each step is explained below, taking DefaultConvenion as an example.

Naming the convention

In the module, define a singleton as thus

struct MyConvention <: ScientificTypesBase.Convention end

Adding explicit scitype declarations.

When overloading scitype one needs to dipatch over the convention, as in this example:

ScientificTypesBase.scitype(::Integer, ::MyConvention) = Count

To avoid method ambiguities, avoid dispatching only on the first argument. For example, defining

ScientificTypesBase.scitype(::AbstractFloat, C) = Continous

would lead to ambiguities in another package defining

ScientificTypesBase.scitype(a, ::MyConvention) = Count

Since ScientificTypesBase.jl does not define a single-argument scitype(X) method, an implementation of a new scientific convention will typically want to explicitly implement the single argument method in their package, to save users from needing to explicitly specify a convention. That is, so the user can call scitype(2.3) instead of scitype(2.3, MyConvention()).

For example, one declares:

scitype(X) = scitype(X, MyConvention())

Defining a coerce function

It may be very useful to define a function to coerce machine types so as to correct an unintended scientific interpretation, according to a given convention. In the DefaultConvention convention, this is implemented by defining coerce methods (no stub provided by ScientificTypesBase)

For instance consider the simplified:

function coerce(y::AbstractArray{T}, T2::Type{<:Union{Missing, Continuous}}
                ) where T <: Union{Missing, Real}
    return float(y)
end

Under this definition, coerce([1, 2, 4], Continuous) is mapped to [1.0, 2.0, 4.0], which has scitype AbstractVector{Continuous}.

In the case of tabular data, one might additionally define coerce methods to selectively coerce data in specified columns. See ScientificTypes for examples.