Logical Factorisation Machines

ICML 2018 paper on tensor decomposition

ICML 2017 paper on matrix factorisation

This package generalises the deprecated OrMachine package. If you are looking for an implementation of Boolean Matrix Factorisation or Boolean Tensor Factorisation, you should use Logical Factorisation Machines with the default model OR-AND.

This requires Python 3 and the numba package. The easiest way is to use the Anaconda Python distribution. See here numba installation instructions.

For installation go to the cloned directory and do pip install ..

Basic usage example

All (optional) steps can be ignored.

import lom
import lom.auxiliary_functions as aux

# generate toy data
N = 20
D = 20
L = 3
Z = np.array(np.random.rand(N, L) > .5, dtype=np.int8)
U = np.array(np.random.rand(D, L) > .5, dtype=np.int8)
X = aux.lom_generate_data([2 * Z-1, 2 * U-1], model='OR-AND') # take Boolean product
X_noisy = aux.add_bernoulli_noise_2d(X, p=.1) # add noise

# initialise model
orm = lom.Machine()
data = orm.add_matrix(X_noisy, fixed=True)
layer = orm.add_layer(latent_size=3, child=data, model='OR-AND')

# initialise factors (optional)
layer.factors[0].val = np.array( 2*(np.random.rand(N, L) > .5) - 1, dtype=np.int8)

# Fix particular entries (1s in fixed_entries matrix) (optional)
layer.factors[1].fixed_entries = np.zeros(layer.factors[1]().shape, dtype=np.int8)
layer.factors[1].fixed_entries[0,:] = 1

# Set priors beta prior on sigmoid(lambda) (optional)
layer.lbda.beta_prior = (1,1)

# Set iid bernoulli priors on factor matrix entries (optional)
layer.factors[1].bernoulli_prior = .5

# Use annealing to improve convergence (optional, not needed in general).
orm.anneal = True
layer.lbda.val = 3.0 # if annealing: target temperature, otherwise initial value

# run inference
orm.infer(burn_in_min=100, burn_in_max=1000, no_samples=50)

# inspect the factor mean
[layer.factors[i].show() for i in range(len(layer.factors))]

# inspect the reconstruction
fig, ax = aux.plot_matrix(X_noisy)
ax.set_title('Input data')

fig, ax = aux.plot_matrix(layer.output(technique='factor_map'))
ax.set_title('Reconstruction')

fig, ax = aux.plot_matrix(X)
ax.set_title('Noisefree data')