API

StableRulesClassifier

A model type for constructing a stable rules classifier, based on SIRUS.jl, and implementing the MLJ model interface.

From MLJ, the type can be imported using

StableRulesClassifier = @load StableRulesClassifier pkg=SIRUS

Do model = StableRulesClassifier() to construct an instance with default hyper-parameters. Provide keyword arguments to override hyper-parameter defaults, as in StableRulesClassifier(rng=...).

StableRulesClassifier implements the explainable rule-based model based on a random forest.

Training data

In MLJ or MLJBase, bind an instance model to data with

mach = machine(model, X, y)

where

• X: any table of input features (eg, a DataFrame) whose columns each have one of the following element scitypes: Continuous, Count, or <:OrderedFactor; check column scitypes with schema(X)

• y: the target, which can be any AbstractVector whose element scitype is <:OrderedFactor or <:Multiclass; check the scitype with scitype(y)

Train the machine with fit!(mach, rows=...).

Hyperparameters

• rng::AbstractRNG=default_rng(): Random number generator. Using a StableRNG from StableRNGs.jl is advised.

• partial_sampling::Float64=0.7: Ratio of samples to use in each subset of the data. The default should be fine for most cases.

• n_trees::Int=1000: The number of trees to use. It is advisable to use at least thousand trees to for a better rule selection, and in turn better predictive performance.

• max_depth::Int=2: The depth of the tree. A lower depth decreases model complexity and can therefore improve accuracy when the sample size is small (reduce overfitting).

• q::Int=10: Number of cutpoints to use per feature. The default value should be fine for most situations.

• min_data_in_leaf::Int=5: Minimum number of data points per leaf.

• max_rules::Int=10: This is the most important hyperparameter after lambda. The more rules, the more accurate the model should be. If this is not the case, tune lambda first. However, more rules will also decrease model interpretability. So, it is important to find a good balance here. In most cases, 10 to 40 rules should provide reasonable accuracy while remaining interpretable.

• lambda::Float64=1.0: The weights of the final rules are determined via a regularized regression over each rule as a binary feature. This hyperparameter specifies the strength of the ridge (L2) regularizer. SIRUS is very sensitive to the choice of this hyperparameter. Ensure that you try the full range from 10^-4 to 10^4 (e.g., 0.001, 0.01, ..., 100). When trying the range, one good check is to verify that an increase in max_rules increases performance. If this is not the case, then try a different value for lambda.

Fitted parameters

The fields of fitted_params(mach) are:

• fitresult: A StableRules object.

Operations

• predict(mach, Xnew): Return a vector of predictions for each row of Xnew.

StableRulesRegressor

A model type for constructing a stable rules regressor, based on SIRUS.jl, and implementing the MLJ model interface.

From MLJ, the type can be imported using

StableRulesRegressor = @load StableRulesRegressor pkg=SIRUS

Do model = StableRulesRegressor() to construct an instance with default hyper-parameters. Provide keyword arguments to override hyper-parameter defaults, as in StableRulesRegressor(rng=...).

StableRulesRegressor implements the explainable rule-based regression model based on a random forest.

Training data

In MLJ or MLJBase, bind an instance model to data with

mach = machine(model, X, y)

where

• X: any table of input features (eg, a DataFrame) whose columns each have one of the following element scitypes: Continuous, Count, or <:OrderedFactor; check column scitypes with schema(X)

• y: the target, which can be any AbstractVector whose element scitype is <:OrderedFactor or <:Multiclass; check the scitype with scitype(y)

Train the machine with fit!(mach, rows=...).

Hyperparameters

• rng::AbstractRNG=default_rng(): Random number generator. Using a StableRNG from StableRNGs.jl is advised.

• partial_sampling::Float64=0.7: Ratio of samples to use in each subset of the data. The default should be fine for most cases.

• n_trees::Int=1000: The number of trees to use. It is advisable to use at least thousand trees to for a better rule selection, and in turn better predictive performance.

• max_depth::Int=2: The depth of the tree. A lower depth decreases model complexity and can therefore improve accuracy when the sample size is small (reduce overfitting).

• q::Int=10: Number of cutpoints to use per feature. The default value should be fine for most situations.

• min_data_in_leaf::Int=5: Minimum number of data points per leaf.

• max_rules::Int=10: This is the most important hyperparameter after lambda. The more rules, the more accurate the model should be. If this is not the case, tune lambda first. However, more rules will also decrease model interpretability. So, it is important to find a good balance here. In most cases, 10 to 40 rules should provide reasonable accuracy while remaining interpretable.

• lambda::Float64=1.0: The weights of the final rules are determined via a regularized regression over each rule as a binary feature. This hyperparameter specifies the strength of the ridge (L2) regularizer. SIRUS is very sensitive to the choice of this hyperparameter. Ensure that you try the full range from 10^-4 to 10^4 (e.g., 0.001, 0.01, ..., 100). When trying the range, one good check is to verify that an increase in max_rules increases performance. If this is not the case, then try a different value for lambda.

Fitted parameters

The fields of fitted_params(mach) are:

• fitresult: A StableRules object.

Operations

• predict(mach, Xnew): Return a vector of predictions for each row of Xnew.

StableForestClassifier

A model type for constructing a stable forest classifier, based on SIRUS.jl, and implementing the MLJ model interface.

From MLJ, the type can be imported using

StableForestClassifier = @load StableForestClassifier pkg=SIRUS

Do model = StableForestClassifier() to construct an instance with default hyper-parameters. Provide keyword arguments to override hyper-parameter defaults, as in StableForestClassifier(rng=...).

StableForestClassifier implements the random forest classifier with a stabilized forest structure (Bénard et al., 2021). This stabilization increases stability when extracting rules. The impact on the predictive accuracy compared to standard random forests should be relatively small.

Training data

In MLJ or MLJBase, bind an instance model to data with

mach = machine(model, X, y)

where

• X: any table of input features (eg, a DataFrame) whose columns each have one of the following element scitypes: Continuous, Count, or <:OrderedFactor; check column scitypes with schema(X)

• y: the target, which can be any AbstractVector whose element scitype is <:OrderedFactor or <:Multiclass; check the scitype with scitype(y)

Train the machine with fit!(mach, rows=...).

Hyperparameters

• rng::AbstractRNG=default_rng(): Random number generator. Using a StableRNG from StableRNGs.jl is advised.
• partial_sampling::Float64=0.7: Ratio of samples to use in each subset of the data. The default should be fine for most cases.
• n_trees::Int=1000: The number of trees to use. It is advisable to use at least thousand trees to for a better rule selection, and in turn better predictive performance.
• max_depth::Int=2: The depth of the tree. A lower depth decreases model complexity and can therefore improve accuracy when the sample size is small (reduce overfitting).
• q::Int=10: Number of cutpoints to use per feature. The default value should be fine for most situations.
• min_data_in_leaf::Int=5: Minimum number of data points per leaf.

Fitted parameters

The fields of fitted_params(mach) are:

• fitresult: A StableForest object.

Operations

• predict(mach, Xnew): Return a vector of predictions for each row of Xnew.

StableForestRegressor

A model type for constructing a stable forest regressor, based on SIRUS.jl, and implementing the MLJ model interface.

From MLJ, the type can be imported using

StableForestRegressor = @load StableForestRegressor pkg=SIRUS

Do model = StableForestRegressor() to construct an instance with default hyper-parameters. Provide keyword arguments to override hyper-parameter defaults, as in StableForestRegressor(rng=...).

StableForestRegressor implements the random forest regressor with a stabilized forest structure (Bénard et al., 2021).

Training data

In MLJ or MLJBase, bind an instance model to data with

mach = machine(model, X, y)

where

• X: any table of input features (eg, a DataFrame) whose columns each have one of the following element scitypes: Continuous, Count, or <:OrderedFactor; check column scitypes with schema(X)

• y: the target, which can be any AbstractVector whose element scitype is <:OrderedFactor or <:Multiclass; check the scitype with scitype(y)

Train the machine with fit!(mach, rows=...).

Hyperparameters

• rng::AbstractRNG=default_rng(): Random number generator. Using a StableRNG from StableRNGs.jl is advised.
• partial_sampling::Float64=0.7: Ratio of samples to use in each subset of the data. The default should be fine for most cases.
• n_trees::Int=1000: The number of trees to use. It is advisable to use at least thousand trees to for a better rule selection, and in turn better predictive performance.
• max_depth::Int=2: The depth of the tree. A lower depth decreases model complexity and can therefore improve accuracy when the sample size is small (reduce overfitting).
• q::Int=10: Number of cutpoints to use per feature. The default value should be fine for most situations.
• min_data_in_leaf::Int=5: Minimum number of data points per leaf.

Fitted parameters

The fields of fitted_params(mach) are:

• fitresult: A StableForest object.

Operations

• predict(mach, Xnew): Return a vector of predictions for each row of Xnew.

SubClause(
    feature::Int,
    feature_name::AbstractString,
    splitval::Number,
    direction::Symbol
)

A subclause denotes a conditional on one feature. Each rule contains a clause with one or more subclauses. For example, the rule if X[i, 1] > 3 & X[i, 2] < 4, then ... contains two subclauses.

A subclause is equivalent to a split in a decision tree. In other words, each rule is based on one or more subclauses. In pratise, a rule is based on at most two subclauses (has at most two subclauses). The reason for this is that rules with more than two subclauses will not end up in the final model, as is discussed in the original SIRUS paper.

The data inside a SubClause can be accessed via

• feature(::SubClause),
• feature_name(::SubClause),
• splitval(::SubClause), and
• direction(::SubClause).

Note: this name is not perfect. A formally better name would be "predicate atom", but that takes more characters and is also not very intuitive. Instead, the word Clause and SubClause seemed pretty short and clear.

Clause(subclauses::Vector{SubClause})

A clause denotes a conditional on one or more features. Each rule contains a clause with one or more subclauses.

A clause is equivalent to a path in a decision tree. For example, the clause X[i, 1] > 3 & X[i, 2] < 4 can be interpreted as a path going through two nodes.

In the original SIRUS paper, a path of length d is defined as consisting of d subclauses. As discussed above, in practice the number of subclauses or subclauses d ≤ 2.

Note that a path can also be a path to a node; not necessarily a leaf.

Data can be accessed via subclauses.

Clauses can be constructed from a textual representation:

Example

julia> Clause(" X[i, 1] < 32000 ")
Clause(" X[i, 1] < 32000.0 ")

Rule(clause::Clause, then::LeafContent, otherwise::LeafContent)

A rule is a clause with a then and otherwise probability. For example, the rule if X[i, 1] > 3 & X[i, 2] < 4, then 0.1 else 0.2 is a rule with two subclauses. The name otherwise is used internally instead of else since else is a reserved keyword.

Data can be accessed via

• clause(::Rule),
• subclauses(::Rule),
• then(::Rule),
• otherwise(::Rule),
• feature(::Rule),
• features(::Rule),
• feature_name(::Rule),
• feature_names(::Rule),
• splitval(::Rule),
• splitvals(::Rule),
• direction(::Rule), and
• directions(::Rule).

Rules can be constructed from a textual representation:

Example

julia> Rule(Clause(" X[i, 1] < 32000 "), [0.1], [0.4])
Rule(Clause(" X[i, 1] < 32000.0 "), [0.1], [0.4])

feature(s::SubClause) -> Int

Return the feature number for a subclause.

feature(rule::Rule) -> Int

Return the feature number for a rule with one subclause. Throws an error if the rule has multiple subclauses. Use features for rules with multiple subclauses.

features(rule::Rule) -> Vector{Int}

Return a vector of feature numbers; one for each clause in rule.

feature_name(s::SubClause) -> String

Return the feature name for a subclause.

feature_name(rule::Rule) -> String

Return the feature name for a rule with one subclause. Throws an error if the rule has multiple subclauses. Use feature_names for rules with multiple subclauses.

feature_names(rule::Rule) -> Vector{String}

Return a vector of feature names; one for each clause in rule.

splitval(s::SubClause)

Return the split value for a subclause. The function currently returns a Float32 but this might change in the future.

splitval(rule::Rule)

Return the splitvalue for a rule with one subclause. Throws an error if the rule has multiple subclauses. Use splitvals for rules with multiple subclauses.

splitvals(rule::Rule)

Return the splitvalues for a rule; one for each subclause.

clause(rule::Rule) -> Clause

Return the clause for a rule. The clause is a path in a decision tree after the conversion to rules. A clause consists of one or more subclauses.

subclauses(c::Clause) -> Vector{SubClause}

Return the subclauses for a clause.

subclauses(rule::Rule) -> Vector{SubClause}

Return the subclauses for a rule.

direction(s::SubClause) -> Symbol

Return the direction of the comparison for a subclause. Can be either :L or :R, which is equivalent to < or ≥ respectively.

direction(rule::Rule) -> Symbol

Return the direction for a rule with one subclause. Throws an error if the rule has multiple subclauses. Use directions for rules with multiple subclauses.

directions(rule::Rule) -> Vector{Symbol}

Return a vector of split directions; one for each clause in rule.

feature_importance(
    models::Union{StableRules, Vector{StableRules}},
    feature_name::AbstractString
)

Estimate the importance of the given feature_name. The aim is to satisfy the following property, so that the features can be ordered by importance:

Given two features A and B, if A has more effect on the outcome, then feature_importance(model, A) > feature_importance(model, B).

This is based on the gap_size function. The gap size is the difference between the then and otherwise (else) probabilities. A smaller gap size implies a smaller CART-splitting criterion, which implies a smaller occurrence frequency (see the appendix at https://proceedings.mlr.press/v130/benard21a.html for an example).

feature_importances(
    models::Union{StableRules, Vector{StableRules}}
    feat_names::Vector{String}
)::Vector{NamedTuple{(:feature_name, :importance), Tuple{String, Float64}}}

Return the feature names and importances, sorted by feature importance in descending order.

then(rule::Rule)

Return the then probabilities for a rule. The return type is a vector of probabilities; the exact element type may change over time.

otherwise(rule::Rule)

Return the otherwise probabilities for a rule. The return type is a vector of probabilities; the exact element type may change over time.

gap_size(rule::Rule)

Return the gap size for a rule. The gap size is used by Bénard et al. in the appendix of their PMLR paper (https://proceedings.mlr.press/v130/benard21a.html). Via an example, they specify that the gap size is the difference between the then and otherwise (else) probabilities.

A smaller gap size implies a smaller CART-splitting criterion, which implies a smaller occurrence frequency.

cutpoints(V::AbstractVector, q::Int)

Return a vector of q cutpoints taken from the empirical distribution from data V."

cutpoints(X, q::Int)

Return a vector of vectors containing

• one inner vector for each feature in the dataset X and
• inner vectors containing q unique cutpoints, that is, length(V[i]) ≤ q for all i in V.

Using unique here to avoid checking splits twice.

satisfies(row::AbstractVector, rule::Rule) -> Bool

Return whether data row satisfies rule.

unpack_rule(rule::Rule) -> NamedTuple

Unpack a rule into it's components. This is useful for plotting. It returns a named tuple with the following fields:

• feature
• feature_name
• splitval
• direction
• then
• otherwise

unpack_model(model::StableRules) -> Vector{NamedTuple}

Unpack a model containing only single subclauses (max_depth=1) into it's components. This is useful for plotting. It returns a vector of named tuples with the following fields:

• weight
• feature
• feature_name
• splitval
• direction
• then
• otherwise

One row for each rule in the model.

unpack_models(
    models::Vector{StableRules},
    feature_name::String
) -> Vector{NamedTuple}

Unpack a vector of models containing only single subclauses (max_depth=1) into it's components. This is useful when plotting the rules that the model has learned for each feature. It returns a vector of named tuples with the following fields for each rule in the models that contains feature_name:

• weight
• feature
• feature_name
• splitval
• direction
• then
• otherwise