# Composing Models

Three common ways of combining multiple models together have out-of-the-box implementations in MLJ:

- Linear Pipelines (
`Pipeline`

)- 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`

). To include transformations of the target variable in a supervised pipeline model, see Target Transformations. - Homogeneous Ensembles (
`EnsembleModel`

) - 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 implemented here is known as observation bagging. - Model Stacking - (
`Stack`

) for combining the predictions of a smaller number of models of possibly*different*types, 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 implementation of learning networks, which have been described more abstractly in the article:

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 on 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`+`

,`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 bound to data 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. (This represents a model we could alternatively build using the `TransformedTargetModel`

wrapper and a pipeline.) Here we have only dynamic operations, labelled blue. The machines are in green. Notice that two operations both use `box`

, which stores the learned Box-Cox 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)
train, test = partition(eachindex(y), 0.8);
```

Step one is to wrap the data in *source nodes*:

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

Source @088 ⏎ `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, as discussed 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:

`ys()[1:2]`

2-element Vector{Float64}: 0.16301347080742748 0.4871169683975597

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 trained 0 times; caches data model: Standardizer(features = Symbol[], …) args: 1: Source @357 ⏎ `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)`

Node args: 1: Source @357 formula: transform( machine(Standardizer(features = Symbol[], …), …), Source @357)

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 the 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

x1 | x2 | x3 | |
---|---|---|---|

Float64 | Float64 | Float64 | |

1 | -0.841196 | -0.111359 | 1.33483 |

2 | -1.13148 | 1.03332 | -0.694535 |

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 can 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);
```

Node args: 1: Node formula: inverse_transform( machine(UnivariateBoxCoxTransformer(n = 171, …), …), predict( machine(RidgeRegressor(lambda = 0.1, …), …), transform( machine(Standardizer(features = Symbol[], …), …), Source @357)))

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
```

0.026720266064268652

We can change a hyperparameter and retrain:

```
ridge_model.lambda = 0.01
fit!(yhat, rows=train);
```

Node args: 1: Node formula: inverse_transform( machine(UnivariateBoxCoxTransformer(n = 171, …), …), predict( machine(RidgeRegressor(lambda = 0.01, …), …), transform( machine(Standardizer(features = Symbol[], …), …), Source @357)))

And re-evaluate:

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

0.02690199873622423

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 a`ridge_model`

hyperparameter is changed.

#### Multithreaded training

A more complicated learning network (e.g., some inhomogeneous ensemble of supervised models) may contain machines that can be trained in parallel. In that case, a call to a node `N`

, such as `fit!(N, accleration=CPUThreads())`

, will parallelize the training using multithreading.

### Learning network machines

As we show shortly, 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 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 trained 0 times; does not cache data model: DeterministicSurrogate() args: 1: Source @357 ⏎ `Table{AbstractVector{Continuous}}` 2: Source @088 ⏎ `AbstractVector{Continuous}`

Notice that a keyword 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

```
fit!(mach)
predict(mach, X[test,:]);
```

is equivalent to

```
fit!(yhat)
yhat(X[test,:]);
```

Like an ordinary machine, once can call `report(mach)`

and `fitted_params(mach)`

. While its main purpose is for export (see below), this machine can even be evaluated:

`evaluate!(mach, resampling=CV(nfolds=3), measure=LPLoss(p=2))`

PerformanceEvaluation object with these fields: measure, operation, measurement, per_fold, per_observation, fitted_params_per_fold, report_per_fold, train_test_rows Extract: ┌──────────┬───────────┬─────────────┬─────────┬──────────────────────────────┐ │ measure │ operation │ measurement │ 1.96*SE │ per_fold │ ├──────────┼───────────┼─────────────┼─────────┼──────────────────────────────┤ │ LPLoss( │ predict │ 0.00151 │ 0.00194 │ [0.00306, 0.000352, 0.00111] │ │ p = 2) │ │ │ │ │ └──────────┴───────────┴─────────────┴─────────┴──────────────────────────────┘

For more on constructing learning network machines, see `machine`

.

A learning network machine can also include the additional internal state in its report (as well as in the report of the corresponding exported model). See Exposing internal state of a learning network for this advanced feature.

#### Learning network machines with multithreading

To indicate that a learning network machine should be trained using multithreading (see above for the node case) add the `acceleration=CPUThreads()`

keyword argument to the machine constructor, as in

`machine(Deterministic(), Xs, ys; predict=yhat, acceleration=CPUThreads()) `

## 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
regressor=ridge_model
end
end
```

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
regressor::Deterministic=ridge_model
end
input_scitype = Table(Continuous,Finite)
target_scitype = AbstractVector{<:Continuous}
end
```

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

```
julia> composite = WrappedRegressor()
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
```

All the objects defined in an `@from_network`

call need to be in the global scope of the module from which it is called. A more robust method for exporting learning networks is described under "Method II" below.

### Method II: Finer control

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 also avoids the limitations of using a macro. 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 of the learning network we just exported using Method I.

The `mutable struct`

definition looks like this:

```
mutable struct WrappedRegressor2 <: DeterministicComposite
regressor
end
# 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 MLJ.fit(model::WrappedRegressor2, 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)
end
```

This completes the export process.

Notes:

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 primitivemodelinterface, implemented for each algorithm. Each supervised model type (eg,`RidgeRegressor`

) requires model`fit`

and`predict`

methods, which are called by the correspondingmachine`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 hyperparameters: 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
end
function MLJ.fit(composite::Composite, 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 the 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)
end
kmeans = (@load KMeans pkg=Clustering)()
my_composite = MyComposite(kmeans, nothing, 0.5)
```

MyComposite( 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, operation, measurement, per_fold, per_observation, fitted_params_per_fold, report_per_fold, train_test_rows Extract: ┌─────────────────────┬───────────┬─────────────┬─────────┬───────────────────── │ measure │ operation │ measurement │ 1.96*SE │ per_fold ⋯ ├─────────────────────┼───────────┼─────────────┼─────────┼───────────────────── │ MeanAbsoluteError() │ predict │ 0.275 │ 0.0199 │ [0.271, 0.319, 0.2 ⋯ └─────────────────────┴───────────┴─────────────┴─────────┴───────────────────── 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)
```

Node args: 1: Node formula: #96( +( #98( predict( machine(RidgeRegressor(lambda = 0.1, …), …), transform( machine(OneHotEncoder(features = Symbol[], …), …), Source @245))), #98( predict( machine(KNNRegressor(K = 7, …), …), transform( machine(OneHotEncoder(features = Symbol[], …), …), Source @245)))))

Exporting this learning network as a stand-alone model:

```
@from_network machine(Deterministic(), Xs, ys; predict=yhat) begin
mutable struct DoubleRegressor
regressor1=model1
regressor2=model2
end
end
```

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 the 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 the MLJ source code (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],)
```

## Exposing the internal state of a learning network

This section describes an advanced feature.

Suppose you have a learning network that you would like to export as a new stand-alone model type `MyModel`

. Having bound `MyModel`

to some data in a machine `mach`

, you would like to arrange that `report(mach)`

will record some additional information about the internal state of the learning network that was built internally, when you called `fit!(mach)`

. This is possible by specifying the relevant node or nodes when constructing the associated learning network machine (see Learning network machines above) by including the `report`

keyword argument, as in

`mach = machine(Probabilistic(), Xs, ys, predict=yhat, report=(mean=N1, stderr=N2))`

Here, `yhat`

, `N1`

and `N2`

are nodes in the learning network and `mean`

and `stderr`

are the desired key names for the machine's report. After training this machine, `report(mach).mean`

will return the value of `N1()`

when the underlying learning network was trained, while `report(mach).stderr`

will return the value of `N2()`

.

Note that as `N1`

and `N2`

are called with no arguments, they do not see "production" data, which is a point of difference with the `predict`

node `yhat`

, which is called on the production data `Xnew`

on a call such as `predict(mach, Xnew)`

. However, this also means the nodes can have multiple origin nodes (query `origins`

for details). This is indeed the case in the following dummy example, recording a training error in the composite model report:

```
using MLJ
import MLJModelInterface
struct MyModel <: ProbabilisticComposite
model
end
function MLJModelInterface.fit(composite::MyModel, verbosity, X, y)
Xs = source(X)
ys = source(y)
mach = machine(composite.model, Xs, ys)
yhat = predict(mach, Xs)
e = @node auc(yhat, ys) # <------ node whose state we wish to export
network_mach = machine(Probabilistic(),
Xs,
ys,
predict=yhat,
report=(training_error=e,)) # <------ how we export additional node(s)
return!(network_mach, composite, verbosity)
end
X, y = make_moons()
composite = MyModel(ConstantClassifier())
mach = machine(composite, X, y) |> fit!
err = report(mach).training_error # <------ accesssing the node state
yhat = predict(mach, rows=:);
@assert err ≈ auc(yhat, y) # true
```

## 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 the 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 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 can reference concrete data. A `Source`

object has a single field, `data`

.

`MLJBase.Source`

— Type`MLJBase.source`

— Method`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`

, `sources`

, `origins`

, `node`

.

`MLJBase.rebind!`

— Function`rebind!(s, X)`

Attach new data `X`

to an existing source node `s`

. Not a public method.

`MLJBase.sources`

— Function`MLJBase.origins`

— Function`origins(N)`

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.

### Nodes

`MLJBase.Node`

— Type`Node{T<:Union{Machine,Nothing}}`

Type for nodes in a learning network that are not `Source`

nodes.

The key components of a Node are:

An

*operation*, which will either be static (a fixed function) or dynamic (such as`predict`

or`transform`

).A

`Machine`

object, on which to dispatch the operation (`nothing`

if the operation is static). The training arguments of the machine are generally other nodes, including`Source`

nodes.Upstream connections to other nodes, called its

*arguments*, possibly including`Source`

nodes, one for each data argument of the operation (typically there's just one).

When a node `N`

is called, as in `N()`

, it applies the operation on the machine (if there is one) together with the outcome of calls to its node arguments, to compute the return value. For details on a node's calling behavior, see `node`

.

`MLJBase.node`

— Function`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.

`MLJBase.@node`

— Macro`@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.

**Examples**

```
X = source(π)
W = @node sin(X)
julia> W()
0
X = source(1:10)
Y = @node selectrows(X, 3:4)
julia> Y()
3:4
julia> Y(["one", "two", "three", "four"])
2-element Array{Symbol,1}:
"three"
"four"
X1 = source(4)
X2 = source(5)
add(a, b, c) = a + b + c
N = @node add(X1, 1, X2)
julia> N()
10
```

See also `node`

`MLJBase.@from_network`

— Macro```
@from_network mach [mutable] struct NewCompositeModel
...
end
```

or

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

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`

.

**Example**

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
encoder=hot
decision_tree=tree
end
```

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
encoder::OneHotEncoder=hot
classifier::Probabilistic=tree
end
input_scitype = Table(Continuous, Finite)
is_pure_julia = true
end
```

`MLJBase.return!`

— Function`return!(mach::Machine{<:Surrogate}, model, verbosity; acceleration=CPU1())`

The last call in custom code defining the `MLJBase.fit`

method for a new composite model type. Here `model`

is the instance of the new type appearing in the `MLJBase.fit`

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. Specifically, 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, acceleration=acceleration)`

.Records (among other things) a copy of

`model`

in a variable called`cache`

Returns

`cache`

and outcomes of training in an appropriate form (specifically,`(mach.fitresult, cache, mach.report)`

; see Adding Models for General Use for technical details.)

**Example**

The following code defines, "by hand", a new model type `MyComposite`

for composing standardization (whitening) with a deterministic regressor:

```
mutable struct MyComposite <: DeterministicComposite
regressor
end
function MLJBase.fit(model::MyComposite, 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)
end
```