An interface to the Flux deep learning models for the MLJ machine learning framework

MLJFlux makes it possible to apply the machine learning meta-algorithms provided by MLJ - such as out-of-sample performance evaluation and hyper-parameter optimization - to some classes of supervised deep learning models. It does this by providing an interface to the Flux framework.

Each MLJFlux model has a builder hyperparameter, an object encoding instructions for creating a neural network given the data that the model eventually sees (e.g., the number of classes in a classification problem). While each MLJ model has a simple default builder, users will generally need to define their own builders to get good results, and this will require familiarity with the Flux API for defining a neural network chain.

In the future MLJFlux may provided an assortment of more sophisticated canned builders.

using Pkg
Pkg.activate("my_environment", shared=true)
Pkg.add("MLJFlux")
Pkg.add("MLJ")
Pkg.add("RDatasets")  # for the demo below

Following is an introductory example using a default builder and no standardization of input features.

using MLJ
import RDatasets
iris = RDatasets.dataset("datasets", "iris");
y, X = unpack(iris, ==(:Species), colname -> true, rng=123);
@load NeuralNetworkClassifier

julia> clf = NeuralNetworkClassifier()
NeuralNetworkClassifier(
    builder = Short(
            n_hidden = 0,
            dropout = 0.5,
            σ = NNlib.σ),
    finaliser = NNlib.softmax,
    optimiser = ADAM(0.001, (0.9, 0.999), IdDict{Any,Any}()),
    loss = Flux.crossentropy,
    epochs = 10,
    batch_size = 1,
    lambda = 0.0,
    alpha = 0.0,
    optimiser_changes_trigger_retraining = false) @ 1…60

import Random.seed!; seed!(123)
mach = machine(clf, X, y)
fit!(mach)

julia> training_loss = cross_entropy(predict(mach, X), y) |> mean
0.89526004f0

# increase learning rate and add iterations:
clf.optimiser.eta = clf.optimiser.eta * 2
clf.epochs = clf.epochs + 5

julia> fit!(mach, verbosity=2)
[ Info: Updating Machine{NeuralNetworkClassifier{Short,…}} @240.
[ Info: Loss is 0.853
[ Info: Loss is 0.8207
[ Info: Loss is 0.8072
[ Info: Loss is 0.752
[ Info: Loss is 0.7077
Machine{NeuralNetworkClassifier{Short,…}} @ 1…42

julia> training_loss = cross_entropy(predict(mach, X), y) |> mean
0.7076618f0

julia> fitted_params(mach).chain
Chain(Chain(Dense(4, 3, σ), Flux.Dropout{Float64}(0.5, false), Dense(3, 3)), softmax)

r = range(clf, :epochs, lower=1, upper=200, scale=:log10)
curve = learning_curve(clf, X, y,
                       range=r,
                       resampling=Holdout(fraction_train=0.7),
                       measure=cross_entropy)
using Plots
plot(curve.parameter_values,
       curve.measurements,
       xlab=curve.parameter_name,
       xscale=curve.parameter_scale,
       ylab = "Cross Entropy")

In MLJ a model is a mutable struct storing hyperparameters for some learning algorithm indicated by the model name, and that's all. In particular, an MLJ model does not store learned parameters.

Warning: In Flux the term "model" has another meaning. However, as all Flux "models" used in MLJFLux are Flux.Chain objects, we call them chains, and restrict use of "model" to models in the MLJ sense.

MLJFlux provides four model types, for use with input features X and targets y of the scientific type indicated in the table below. The parameters n_in and n_out refer to information passed to the builder, as described under Defining a new builder below.

Table 1. Input and output types for MLJFlux models

Any AbstractMatrix{<:AbstractFloat} object Xmat can be forced to have scitype Table(Continuous) by replacing it with X = MLJ.table(Xmat). Furthermore, this wrapping, and subsequent unwrapping under the hood, will compile to a no-op. At present this includes support for sparse matrix data, but the implementation has not been optimized for sparse data at this time and so should be used with caution.

Instructions for coercing common image formats into some AbstractVector{<:Image} are here.

MLJ provides two simple builders out of the box:

• MLJFlux.Linear(σ=...) builds a fully connected two layer network with n_in inputs and n_out outputs, with activation function σ, defaulting to a MLJFlux.relu.

• MLJFlux.Short(n_hidden=..., dropout=..., σ=...) builds a full-connected three-layer network with n_in inputs and n_out outputs using n_hidden nodes in the hidden layer and the specified dropout (defaulting to 0.5). An activation function σ is applied between the hidden and final layers. If n_hidden=0 (the default) then n_hidden is the geometric mean of the number of input and output nodes.

See Table 1 above to see how n_in and n_out relate to the data.

All models share the following hyper-parameters:

1. builder: Default = MLJFlux.Linear(σ=Flux.relu) (regressors) or MLJFlux.Short(n_hidden=0, dropout=0.5, σ=Flux.σ) (classifiers)

2. optimiser: The optimiser to use for training. Default = Flux.ADAM()

3. loss: The loss function used for training. Default = Flux.mse (regressors) and Flux.crossentropy (classifiers)

4. n_epochs: Number of epochs to train for. Default = 10

5. batch_size: The batch_size for the data. Default = 1

6. lambda: The regularization strength. Default = 0. Range = [0, ∞)

7. alpha: The L2/L1 mix of regularization. Default = 0. Range = [0, 1]

8. acceleration: Use CUDALibs() for training on GPU; default is CPU1().

9. optimiser_changes_trigger_retraining: True if fitting an associated machine should trigger retraining from scratch whenever the optimiser changes. Default = false

The classifiers have an additional hyperparameter finaliser (default = Flux.softmax) which is the operation applied to the unnormalized output of the final layer to obtain probabilities (outputs summing to one). Default = Flux.softmax. It should return a vector of the same length as its input.

Following is an example defining a new builder for creating a simple fully-connected neural network with two hidden layers, with n1 nodes in the first hidden layer, and n2 nodes in the second, for use in any of the first three models in Table 1. The definition includes one mutable struct and one method:

mutable struct MyNetwork <: MLJFlux.Builder
    n1 :: Int
    n2 :: Int
end

function MLJFlux.build(nn::MyNetwork, n_in, n_out)
    return Chain(Dense(n_in, nn.n1), Dense(nn.n1, nn.n2), Dense(nn.n2, n_out))
end

Note here that n_in and n_out depend on the size of the data (see Table 1).

More generally, defining a new builder means defining a new struct sub-typing MLJFlux.Builder and defining a new MLJFlux.build method with one of these signatures:

MLJFlux.build(builder::MyNetwork, n_in, n_out)
MLJFlux.build(builder::MyNetwork, n_in, n_out, n_channels) # for use with `ImageClassifier`

This method must return a Flux.Chain instance, chain, subject to the following conditions:

• chain(x) must make sense:

  • for any x <: Vector{<:AbstractFloat} of length n_in (for use with one of the first three model types); or

  • for any x <: Array{<:Float32, 3} of size (W, H, n_channels), where n_in = (W, H) and n_channels is 1 or 3 (for use with ImageClassifier)

• The object returned by chain(x) must be an AbstractFloat vector of length n_out.

For an builder example for use with ImageClassifier see below.

Currently, the loss function specified by loss=... is applied internally by Flux and needs to conform to the Flux API. You cannot, for example, supply one of MLJ's probabilistic loss functions, such as MLJ.cross_entropy to one of the classifiers constructors, although you should use MLJ loss functions in MLJ meta-algorithms.

We define a builder that builds a chain with six alternating convolution and max-pool layers, and a final dense layer, which we apply to the MNIST image dataset.

First we define a generic builder (working for any image size, color or gray):

using MLJ
using Flux

# helper function
function flatten(x::AbstractArray)
    return reshape(x, :, size(x)[end])
end

import MLJFlux
mutable struct MyConvBuilder <: MLJFlux.Builder
    filter_size::Int
    channels1::Int
    channels2::Int
    channels3::Int
end

function MLJFlux.build(b::MyConvBuilder, n_in, n_out, n_channels)

    k, c1, c2, c3 = b.filter_size, b.channels1, b.channels2, b.channels3

    mod(k, 2) == 1 || error("`filter_size` must be odd. ")

    # padding to preserve image size on convolution:
    p = div(k - 1, 2)

    # compute size, in first two dims, of output of final maxpool layer:
    half(x) = div(x, 2)
    h = n_in[1] |> half |> half |> half
    w = n_in[2] |> half |> half |> half

    return Chain(
        Conv((k, k), n_channels => c1, pad=(p, p), relu),
        MaxPool((2, 2)),
        Conv((k, k), c1 => c2, pad=(p, p), relu),
        MaxPool((2, 2)),
        Conv((k, k), c2 => c3, pad=(p, p), relu),
        MaxPool((2 ,2)),
        flatten,
        Dense(h*w*c3, n_out))
end

Next, we load some of the MNIST data and check scientific types conform to those is the table above:

N = 1000
X, y = Flux.Data.MNIST.images()[1:N], Flux.Data.MNIST.labels()[1:N];

julia> scitype(X)
AbstractArray{GrayImage{28,28},1}

julia> scitype(y)
AbstractArray{Count,1}

For classifiers, target must have element scitype <: Finite, so we fix this:

y = coerce(y, Multiclass);

Instantiating an image classifier model:

@load ImageClassifier
clf = ImageClassifier(builder=MyConvBuilder(3, 16, 32, 32),
                      epochs=10,
                      loss=Flux.crossentropy)

And evaluating the accuracy of the model on a 30% holdout set:

mach = machine(clf, X, y)

julia> evaluate!(mach,
                 resampling=Holdout(rng=123, fraction_train=0.7),
                 operation=predict_mode,
                 measure=misclassification_rate)
┌────────────────────────┬───────────────┬────────────┐
│ _.measure              │ _.measurement │ _.per_fold │
├────────────────────────┼───────────────┼────────────┤
│ misclassification_rate │ 0.0467        │ [0.0467]   │
└────────────────────────┴───────────────┴────────────┘