Composing Models

MLJ provides three common ways of combining multiple models together out of the box:

  • Linear Pipelines - for unbranching chains that take the output of one model (e.g., dimension reduction, such as PCA) and make it the input of the next model in the chain (e.g., a classification model, such as EvoTreeClassifier)
  • Homogeneous Ensembles - for blending the predictions of multiple supervised models all of the same type, but which receive different views of the training data to reduce overall variance. The technique is known as observation bagging. Bagging decision trees, like a DecisionTreeClassifier, gives what is known as a random forest, although MLJ also provides several canned random forest models.
  • Model Stacking - for combining the predictions of a smaller number of models of possibly different type, with the help of an adjudicating model.

We note that composite models share all of the functionality of ordinary models. Their main novelty is that they include other models as hyper-parameters.

Finally, MLJ provides a powerful way to combine machine models in flexible learning networks. By wrapping training data in source nodes before calling functions like machine, predict and transform, a complicated user workflow which already combines multiple models is transformed into a blueprint for a new stand-alone composite model type. For example, MLJ's Stack model is implemented using a learning network. The remainder of this page is devoted to explaining this advanced feature.

Learning Networks

Below is a practical guide to the MLJ implementantion of learning networks, which have been described more abstractly in the article:

Anthony D. Blaom and Sebastian J. Voller (2020): Flexible model composition in machine learning and its implementation in MLJ. Preprint, arXiv:2012.15505

We assuming familiarity with the basics outlined in Getting Started. The syntax for building a learning network is essentially an extension of the basic syntax but with data containers replaced with nodes of a graph.

It is important to distinguish between learning networks and the composite MLJ model types they are used to define.

A learning network is a directed acyclic graph whose nodes are objects that can be called to obtained data, either for training a machine, or for using as input to an operation. An operation is either:

  • static, that is, an ordinary function, such as such as +, log or vcat; or

  • dynamic, that is, an operation such as predict or transform which is dispatched on both data and a training outcome attached to some machine.

Since the result of calling a node depends on the outcome of training events (and may involve lazy evaluation) one may think of a node as "dynamic" data, as opposed to the "static" data appearing in an ordinary MLJ workflow.

Different operations can dispatch on the same machine (i.e., can access a common set of learned parameters) and different machines can point to the same model (allowing for hyperparameter coupling).

By contrast, an exported learning network is a learning network exported as a stand-alone, re-usable Model object, to which all the MLJ Model meta-algorithms can be applied (ensembling, systematic tuning, etc).

By specifying data at the source nodes of a learning network, one can use and test the learning network as it is defined, which is also a good way to understand how learning networks work under the hood. This data, if specified, is ignored in the export process, for the exported composite model, like any other model, is not associated with any data until wrapped in a machine.

In MLJ learning networks treat the flow of information during training and prediction/transforming separately.

Building a simple learning network

The diagram below depicts a learning network which standardizes the input data X, learns an optimal Box-Cox transformation for the target y, predicts new target values using ridge regression, and then inverse-transforms those predictions to restore them to the original scale. Here we have only dynamic operations, labelled blue; the machines are in green. Notice that two operations both use stand, which stores the learned standardization scale parameters. The lower "Training" panel indicates which nodes are used to train each machine, and what model each machine is associated with.

Looking ahead, we note that the new composite model type we will create later will be assigned a single hyperparameter regressor, and the learning network model RidgeRegressor(lambda=0.1) will become this parameter's default value. Since model hyperparameters are mutable, this regressor can be changed to a different one (e.g., HuberRegressor()).

For testing purposes, we'll use a small synthetic data set:

using Statistics
import DataFrames

x1 = rand(300)
x2 = rand(300)
x3 = rand(300)
y = exp.(x1 - x2 -2x3 + 0.1*rand(300))
X = DataFrames.DataFrame(x1=x1, x2=x2, x3=x3)
([1, 2, 3, 4, 5, 6, 7, 8, 9, 10  …  231, 232, 233, 234, 235, 236, 237, 238, 239, 240], [241, 242, 243, 244, 245, 246, 247, 248, 249, 250  …  291, 292, 293, 294, 295, 296, 297, 298, 299, 300])

Step one is to wrap the data in source nodes:

Xs = source(X)
ys = source(y)
Source @732 ⏎ `AbstractVector{Continuous}`

Note. One can omit the specification of data at the source nodes (by writing instead Xs = source() and ys = source()) and still export the resulting network as a stand-alone model using the @from_network macro described later; see the example under Static operations on nodes. However, one will be unable to fit or call network nodes, as illustrated below.

The contents of a source node can be recovered by simply calling the node with no arguments:

2-element Vector{Float64}:

We label the nodes that we will define according to their outputs in the diagram. Notice that the nodes z and yhat use the same machine, namely box, for different operations.

To construct the W node we first need to define the machine stand that it will use to transform inputs.

stand_model = Standardizer()
stand = machine(stand_model, Xs)
Machine{Standardizer,…} trained 0 times; caches data
    1:	Source @214 ⏎ `Table{AbstractVector{Continuous}}`

Because Xs is a node, instead of concrete data, we can call transform on the machine without first training it, and the result is the new node W, instead of concrete transformed data:

W = transform(stand, Xs)
    1:	Source @214
        Source @214)

To get actual transformed data we call the node appropriately, which will require we first train the node. Training a node, rather than a machine, triggers training of all necessary machines in the network.

fit!(W, rows=train)
W()           # transform all data
W(rows=test ) # transform only test data
W(X[3:4,:])   # transform any data, new or old

2 rows × 3 columns


If you like, you can think of W (and the other nodes we will define) as "dynamic data": W is data, in the sense that it an be called ("indexed") on rows, but dynamic, in the sense the result depends on the outcome of training events.

The other nodes of our network are defined similarly:

RidgeRegressor = @load RidgeRegressor pkg=MultivariateStats
box_model = UnivariateBoxCoxTransformer()  # for making data look normally-distributed
box = machine(box_model, ys)
z = transform(box, ys)

ridge_model = RidgeRegressor(lambda=0.1)
ridge =machine(ridge_model, W, z)
zhat = predict(ridge, W)

yhat = inverse_transform(box, zhat);
    1:	Node{Machine{RidgeRegressor,…}}
                Source @214)))

We are ready to train and evaluate the completed network. Notice that the standardizer, stand, is not retrained, as MLJ remembers that it was trained earlier:

fit!(yhat, rows=train);
rms(y[test], yhat(rows=test)) # evaluate

We can change a hyperparameters and retrain:

ridge_model.lambda = 0.01
fit!(yhat, rows=train);
    1:	Node{Machine{RidgeRegressor,…}}
                Source @214)))

And re-evaluate:

rms(y[test], yhat(rows=test))

Notable feature. The machine, ridge::Machine{RidgeRegressor}, is retrained, because its underlying model has been mutated. However, since the outcome of this training has no effect on the training inputs of the machines stand and box, these transformers are left untouched. (During construction, each node and machine in a learning network determines and records all machines on which it depends.) This behavior, which extends to exported learning networks, means we can tune our wrapped regressor (using a holdout set) without re-computing transformations each time the hyperparameter is changed.

Learning network machines

As we show next, a learning network needs to be exported to create a new stand-alone model type. Instances of that type can be bound with data in a machine, which can then be evaluated, for example. Somewhat paradoxically, one can wrap a learning network in a certain kind of machine, called a learning network machine, before exporting it, and in fact, the export process actually requires us to do so. Since a composite model type does not yet exist, one constructs the machine using a "surrogate" model, whose name indicates the ultimate model supertype (Deterministic, Probabilistic, Unsupervised or Static). This surrogate model has no fields.

Continuing with the example above:

surrogate = Deterministic()
mach = machine(surrogate, Xs, ys; predict=yhat);
Machine{DeterministicSurrogate,…} trained 0 times; does not cache data
    1:	Source @214 ⏎ `Table{AbstractVector{Continuous}}`
    2:	Source @732 ⏎ `AbstractVector{Continuous}`

Notice that a key-word argument declares which node is for making predictions, and the arguments Xs and ys declare which source nodes receive the input and target data. With mach constructed in this way, the code

predict(mach, X[test,:]);
[ Info: Training Machine{UnivariateBoxCoxTransformer,…}.
[ Info: Training Machine{Standardizer,…}.
[ Info: Training Machine{RidgeRegressor,…}.

is equivalent to

[ Info: Not retraining Machine{UnivariateBoxCoxTransformer,…}. Use `force=true` to force.
[ Info: Not retraining Machine{Standardizer,…}. Use `force=true` to force.
[ Info: Not retraining Machine{RidgeRegressor,…}. Use `force=true` to force.

While it's main purpose is for export (see below), this machine can actually be evaluated:

evaluate!(mach, resampling=CV(nfolds=3), measure=LPLoss(p=2))
PerformanceEvaluation object with these fields:
  measure, measurement, operation, per_fold,
  per_observation, fitted_params_per_fold,
  report_per_fold, train_test_pairs
│ measure       │ measurement │ operation │ per_fold                      │
│ LPLoss(p = 2) │ 0.00108     │ predict   │ [0.00225, 0.000587, 0.000407] │

For more on constructing learning network machines, see machine.

Exporting a learning network as a stand-alone model

Having satisfied that our learning network works on the synthetic data, we are ready to export it as a stand-alone model.

Method I: The @from_network macro

Having defined a learning network machine, mach, as above, the following code defines a new model subtype WrappedRegressor <: Supervised with a single field regressor:

@from_network mach begin
	mutable struct WrappedRegressor

Note the declaration of the default value ridge_model, which must refer to an actual model appearing in the learning network. It can be typed, as in the alternative declaration below, which also declares some traits for the type (as shown by info(WrappedRegressor); see also Trait declarations).

@from_network mach begin
	mutable struct WrappedRegressor
	input_scitype = Table(Continuous,Finite)
	target_scitype = AbstractVector{<:Continuous}

We can now create an instance of this type and apply the meta-algorithms that apply to any MLJ model:

julia> composite = WrappedRegressor()
	regressor = RidgeRegressor(
			lambda = 0.01))

X, y = @load_boston;
evaluate(composite, X, y, resampling=CV(), measure=l2, verbosity=0)

Since our new type is mutable, we can swap the RidgeRegressor out for any other regressor:

KNNRegressor = @load KNNRegressor
composite.regressor = KNNRegressor(K=7)
julia> composite
WrappedRegressor(regressor = KNNRegressor(K = 7,
										  algorithm = :kdtree,
										  metric = Distances.Euclidean(0.0),
										  leafsize = 10,
										  reorder = true,
										  weights = :uniform,),) @ 2…63

Method II: Finer control (advanced)

This section describes an advanced feature that can be skipped on a first reading.

In Method I above, only models appearing in the network will appear as hyperparameters of the exported composite model. There is a second more flexible method for exporting the network, which allows finer control over the exported Model struct, and which also avoids macros. The two steps required are:

  • Define a new mutable struct model type.

  • Wrap the learning network code in a model fit method.

Let's start with an elementary illustration in the learning network we just exported using Method I.

The mutable struct definition looks like this:

mutable struct WrappedRegressor2 <: DeterministicComposite

# keyword constructor
WrappedRegressor2(; regressor=RidgeRegressor()) = WrappedRegressor2(regressor)

The other supertype options are ProbabilisticComposite, IntervalComposite, UnsupervisedComposite and StaticComposite.

We now simply cut and paste the code defining the learning network into a model fit method (as opposed to a machine fit! method):

function, verbosity::Integer, X, y)
	Xs = source(X)
	ys = source(y)

	stand_model = Standardizer()
	stand = machine(stand_model, Xs)
	W = transform(stand, Xs)

	box_model = UnivariateBoxCoxTransformer()
	box = machine(box_model, ys)
	z = transform(box, ys)

	ridge_model = model.regressor        ###
	ridge =machine(ridge_model, W, z)
	zhat = predict(ridge, W)

	yhat = inverse_transform(box, zhat)

	mach = machine(Deterministic(), Xs, ys; predict=yhat)
	return!(mach, model, verbosity)

This completes the export process.


  • The line marked ###, where the new exported model's hyperparameter regressor is spliced into the network, is the only modification to the previous code.

  • After defining the network there is the additional step of constructing and fitting a learning network machine (see above).

  • The last call in the function return!(mach, model, verbosity) calls fit! on the learning network machine mach and splits it into various pieces, as required by the MLJ model interface. See also the return! doc-string.

  • Important note An MLJ fit method is not allowed to mutate its model argument.

What's going on here? MLJ's machine interface is built atop a more primitive model interface, implemented for each algorithm. Each supervised model type (eg, RidgeRegressor) requires model fit and predict methods, which are called by the corresponding machine fit! and predict methods. We don't need to define a model predict method here because MLJ provides a fallback which simply calls the predict on the learning network machine created in the fit method.

A composite model coupling component model hyper-parameters

We now give a more complicated example of a composite model which exposes some parameters used in the network that are not simply component models. The model combines a clustering model (e.g., KMeans()) for dimension reduction with ridge regression, but has the following "coupling" of the hyper parameters: The ridge regularization depends on the number of clusters used (with less regularization for a greater number of clusters) and a user-specified "coupling" coefficient K.

RidgeRegressor = @load RidgeRegressor pkg=MLJLinearModels

mutable struct MyComposite <: DeterministicComposite
	clusterer     # the clustering model (e.g., KMeans())
	ridge_solver  # a ridge regression parameter we want to expose
	K::Float64    # a "coupling" coefficient

function, verbosity, X, y)

	Xs = source(X)
	ys = source(y)

	clusterer = composite.clusterer
	k = clusterer.k

	clustererM = machine(clusterer, Xs)
	Xsmall = transform(clustererM, Xs)

	# the coupling: ridge regularization depends on number of
	# clusters (and the specified coefficient `K`):
	lambda = exp(-composite.K/clusterer.k)

	ridge = RidgeRegressor(lambda=lambda, solver=composite.ridge_solver)
	ridgeM = machine(ridge, Xsmall, ys)

	yhat = predict(ridgeM, Xsmall)

	mach = machine(Deterministic(), Xs, ys; predict=yhat)
	return!(mach, composite, verbosity)


kmeans = (@load KMeans pkg=Clustering)()
my_composite = MyComposite(kmeans, nothing, 0.5)
    clusterer = KMeans(
            k = 3,
            metric = Distances.SqEuclidean(0.0)),
    ridge_solver = nothing,
    K = 0.5)
evaluate(my_composite, X, y, measure=MeanAbsoluteError(), verbosity=0)
PerformanceEvaluation object with these fields:
  measure, measurement, operation, per_fold,
  per_observation, fitted_params_per_fold,
  report_per_fold, train_test_pairs
│ measure             │ measurement │ operation │ per_fold                     ⋯
│ MeanAbsoluteError() │ 0.127       │ predict   │ [0.147, 0.0919, 0.131, 0.211 ⋯
                                                                1 column omitted

Static operations on nodes

Continuing to view nodes as "dynamic data", we can, in addition to applying "dynamic" operations like predict and transform to nodes, overload ordinary "static" (unlearned) operations as well. These operations can be ordinary functions (with possibly multiple arguments) or they could be functions with parameters, such as "take a weighted average of two nodes", where the weights are parameters. Here we address the simpler case of ordinary functions. For the parametric case, see "Static transformers" in Transformers and Other Unsupervised Models

Let us first give a demonstration of operations that work out-of-the-box. These include:

  • addition and scalar multiplication

  • exp, log, vcat, hcat

  • tabularization (MLJ.table) and matrixification (MLJ.matrix)

As a demonstration of some of these, consider the learning network below that: (i) One-hot encodes the input table X; (ii) Log transforms the continuous target y; (iii) Fits specified K-nearest neighbour and ridge regressor models to the data; (iv) Computes an average of the individual model predictions; and (v) Inverse transforms (exponentiates) the blended predictions.

Note, in particular, the lines defining zhat and yhat, which combine several static node operations.

RidgeRegressor = @load RidgeRegressor pkg=MultivariateStats
KNNRegressor = @load KNNRegressor

Xs = source()
ys = source()

hot = machine(OneHotEncoder(), Xs)

# W, z, zhat and yhat are nodes in the network:

W = transform(hot, Xs) # one-hot encode the input
z = log(ys)            # transform the target

model1 = RidgeRegressor(lambda=0.1)
model2 = KNNRegressor(K=7)

mach1 = machine(model1, W, z)
mach2 = machine(model2, W, z)

# average the predictions of the KNN and ridge models:
zhat = 0.5*predict(mach1, W) + 0.5*predict(mach2, W)

# inverse the target transformation
yhat = exp(zhat)
    1:	Node{Nothing}
                        Source @536))),
                        Source @536)))))

Exporting this learning network as a stand-alone model:

@from_network machine(Deterministic(), Xs, ys; predict=yhat) begin
	mutable struct DoubleRegressor

To deal with operations on nodes not supported out-of-the box, one can use the @node macro. Supposing, in the preceding example, we wanted the geometric mean rather than arithmetic mean. Then, the definition of zhat above can be replaced with

yhat1 = predict(mach1, W)
yhat2 = predict(mach2, W)
gmean(y1, y2) = sqrt.(y1.*y2)
zhat = @node gmean(yhat1, yhat2)

There is also a node function, which would achieve the same in this way:

zhat = node((y1, y2)->sqrt.(y1.*y2), predict(mach1, W), predict(mach2, W))

More node examples

Here are some examples taken from MLJ source (at work in the example above) for overloading common operations for nodes:

Base.log(v::Vector{<:Number}) = log.(v)
Base.log(X::AbstractNode) = node(log, X)

import Base.+
+(y1::AbstractNode, y2::AbstractNode) = node(+, y1, y2)
+(y1, y2::AbstractNode) = node(+, y1, y2)
+(y1::AbstractNode, y2) = node(+, y1, y2)

Here AbstractNode is the common super-type of Node and Source.

And a final example, using the @node macro to row-shuffle a table:

using Random
X = (x1 = [1, 2, 3, 4, 5],
	 x2 = [:one, :two, :three, :four, :five])
rows(X) = 1:nrows(X)

Xs = source(X)
rs  = @node rows(Xs)
W = @node selectrows(Xs, @node shuffle(rs))

julia> W()
(x1 = [5, 1, 3, 2, 4],
 x2 = Symbol[:five, :one, :three, :two, :four],)

The learning network API

Two new julia types are part of learning networks: Source and Node.

Formally, a learning network defines two labeled directed acyclic graphs (DAG's) whose nodes are Node or Source objects, and whose labels are Machine objects. We obtain the first DAG from directed edges of the form $N1 -> N2$ whenever $N1$ is an argument of $N2$ (see below). Only this DAG is relevant when calling a node, as discussed in examples above and below. To form the second DAG (relevant when calling or calling fit! on a node) one adds edges for which $N1$ is training argument of the the machine which labels $N1$. We call the second, larger DAG, the completed learning network (but note only edges of the smaller network are explicitly drawn in diagrams, for simplicity).

Source nodes

Only source nodes reference concrete data. A Source object has a single field, data.

Xs = source(X=nothing)

Define, a learning network Source object, wrapping some input data X, which can be nothing for purposes of exporting the network as stand-alone model. For training and testing the unexported network, appropriate vectors, tables, or other data containers are expected.

The calling behaviour of a Source object is this:

Xs() = X
Xs(rows=r) = selectrows(X, r)  # eg, X[r,:] for a DataFrame
Xs(Xnew) = Xnew

See also: [@from_network](@ref], sources, origins, node.

rebind!(s, X)

Attach new data X to an existing source node s. Not a public method.


A vector of all sources referenced by calls N() and fit!(N). These are the sources of the ancestor graph of N when including training edges.

Not to be confused with origins(N), in which training edges are excluded.

See also: origins, source.


Return a list of all origins of a node N accessed by a call N(). These are the source nodes of ancestor graph of N if edges corresponding to training arguments are excluded. A Node object cannot be called on new data unless it has a unique origin.

Not to be confused with sources(N) which refers to the same graph but without the training edge deletions.

See also: node, source.


The key components of a Node are:

  • An operation, which will either be static (a fixed function) or dynamic (such as predict or transform, dispatched on a machine).

  • A machine on which to dispatch the operation (void if the operation is static). The training arguments of the machine are generally other nodes.

  • Upstream connections to other nodes (including source nodes) specified by arguments (one for each argument of the operation).

N = node(f::Function, args...)

Defines a Node object N wrapping a static operation f and arguments args. Each of the n elements of args must be a Node or Source object. The node N has the following calling behaviour:

N() = f(args[1](), args[2](), ..., args[n]())
N(rows=r) = f(args[1](rows=r), args[2](rows=r), ..., args[n](rows=r))
N(X) = f(args[1](X), args[2](X), ..., args[n](X))

J = node(f, mach::Machine, args...)

Defines a dynamic Node object J wrapping a dynamic operation f (predict, predict_mean, transform, etc), a nodal machine mach and arguments args. Its calling behaviour, which depends on the outcome of training mach (and, implicitly, on training outcomes affecting its arguments) is this:

J() = f(mach, args[1](), args[2](), ..., args[n]())
J(rows=r) = f(mach, args[1](rows=r), args[2](rows=r), ..., args[n](rows=r))
J(X) = f(mach, args[1](X), args[2](X), ..., args[n](X))

Generally n=1 or n=2 in this latter case.

predict(mach, X::AbsractNode, y::AbstractNode)
predict_mean(mach, X::AbstractNode, y::AbstractNode)
predict_median(mach, X::AbstractNode, y::AbstractNode)
predict_mode(mach, X::AbstractNode, y::AbstractNode)
transform(mach, X::AbstractNode)
inverse_transform(mach, X::AbstractNode)

Shortcuts for J = node(predict, mach, X, y), etc.

Calling a node is a recursive operation which terminates in the call to a source node (or nodes). Calling nodes on new data X fails unless the number of such nodes is one.

See also: @node, source, origins.

@node f(...)

Construct a new node that applies the function f to some combination of nodes, sources and other arguments.

Important. An argument not in global scope is assumed to be a node or source.


X = source(π)
W = @node sin(X)
julia> W()

X = source(1:10)
Y = @node selectrows(X, 3:4)
julia> Y()

julia> Y(["one", "two", "three", "four"])
2-element Array{Symbol,1}:

X1 = source(4)
X2 = source(5)
add(a, b, c) = a + b + c
N = @node add(X1, 1, X2)
julia> N()

See also node

@from_network mach [mutable] struct NewCompositeModel


@from_network mach begin
    [mutable] struct NewCompositeModel
    <optional trait declarations>

Create a new stand-alone model type called NewCompositeModel, using the specified learning network machine mach as a blueprint.

For more on learning network machines, see machine.


Consider the following simple learning network for training a decision tree after one-hot encoding the inputs, and forcing the predictions to be point-predictions (rather than probabilistic):

Xs = source()
ys = source()

hot = OneHotEncoder()
tree = DecisionTreeClassifier()

W = transform(machine(hot, Xs), Xs)
yhat = predict_mode(machine(tree, W, ys), W)

A learning network machine is defined by

mach = machine(Deterministic(), Xs, ys; predict=yhat)

To specify a new Deterministic composite model type WrappedTree we specify the model instances appearing in the network as "default" values in the following decorated struct definition:

@from_network mach struct WrappedTree

and create a new instance with WrappedTree().

To allow the second model component to be replaced by any other probabilistic model we instead make a mutable struct declaration and, if desired, annotate types appropriately. In the following code illustration some model trait declarations have also been added:

@from_network mach begin
    mutable struct WrappedTree
    input_scitype = Table(Continuous, Finite)
    is_pure_julia = true
return!(mach::Machine{<:Surrogate}, model, verbosity)

The last call in custom code defining the method for a new composite model type. Here model is the instance of the new type appearing in the signature, while mach is a learning network machine constructed using model. Not relevant when defining composite models using @pipeline or @from_network.

For usage, see the example given below. Specificlly, the call does the following:

  • Determines which hyper-parameters of model point to model instances in the learning network wrapped by mach, for recording in an object called cache, for passing onto the MLJ logic that handles smart updating (namely, an MLJBase.update fallback for composite models).

  • Calls fit!(mach, verbosity=verbosity).

  • Moves any data in source nodes of the learning network into cache (for data-anonymization purposes).

  • Records a copy of model in cache.

  • Returns cache and outcomes of training in an appropriate form (specifically, (mach.fitresult, cache,; see Adding Models for General Use for technical details.)


The following code defines, "by hand", a new model type MyComposite for composing standardization (whitening) with a deterministic regressor:

mutable struct MyComposite <: DeterministicComposite

function, verbosity, X, y)
    Xs = source(X)
    ys = source(y)

    mach1 = machine(Standardizer(), Xs)
    Xwhite = transform(mach1, Xs)

    mach2 = machine(model.regressor, Xwhite, ys)
    yhat = predict(mach2, Xwhite)

    mach = machine(Deterministic(), Xs, ys; predict=yhat)
    return!(mach, model, verbosity)

See more on fitting nodes at fit! and fit_only!.