Restricted Boltzmann machines and deep belief networks in Julia

```
Pkg.add("Boltzmann")
```

installing latest development version:

```
Pkg.clone("https://github.com/dfdx/Boltzmann.jl")
```

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.

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.

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)
```

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.

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)
end
```