Composing Models

MLJ has a flexible interface for composing multiple machine learning elements to form a learning network, whose complexity can extend beyond the "pipelines" of other machine learning toolboxes. While these learning networks can be applied directly to learning tasks, they are more commonly used to specify new re-usable, stand-alone, composite model types, that behave like any other model type. The main novelty of composite models is that they include other models as hyper-parameters.

That said, MLJ also provides dedicated syntax for the most common composition use-cases, which are described first below. A description of the general framework begins at Learning Networks.

Linear pipelines

In MLJ a pipeline is a composite model in which models are chained together in a linear (non-branching) chain. Pipelines can include learned or static target transformations, if one of the models is supervised.

To illustrate basic construction of a pipeline, consider the following toy data:

using MLJ
X = (age    = [23, 45, 34, 25, 67],
     gender = categorical(['m', 'm', 'f', 'm', 'f']));
height = [67.0, 81.5, 55.6, 90.0, 61.1];

5-element Array{Float64,1}:
 67.0
 81.5
 55.6
 90.0
 61.1

The code below creates a new pipeline model type called MyPipe for performing the following operations:

• standardize the target variable :height to have mean zero and standard deviation one
• coerce the :age field to have Continuous scitype
• one-hot encode the categorical feature :gender
• train a K-nearest neighbor model on the transformed inputs and transformed target
• restore the predictions of the KNN model to the original :height scale (i.e., invert the standardization)

The code also creates an instance of the new pipeline model type, called pipe, whose hyperparameters hot, knn, and stand are the component model instances specified in the macro expression:

MLJModels.NearestNeighbors_.KNNRegressor(K = 5,
                                         algorithm = :kdtree,
                                         metric = Distances.Euclidean(0.0),
                                         leafsize = 10,
                                         reorder = true,
                                         weights = :uniform,) @ 9…70

julia> pipe = @pipeline MyPipe(X -> coerce(X, :age=>Continuous),
                               hot = OneHotEncoder(),
                               regressor = KNNRegressor(K=3),
                               target = UnivariateStandardizer())

MyPipe(hot = OneHotEncoder(features = Symbol[],
                           drop_last = false,
                           ordered_factor = true,),
       regressor = KNNRegressor(K = 3,
                          metric = MLJModels.KNN.euclidean,
                          kernel = MLJModels.KNN.reciprocal,),
       target = UnivariateStandardizer(),) @ 1…16

We can, for example, evaluate the pipeline like we would any other model:

julia> pipe.regressor.K = 2
julia> pipe.hot.drop_last = true
julia> evaluate(pipe, X, height, resampling=Holdout(), measure=rms, verbosity=2)

[ Info: Training Machine{MyPipe} @ 4…44.
[ Info: Training NodalMachine{OneHotEncoder} @ 1…16.
[ Info: Spawning 1 sub-features to one-hot encode feature :gender.
[ Info: Training NodalMachine{UnivariateStandardizer} @ 5…65.
[ Info: Training NodalMachine{KNNRegressor} @ 1…49.
(measure = MLJBase.RMS[rms],
 measurement = [10.0336],
 per_fold = Array{Float64,1}[[10.0336]],
 per_observation = Missing[missing],)

Incidentally, there is nothing preventing the user from replacing the regressor component in this pipeline with different deterministic regressor:

julia> pipe.regressor = @load RidgeRegressor pkg=MultivariateStats
julia> pipe

MyPipe(hot = OneHotEncoder(features = Symbol[],
                           drop_last = false,
                           ordered_factor = true,),
       regressor = RidgeRegressor(lambda = 1.0,),
       target = UnivariateStandardizer(),) @ 1…16

For important details on including target transformations, see below.

@pipeline NewPipeType(fld1=model1, fld2=model2, ...)
@pipeline NewPipeType(fld1=model1, fld2=model2, ...) prediction_type=:probabilistic

@pipeline MyPipe(X -> coerce(X, :age=>Continuous),
                 hot=OneHotEncoder(),
                 cnst=ConstantClassifier(),
                 yhat -> mode.(yhat))

@load KNNRegressor
@pipeline MyPipe(hot=OneHotEncoder(),
                 knn=KNNRegressor(),
                 target=UnivariateTransformer())

@load KNNRegressor
@pipeline MyPipe(hot=OneHotEncoder(),
                 knn=KNNRegressor(),
                 target = v -> log.(v),
                 inverse = v -> exp.(v))

Homogeneous Ensembles

For performance reasons, creating a large ensemble of models sharing a common set of hyperparameters is achieved in MLJ through a model wrapper, rather than through the learning networks API. See the separate Homogeneous Ensembles section for details.

Learning Networks

Hand-crafting a learning network, as outlined below, is a relatively advanced MLJ feature, 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 ("dynamic data").

In MLJ, a learning network is a directed acyclic graph whose nodes apply an operation, such as predict or transform, using a fixed machine (requiring training) - or which, alternatively, applies a regular (untrained) mathematical operation, such as +, log or vcat, to its input(s). In practice, a learning network works with fixed sources for its training/evaluation data, but can be built and tested in stages. 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).

Different nodes can point to the same machine (i.e., can access a common set of learned parameters) and different machines can wrap a common model (allowing for hyperparameters in different machines to be coupled).

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 predicting separately. Also, different nodes may use the same parameters (fitresult) learned during the training of some model (that is, point to a common nodal machine; see below). For these reasons, simple examples may appear more slightly more complicated than in other frameworks. However, in more sophisticated applications, the extra flexibility is essential.

Building a simple learning network

The diagram above 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, for later comparison with the original test data. The machines, labeled in yellow, are where data to be used for training enters a node, and where training outcomes are stored, as in the basic fit/predict scenario.

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, DataFrames

MLJModels.MultivariateStats_.RidgeRegressor(lambda = 1.0,) @ 6…57

x1 = rand(300)
x2 = rand(300)
x3 = rand(300)
y = exp.(x1 - x2 -2x3 + 0.1*rand(300))
X = DataFrame(x1=x1, x2=x2, x3=x3)

train, test  = partition(eachindex(y), 0.8)

Xs = source(X)
ys = source(y, kind=:target)

Source @ 3…40

Note. One can omit the specification of data at the source nodes (by writing instead Xs = source() and ys = source(kind=:target)) 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.

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)

NodalMachine @ 6…82 = machine(Standardizer{} @ 1…82, 3…40)

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 @ 1…67 = transform(6…82, 3…40)

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

2×3 DataFrame
│ Row │ x1        │ x2       │ x3        │
│     │ Float64   │ Float64  │ Float64   │
├─────┼───────────┼──────────┼───────────┤
│ 1   │ -0.516373 │ 0.675257 │ 1.27734   │
│ 2   │ 0.63249   │ -1.70306 │ 0.0479891 │

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:

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 @ 1…07 = inverse_transform(1…09, predict(2…66, transform(6…82, 3…40)))

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)

[ Info: Not retraining NodalMachine{Standardizer} @ 6…82. It is up-to-date.
[ Info: Training NodalMachine{UnivariateBoxCoxTransformer} @ 1…09.
[ Info: Training NodalMachine{RidgeRegressor} @ 2…66.
Node @ 1…07 = inverse_transform(1…09, predict(2…66, transform(6…82, 3…40)))

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

0.022837595088079567

We can change a hyperparameters and retrain:

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

[ Info: Not retraining NodalMachine{UnivariateBoxCoxTransformer} @ 1…09. It is up-to-date.
[ Info: Not retraining NodalMachine{Standardizer} @ 6…82. It is up-to-date.
[ Info: Updating NodalMachine{RidgeRegressor} @ 2…66.
Node @ 1…07 = inverse_transform(1…09, predict(2…66, transform(6…82, 3…40)))

And re-evaluate:

rms(y[test], yhat(rows=test))
0.039410306910269116

Notable feature. The machine, ridge::NodalMachine{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 networks with sample weights

To build an exportable learning network supporting sample weights, create a source node with ws = source(w; kind=:weights) or ws = source(; kind=weights).

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

The following call simultaneously defines a new model subtype WrappedRegressor <: Supervised and returns an instance of this type, bound to wrapped_regressor:

wrapped_regressor = @from_network WrappedRegressor(regressor=ridge_model) <= yhat

WrappedRegressor(regressor = RidgeRegressor(lambda = 1.0,),) @ 2…63

Any MLJ work-flow can be applied to this composite model:

X, y = @load_boston
evaluate(wrapped_regressor, X, y, resampling=CV(), measure=rms, verbosity=0)

(measure = MLJBase.RMS[rms],
 measurement = [5.26949],
 per_fold = Array{Float64,1}[[3.02163, 4.75385, 5.01146, 4.22582, 8.93383, 3.47707]],
 per_observation = Missing[missing],)

Notes:

• A deep copy of the original learning network ridge_model has become the default value for the field regressor of the new WrappedRegressor struct.

• It is important to have labeled the target source, as in ys = source(y, kind=:target), to ensure the network is exported as a supervised model.

• One can can also use the @from_network to export unsupervised learning networks and the syntax is the same. For example:

langs_composite = @from_network LangsComposite(pca=network_pca) <= Xout

• For a supervised network making probabilistic predictions, one

must add prediction_type=:probabilistic to the end of the @from network call. For example:

petes_composite = @from_network PetesComposite(tree_classifier=network_tree) prediction_type=:probabilistic

Returning to the WrappedRegressor model, we can change the regressor being wrapped if so desired:

wrapped_rgs.regressor = KNNRegressor(K=7)
wrapped_rgs

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 described 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.

We now demonstrate this second method to the preceding example. To see how to use the method to expose user-specified hyperparameters that are not component models, see here.

All learning networks that make deterministic (respectively, probabilistic) predictions export to models of subtype DeterministicNetwork (respectively, ProbabilisticNetwork), Unsupervised learning networks export to UnsupervisedNetwork model subtypes. So our mutable struct definition looks like this:

mutable struct WrappedRegressor2 <: DeterministicNetwork
    regressor
end

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

We now simply cut and paste the code defining the learning network into a model fit method (as opposed to machine fit! methods, which internally dispatch model fit methods on the data bound to the machine):

import MLJBase
function MLJBase.fit(model::WrappedRegressor2, verbosity::Integer, X, y)
    Xs = source(X)
    ys = source(y, kind=:target)

    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)
    fit!(yhat, verbosity=0)

    return fitresults(yhat)
end

The line marked ###, where the new exported model's hyperparameter regressor is spliced into the network, is the only modification. This completes the export process.

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 terminating node of the network built in fit on the data supplied. The expression fitresults(yhat) bundles the terminal node yhat with reports (one for each machine in the network) and moves training data out to a bundled cache object. This ensures machines wrapping exported model instances do not contain actual training data in their fitresult fields.

X, y = @load_boston
wrapped_regressor2 = WrappedRegressor2()
evaluate(wrapped_regressor2, X, y, resampling=CV(), measure=rms, verbosity=0)

(measure = MLJBase.RMS[rms],
 measurement = [5.26287],
 per_fold = Array{Float64,1}[[3.01228, 4.73544, 5.01316, 4.21653, 8.9335, 3.45975]],
 per_observation = Missing[missing],)

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. Common operations, like addition, scalar multiplication, exp, log, vcat, hcat, tabularization (MLJ.table) and matrixification (MLJ.matrix) work out-of-the box.

As a demonstration, 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.

@load RidgeRegressor pkg=MultivariateStats
@load KNNRegressor

Xs = source()
ys = source(kind=:target)

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)

Exporting this learning network as a stand-alone model:

julia> @from_network DoubleRegressor1(regressor1=model1, regressor2=model2) <= yhat
DoubleRegressor1(regressor1 = RidgeRegressor(lambda = 0.1,),
                 regressor2 = KNNRegressor(K = 7,
                                           algorithm = :kdtree,
                                           metric = Distances.Euclidean(0.0),
                                           leafsize = 10,
                                           reorder = true,
                                           weights = :uniform,),) @ 1…93

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

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

Finally, suppose we want a weighted average of the two models, with the weighting controlled by a user-specified parameter mix (the weights being (1 - mix) and mix respectively). We can either use the advanced export Method II above to arrange for our exported model to include mix as a hyperparameter (because @from_network can only expose component models as hyperparameters of the composite) or we can encode the weighting operation in a new custom "static" model type defined in the following way:

mutable struct Averager <: Static
    mix::Float64
end

import MLJBase
MLJBase.transform(a::Averager, _, y1, y2) = (1 - a.mix)*y1 + a.mix*y2

Such static transformers with (unlearned) parameters can have arbitrarily many inputs, but only one output. In the single input case an inverse_transform can also be defined.

Now that the static transformer Averager is defined, our new definition of zhat and yhat become:

averager_model = Averager(0.5)
y1 = predict(mach1, W)
y2 = predict(mach2, W)
averager = machine(averager_model, y1, y2)
zhat = transform(averager, y1, y1)
yhat = exp(zhat)

Exporting to obtain the composite model instance:

composite = @from_network(DoubleRegressor3(regressor1=model1,
                                           regressor2=model2,
                                           averager=averager_model) <= yhat)

Training on some data, using the default regressors and mix=0.2:

julia> composite.averager.mix = 0.2
julia> evaluate(composite, X, y, resampling=Holdout(fraction_train=0.7), measure=rmsl)

Evaluating over 1 folds: 100%[=========================] Time: 0:00:09
(measure = MLJBase.RMSL[rmsl],
 measurement = [0.546889],
 per_fold = Array{Float64,1}[[0.546889]],
 per_observation = Missing[missing],)

More node examples

A node method allows us to overload a given function to node arguments. Here are some examples taken from MLJ source (at work in the example above):

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.

As a final example, here's how to extend row shuffling to nodes:

using Random
Random.shuffle(X::AbstractNode) = node(Y -> MLJ.selectrows(Y, Random.shuffle(1:nrows(Y))), X)
X = (x1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],
     x2 = [:one, :two, :three, :four, :five, :six, :seven, :eight, :nine, :ten])
Xs = source(X)
W = shuffle(Xs)

Node @ 9…86 = #4(6…62)

W()

(x1 = [1, 4, 3, 6, 8, 5, 7, 2, 9, 10],
 x2 = Symbol[:one, :four, :three, :six, :eight, :five, :seven, :two, :nine, :ten],)

The learning network API

Three julia types are part of learning networks: Source, Node and NodalMachine. A NodalMachine is returned by the machine constructor when given nodal arguments instead of concrete data.

The definitions of Node and NodalMachine are coupled because every NodalMachine has Node objects in its args field (the training arguments specified in the constructor) and every Node must specify a NodalMachine, unless it is static (see below).

Formally, a learning network defines two labeled directed acyclic graphs (DAG's) whose nodes are Node or Source objects, and whose labels are NodalMachine 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 complete learning network below (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)
ys = source(y, kind=:target)
ws = source(w, kind=:weight)

Xs = source()
ys = source(kind=:target)
ws = source(kind=:weight)

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

rebind!(s)

sources(W::AbstractNode; kind=:any)

origins(N)

Nodal machines

The key components of a NodalMachine object are:

• A model, specifying a learning algorithm and hyperparameters.

• Training arguments, which specify the nodes acting as proxies for training data on calls to fit!.

• A fitresult, for storing the outcomes of calls to fit!.

A nodal machine is trained in the same way as a regular machine with one difference: Instead of training the model on the wrapped data indexed on rows, it is trained on the wrapped nodes called on rows, with calling being a recursive operation on nodes within a learning network (see below).

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, dispatched on a nodal machine NodalMachine).

• A nodal machine on which to dispatch the operation (void if the operation is static).

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

• A dependency tape, listing of all upstream nodes in the complete learning network, with an order consistent with the learning network as a DAG.

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

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::NodalMachine, args...)

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))

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)

fit!(N::Node; rows=nothing, verbosity::Int=1, force::Bool=false)

fit!(mach::Machine; rows=nothing, verbosity=1, force=false)

MLJBase.fit(mach.model, verbosity, mach.args...)

fit!(mach::NodalMachine; rows=nothing, verbosity=1, force=false)

MLJBase.fit(mach.model, verbosity, mach.args...)

@from_network(NewCompositeModel(fld1=model1, fld2=model2, ...) <= N
@from_network(NewCompositeModel(fld1=model1, fld2=model2, ...) <= N is_probabilistic=false