SymbolicRegression.jl searches for symbolic expressions which optimize a particular objective.
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Contents:
Contributors โจ
We are eager to welcome new contributors! If you have an idea for a new feature, don't hesitate to share it on the issues page or forums.
Quickstart
Install in Julia with:
using Pkg
Pkg.add("SymbolicRegression")
MLJ Interface
The easiest way to use SymbolicRegression.jl is with MLJ. Let's see an example:
import SymbolicRegression: SRRegressor
import MLJ: machine, fit!, predict, report
# Dataset with two named features:
X = (a = rand(500), b = rand(500))
# and one target:
y = @. 2 * cos(X.a * 23.5) - X.b ^ 2
# with some noise:
y = y .+ randn(500) .* 1e-3
model = SRRegressor(
niterations=50,
binary_operators=[+, -, *],
unary_operators=[cos],
)
Now, let's create and train this model on our data:
mach = machine(model, X, y)
fit!(mach)
You will notice that expressions are printed using the column names of our table. If, instead of a table-like object, a simple array is passed (e.g., X=randn(100, 2)
), x1, ..., xn
will be used for variable names.
Let's look at the expressions discovered:
report(mach)
Finally, we can make predictions with the expressions on new data:
predict(mach, X)
This will make predictions using the expression selected using the function passed to selection_method
. By default this selection is made a mix of accuracy and complexity. For example, we can make predictions using expression 2 with:
mach.model.selection_method = Returns(2)
predict(mach, X)
For fitting multiple outputs, one can use MultitargetSRRegressor
. For a full list of options available to each regressor, see the API page.
Low-Level Interface
The heart of SymbolicRegression.jl is the equation_search
function. This takes a 2D array and attempts to model a 1D array using analytic functional forms. Note: unlike the MLJ interface, this assumes column-major input of shape [features, rows].
import SymbolicRegression: Options, equation_search
X = randn(2, 100)
y = 2 * cos.(X[2, :]) + X[1, :] .^ 2 .- 2
options = Options(
binary_operators=[+, *, /, -],
unary_operators=[cos, exp],
populations=20
)
hall_of_fame = equation_search(
X, y, niterations=40, options=options,
parallelism=:multithreading
)
You can view the resultant equations in the dominating Pareto front (best expression seen at each complexity) with:
import SymbolicRegression: calculate_pareto_frontier
dominating = calculate_pareto_frontier(hall_of_fame)
This is a vector of PopMember
type - which contains the expression along with the score. We can get the expressions with:
trees = [member.tree for member in dominating]
Each of these equations is a Node{T}
type for some constant type T
(like Float32
).
You can evaluate a given tree with:
import SymbolicRegression: eval_tree_array
tree = trees[end]
output, did_succeed = eval_tree_array(tree, X, options)
The output
array will contain the result of the tree at each of the 100 rows. This did_succeed
flag detects whether an evaluation was successful, or whether encountered any NaNs or Infs during calculation (such as, e.g., sqrt(-1)
).
Constructing trees
You can also manipulate and construct trees directly. For example:
import SymbolicRegression: Options, Node, eval_tree_array
options = Options(;
binary_operators=[+, -, *, ^, /], unary_operators=[cos, exp, sin]
)
x1, x2, x3 = [Node(; feature=i) for i=1:3]
tree = cos(x1 - 3.2 * x2) - x1^3.2
This tree has Float64
constants, so the type of the entire tree will be promoted to Node{Float64}
.
We can convert all constants (recursively) to Float32
:
float32_tree = convert(Node{Float32}, tree)
We can then evaluate this tree on a dataset:
X = rand(Float32, 3, 100)
output, did_succeed = eval_tree_array(tree, X, options)
Exporting to SymbolicUtils.jl
We can view the equations in the dominating Pareto frontier with:
dominating = calculate_pareto_frontier(hall_of_fame)
We can convert the best equation to SymbolicUtils.jl with the following function:
import SymbolicRegression: node_to_symbolic
eqn = node_to_symbolic(dominating[end].tree, options)
println(simplify(eqn*5 + 3))
We can also print out the full pareto frontier like so:
import SymbolicRegression: compute_complexity, string_tree
println("Complexity\tMSE\tEquation")
for member in dominating
complexity = compute_complexity(member, options)
loss = member.loss
string = string_tree(member.tree, options)
println("$(complexity)\t$(loss)\t$(string)")
end
Code structure
SymbolicRegression.jl is organized roughly as follows. Rounded rectangles indicate objects, and rectangles indicate functions.
(if you can't see this diagram being rendered, try pasting it into mermaid-js.github.io/mermaid-live-editor)
The HallOfFame
objects store the expressions with the lowest loss seen at each complexity.
The dependency structure of the code itself is as follows:
Bash command to generate dependency structure from src
directory (requires vim-stream
):
echo 'stateDiagram-v2'
IFS=$'\n'
for f in *.jl; do
for line in $(cat $f | grep -e 'import \.\.' -e 'import \.'); do
echo $(echo $line | vims -s 'dwf:d$' -t '%s/^\.*//g' '%s/Module//g') $(basename "$f" .jl);
done;
done | vims -l 'f a--> ' | sort
Search options
See https://astroautomata.com/SymbolicRegression.jl/stable/api/#Options