Restricted Boltzmann Machines in Julia
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October 2014


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Restricted Boltzmann machines and deep belief networks in Julia



installing latest development version:


RBM Basic Usage

Train RBM:

using Boltzmann

X = randn(100, 2000)    # 2000 observations (examples) 
                        #  with 100 variables (features) each
X = (X + abs(minimum(X))) / (maximum(X) - minimum(X)) # scale X to [0..1]
rbm = GRBM(100, 50)     # define Gaussian RBM with 100 visible (input) 
                        #  and 50 hidden (output) variables
fit(rbm, X)             # fit model to data 

(for more meaningful dataset see MNIST Example)

After model is fitted, you can extract learned coefficients (a.k.a. weights):

W = coef(rbm)

transform data vectors into new higher-level representation (e.g. for further classification):

Xt = transform(rbm, X)  # vectors of X have length 100, vectors of Xt - length 50

or generate vectors similar to given ones (e.g. for recommendation, see example here)

x = ... 
x_new = generate(rbm, x)

RBMs can handle both - dense and sparse arrays. It cannot, however, handle DataArrays because it's up to application how to treat missing values.

RBM Kinds

This package provides implementation of the 2 most popular kinds of restricted Boltzmann machines:

  • BernoulliRBM: RBM with binary visible and hidden units
  • GRBM: RBM with Gaussian visible and binary hidden units

Bernoulli RBM is classic one and works great for modeling binary (e.g. like/dislike) and nearly binary (e.g. logistic-based) data. Gaussian RBM works better when visible variables approximately follow normal distribution, which is often the case e.g. for image data.

Deep Belief Networks

DBNs are created as a stack of named RBMs. Below is an example of training DBN for MNIST dataset:

using Boltzmann
using MNIST

X, y = traindata()
X = X[:, 1:1000]                     # take only 1000 observations for speed
X = X / (maximum(X) - (minimum(X)))  # normalize to [0..1]

layers = [("vis", GRBM(784, 256)),
          ("hid1", BernoulliRBM(256, 100)),
          ("hid2", BernoulliRBM(100, 100))]
dbn = DBN(layers)
fit(dbn, X)
transform(dbn, X)

Deep Autoencoders

Once built, DBN can be converted into a deep autoencoder. Continuing previous example:

dae = unroll(dbn)

DAEs cannot be trained directly, but can be used to transform input data:

transform(dae, X)

In this case output will have the same dimensionality as input, but with a noise removed.

Integration with Mocha

Mocha.jl is an excellent deep learning framework implementing auto-encoders and a number of fine-tuning algorithms. Boltzmann.jl allows to save pretrained model in a Mocha-compatible file format to be used later on for supervised learning. Below is a snippet of the essential API, while complete code is available in Mocha Export Example:

# pretraining and exporting in Boltzmann.jl
dbn_layers = [("vis", GRBM(100, 50)),
              ("hid1", BernoulliRBM(50, 25)),
              ("hid2", BernoulliRBM(25, 20))]
dbn = DBN(dbn_layers)
fit(dbn, X)
save_params(DBN_PATH, dbn)

# loading in Mocha.jl
backend = CPUBackend()
data = MemoryDataLayer(tops=[:data, :label], batch_size=500, data=Array[X, y])
vis = InnerProductLayer(name="vis", output_dim=50, tops=[:vis], bottoms=[:data])
hid1 = InnerProductLayer(name="hid1", output_dim=25, tops=[:hid1], bottoms=[:vis])
hid2 = InnerProductLayer(name="hid2", output_dim=20, tops=[:hid2], bottoms=[:hid1])
loss = SoftmaxLossLayer(name="loss",bottoms=[:hid2, :label])
net = Net("TEST", backend, [data, vis, hid1, hid2])

h5open(DBN_PATH) do h5
    load_network(h5, net)

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