Overhaul of Algebraic Statistics

experimental/AlgebraicStatistics/README.md

@@ -14,19 +14,19 @@ new functionality.
 
 ## Status
 
-- [ ] Conditional independence models
-  - [ ] Gaussian ideals
+- [X] Conditional independence models
+  - [X] Gaussian ideals
   - [X] Discrete ideals
-- [ ] Directed graphical models (Bayesian networks)
-  - [ ] Markov properties
-  - [ ] Trek separation
+- [X] Directed graphical models (Bayesian networks)
+  - [X] Markov properties
+  - [X] Trek separation
   - [X] Gaussian parametrization
-  - [ ] Discrete parametrization
+  - [X] Discrete parametrization
 - [X] Undirected graphical models (Markov networks)
-  - [ ] Markov properties
+  - [X] Markov properties
   - [X] Gaussian parametrization
-  - [ ] Discrete parametrization
-- [ ] Phylogenetics
+  - [X] Discrete parametrization
+- [X] Phylogenetics
   - [X] Cavender--Farris--Neyman model
   - [X] Jukes--Cantor model
   - [X] Kimura2 / Kimura3

experimental/AlgebraicStatistics/docs/doc.main

@@ -1,11 +1,11 @@
 [
    "Algebraic Statistics" => [
-      "introduction.md",
-      "graphical_models.md",
-      "gaussian_graphical_models.md",
-      "ci.md",
-      "markov.md",
-      "phylogenetics.md",
-      "multigraded_implicitization.md",
+     "introduction.md",
+     "graphical_models.md",
+     "gaussian_graphical_models.md",
+     "markov.md",
+     "phylogenetics.md",
+     "ci.md",
+     "multigraded_implicitization.md"
    ]
 ]

experimental/AlgebraicStatistics/docs/src/ci.md

@@ -21,10 +21,11 @@ to define ideals. Their interpretations as polynomial equations depend
 on the ambient ring ([`markov_ring`](@ref) or [`gaussian_ring`](@ref)).
 
 ```@docs
-ci_stmt(I::Vector{<:VarName}, J::Vector{<:VarName}, K::Vector{<:VarName})
-@CI_str(str)
+ci_stmt
+@CI_str
 Base.:(==)(lhs::CIStmt, rhs::CIStmt)
 Base.hash(stmt::CIStmt, h::UInt)
-ci_statements(random_variables::Vector{<:VarName})
+ci_statements
+ci_ideal
 make_elementary(stmt::CIStmt; semigaussoid=false)
 ```

experimental/AlgebraicStatistics/docs/src/gaussian_graphical_models.md

@@ -6,52 +6,33 @@ DocTestSetup = Oscar.doctestsetup()
 
 # Gaussian Graphical Models
 
-The OSCAR type for graphical models is of parametrized form `GraphicalModel{G, T}` where `T` represents the type of ring in which the vanishing ideal of the model belongs and `G` represents the associated graph. Gaussian graphical models are those where the `T` is of type `GaussianRing` which is a multivariate polynomial ring equipped with some extra features.
-
-## Gaussian Rings
+Gaussian graphical model types are parametrized as `GaussianGraphicalModel{T, L}` where `T` represents the type of graph and `L` represents the labelings of the graph. The parameters `T` and `L` are determined by the graph used to construct the model.
 
 ```@docs
-gaussian_ring(n::Int; s_var_name::VarName="s", K::Field=QQ, cached=false)
-gens(R::GaussianRing)
-covariance_matrix(R::GaussianRing)
-```
-
-## Directed Gaussian Graphical Models
-
-A directed Gaussian graphical model is constructed from `G::Graph{Directed}` and `S::GaussianRing`. Optionally, the user may specify a string `l_var_name::String` which corresponds to the edge weights in the parametrization of the model and a string `w_var_name::String` for labeling the error covariance parameters.
-```@docs
-graphical_model(G::Graph{Directed}, S::GaussianRing; l_var_name::VarName="l", w_var_name::VarName="w", cached=false)
+gaussian_graphical_model
 ```
 
+## Directed Gaussian Graphical Model 
 The parametrization for a directed Gaussian graphical model on a DAG $G$ is built from the weighted adjacency matrix $\Lambda$ and the covariance matrix $\Omega$ of the error terms. The model is then the set of all covariance matrices $\Sigma = (Id - \Lambda)^{-T} \Omega (Id - \Lambda)^{-1}$. $\Lambda$ and $\Omega$ can be built with the following functions:
 ```@docs
-directed_edges_matrix(M::GraphicalModel{Graph{Directed}, GaussianRing})
-error_covariance_matrix(M::GraphicalModel{Graph{Directed}, GaussianRing})
+directed_edges_matrix
+error_covariance_matrix
 ```
 
-It is easy to create new types of graphical models by overloading the methods `directed_edges_matrix` and `error_covariance_matrix`. For instance, colored graphical models may easily be created by creating a new type of `GraphicalModel{G, T}` and a new `directed_edges_matrix` function. The following two functions will then work almost immediately on this new type.
-```@docs
-parametrization(M::GraphicalModel{Graph{Directed}, GaussianRing})
-vanishing_ideal(M::GraphicalModel{Graph{Directed}, GaussianRing})
-```
-
-With almost all graphical models, the vanishing ideal is computed by taking the kernel of the ring map given by `parametrization(M:GraphicalModel{G, T})`. 
-
 
 
-## Undirected Gaussian Graphical Models
+## Undirected Gaussian Graphical Model
+As with their directed counterpart, it is very easy to create new subtypes of graphical models by overloading the function `concentration_matrix` below. Unlike most other types of graphical models though, the vanishing ideal computation of an undirected graphical model is done by eliminating all concentration variables $k_{ij}$ from the ideal given by the equations $\Sigma K - Id$ after saturating by $\det(K)$. 
 
 
-A undirected Gaussian graphical model is constructed from `G::Graph{Undirected}`, `S::GaussianRing`. Optionally, the user may specify a string `k_var_name::String` which corresponds to the entries of the concentration matrix.
 ```@docs
-graphical_model(G::Graph{Undirected}, S::GaussianRing; k_var_name::VarName="k", cached=false)
+concentration_matrix
 ```
 
-As with their directed counterpart, it is very easy to create new subtypes of graphical models by overloading the function `concentration_matrix` below. Unlike most other types of graphical models though, the vanishing ideal computation of an undirected graphical model is done by eliminating all concentration variables $k_{ij}$ from the ideal given by the equations $\Sigma K - Id$ after saturating by $\det(K)$. 
 
+## Gaussian Rings
 
 ```@docs
-concentration_matrix(M::GraphicalModel{Graph{Undirected}, GaussianRing})
-parametrization(M::GraphicalModel{Graph{Undirected}, GaussianRing})
-vanishing_ideal(M::GraphicalModel{Graph{Undirected}, GaussianRing})
+gaussian_ring
+covariance_matrix
 ```

experimental/AlgebraicStatistics/docs/src/graphical_models.md

@@ -4,19 +4,35 @@ CollapsedDocStrings = true
 DocTestSetup = Oscar.doctestsetup()
 ```
 
-# Graphical Models
+# Abstract Graphical Model
 
-The OSCAR type for graphical models is of parametrized form `GraphicalModel{G, T}` where `T` represents the type of ring in which the vanishing ideal of the model belongs and `G` represents the associated graph. This parametrized typing allows the user to easily build upon the existing functionality to work with newer variations on graphical models such as those with colours or hidden variables. 
+Graphical models are a parametrized abstract type `GraphicalModel{T, L}` where `T` is the type of the graph and `L` is the type of labelings of the graph, this is either a `NamedTuple` type or `Nothing`. Being an abstract type there is no constructor for a graphical model. All graphical models are subtypes of `GraphicalModel`, and they inherit their type parameters from the graph that is passed to the constructor. See the section corresponding to the graphical model type you would like to work with. 
 
-Many basic functions are defined for all graphical models `M` such as
+## Attributes
 
-- `graph(M)` refers to the associated graph
-- `ring(M)` to the multivariate polynomial ring where the model resides
-- `param_ring` to the multivariate polynomial ring where the parameters reside
-- `param_gens` to the parameters of the model which are ring variables stored typically stored in a hash table for convenient indexing
+The following functions are attributes for all graphical models.
+```@docs
+model_ring(M::T) where T <: GraphicalModel
+parameter_ring(M::T) where T <: GraphicalModel
+parametrization(M::T) where T <: GraphicalModel
+```
+
+## Vanishing ideal
 
-This part of OSCAR also includes some basic graph functionality such as finding the vertices of a graph or its set of maximal cliques. Lastly, while many methods for graphical models depend heavily on whether or not they are discrete/Gaussian or directed/undirected some functionality is independent of this and thus implemented simultaneously for all graphical models. For example, the vanishing ideal of the model:
+Ensuring that any concrete graphical model (one that is a subtype of `GraphicalModel`) have implementations for the above attributes ensures
+that we can compute the vanishing ideal.
+In can be the case that certain graphical models will benefit from certain algorithms, and in those cases the `vanishing_ideal` will be overloaded for that specific type.
+In all other cases the vanishing ideal computation will fallback to this general function.
+There is a keyword argument for setting algorithm which is set to `:eliminate` by default, other possibilities are `:f4` and `:markov`.
 
+If you are only interested in generators up to a certain degree, considering using [`components_of_kernel`](@ref) with `parametrization`.
 ```@docs
-vanishing_ideal(M::GraphicalModel)
+vanishing_ideal(M::GraphicalModel; algorithm::Symbol = :eliminate)
 ```
+# Extending functionality
+
+One major design decision was to allow for the graphs and their labels to parametrize the graphical models. 
+This allows users to create their own graphical model types and gives them the possibility to overload the appropriate attribute functions.
+In this way, users can reuse the implementations for the functions defined for the abstract grpahical models, 
+which avoids code duplication and also allows for the application of theorems for specific types of graphical models.
+

experimental/AlgebraicStatistics/docs/src/introduction.md

@@ -34,3 +34,4 @@ Please direct questions about this part of OSCAR to the following people:
 - [Benjamin Hollering](https://sites.google.com/view/benhollering)
 - [Marina Garrote López](https://sites.google.com/view/marinagarrotelopez)
 - [Tobias Boege](https://taboege.de/)
+- [Antony Della Vecchia](https://antonydellavecchia.github.io)

experimental/AlgebraicStatistics/docs/src/markov.md

@@ -15,16 +15,12 @@ with the ambient polynomial ring in these ``p`` variables, special forms
 in them like marginals, and conditional independence ideals.
 
 ```@docs
-markov_ring(rvs::Pair{<:VarName, <:AbstractArray}...; unknown::VarName="p", K::Field=QQ, cached=false)
-tensor_ring(rvs::Pair{<:VarName, <:AbstractArray}...; unknown::VarName="p", K::Field=QQ, cached=false)
+markov_ring
 ring(R::MarkovRing)
 random_variables(R::MarkovRing)
-ci_statements(R::MarkovRing)
-unknowns(R::MarkovRing)
 gens(R::MarkovRing)
-find_random_variables(R::MarkovRing, K)
-find_state(R::MarkovRing, K, x)
 state_space(R::MarkovRing, K=random_variables(R))
+parameter_ring(M::DiscreteGraphicalModel{Graph{Undirected}, T}; cached=false) where T
 marginal(R::MarkovRing, K, x)
-ci_ideal(R::MarkovRing, stmts)
+indexed_ring(R::Ring, varnames; kw...)
 ```