Learning Networks

MLJ has a flexible interface for building networks from multiple machine learning elements, whose complexity extend beyond the "pipelines" of other machine learning toolboxes.

Overview

In the future the casual MLJ user will be able to build common pipeline architetures, such as linear compositites and stacks, with simple macro invocations. Handcrafting a learning network, as outlined below, is an 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 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 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).

As we shall see, exporting a learning network as a reusable model, is quite simple. While one can entirely skip the build-and-train steps, experimenting with raw learning networks may be the best way to understand how the stand-alone models work under the hood.

In MLJ learning networks treat the flow of information during training and predicting separately. For this reason, simpler examples may appear more slighlty more complicated than in other approaches. However, in more sophisticated examples, such as stacking, the separation is essential.

Building a simple learning network

The diagram above depicts a learning network which standardises 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 are labelled in yellow. We first need to import the RidgeRegressor model (you will need MLJModels in your load path):

@load RidgeRegressor

To implement the network, we begin by loading data needed for training and evaluation into source nodes. For testing purposes, we'll use a small synthetic data set:

using Statistics, DataFrames
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) 
ys = source(y)
Xs = source(X)

Source @ 3…40

We label nodes we will construct 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.

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

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 WrappedRidgeI <: Supervised and creates an instance of this type wrapped_modelI:

wrapped_ridgeI = @from_network WrappedRidgeI(ridge=ridge_model) <= (Xs, ys, yhat)

Any MLJ workflow can be applied to this composite model:

julia> params(wrapped_ridgeI)

(ridge = (lambda = 0.01,),)

using CSV
X, y = load_boston()()
evaluate(wrapped_ridgeI, X, y, resampling=CV(), measure=rms, verbosity=0)

6-element Array{Float64,1}:
 3.0225867093289347
 4.755707358891049 
 5.011312664189936 
 4.226827668908119 
 8.93385968738185  
 3.4788524973220545

Notes:

A deep copy of the original learning network ridge_model has become the default value for the field ridge of the new WrappedRidgeI struct.
The tuple (Xs, ys, yhat) must always follow the pattern (source node for inputs, source node for target, terminal prediction node), unless this is an unsupervised learning network, in which case the pattern is (soruce node for inputs, terminal transform node).

Method II:

In the method I above, only models appearing in the network will appear as hyperparamers 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 (see the example under Static operations on nodes below) 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.

All learning networks that make determinisic (respectively, probabilistic) predictions export as models of subtype DeterministicNetwork (respectively, ProbabilisticNetwork):

mutable struct WrappedRidgeII <: DeterministicNetwork
    ridge_model
end

# keyword constructor
WrappedRidgeII(; ridge=RidgeRegressor) = WrappedRidgeII(ridge);

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

function MLJ.fit(model::WrappedRidgeII, 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()  # for making data look normally-distributed
    box = machine(box_model, ys)
    z = transform(box, ys)

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

    yhat = inverse_transform(box, zhat)
    fit!(yhat, verbosity=0)
    
    return fitresults(Xs, ys, yhat)
end

The line marked ###, where the new exported model's hyperparameter ridge is spliced into the network, is the only modification.

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 export process is complete:

using CSV
X, y = load_boston()()
evaluate(wrapped_ridgeI, X, y, resampling=CV(), measure=rms, verbosity=0)

6-element Array{Float64,1}:
 3.0225867093289347
 4.755707358891049 
 5.011312664189936 
 4.226827668908119 
 8.93385968738185  
 3.4788524973220545

Another example of an exported learning network is given in the next subsection.

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" operations as well. Common operations, like addition, scalar multiplication, exp and log work out-of-the box. To demonstrate this, consider the code below defining a composite model 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 a weighted average of 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

mutable struct KNNRidgeBlend <:DeterministicNetwork

    knn_model
    ridge_model
    weights::Tuple{Float64, Float64}

end

function MLJ.fit(model::KNNRidgeBlend, verbosity::Integer, X, y)
    
    Xs = source(X) 
    ys = source(y)

    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
    
    ridge_model = model.ridge_model
    knn_model = model.knn_model

    ridge = machine(ridge_model, W, z) 
    knn = machine(knn_model, W, z)

    # average the predictions of the KNN and ridge models
    zhat = model.weights[1]*predict(ridge, W) + weights[2]*predict(knn, W) 

    # inverse the target transformation
    yhat = exp(zhat) 

    fit!(yhat, verbosity=0)
    
    return fitresults(Xs, ys, yhat)
end

using CSV
X, y = load_reduced_ames()()
knn_model = KNNRegressor(K=2)
ridge_model = RidgeRegressor(lambda=0.1)
weights = (0.9, 0.1)
blended_model = KNNRidgeBlend(knn_model, ridge_model, weights)
evaluate(blended_model, X, y, resampling=Holdout(fraction_train=0.7), measure=rmsl)

julia> evaluate!(mach, resampling=Holdout(fraction_train=0.7), measure=rmsl)
┌ Info: Evaluating using a holdout set. 
│ fraction_train=0.7 
│ shuffle=false 
│ measure=MLJ.rmsl 
│ operation=StatsBase.predict 
└ Resampling from all rows. 
mach = NodalMachine{OneHotEncoder} @ 1…14
mach = NodalMachine{RidgeRegressor} @ 1…87
mach = NodalMachine{KNNRegressor} @ 1…02
0.13108966715886725

A node method allows us to overerload 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 supertype 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.

MLJ.source — Method.

Xs = source(X)

Defines a Source object out of data X. The data can be a vector, categorical vector, or table. The calling behaviour of a source node is this:

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

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 fit-result, 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.

MLJ.node — Type.

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::NodalMachine, 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.