matrix_factorization_sgd.py

def matrix_factorization_sgd(
    D, P, Q, steps=5000, alpha=0.0002, beta=0.02):
  P = theano.shared(P.astype(floatX))
  Q = theano.shared(Q.astype(floatX))
  P_i = T.vector()
  Q_j = T.vector()
  i = T.iscalar()
  j = T.iscalar()
  x = T.scalar()
  error = T.sqr(P_i.dot(Q_j) - x)
  regularization = (beta/2.0) * (P_i.dot(P_i) + Q_j.dot(Q_j))
  cost = error + regularization
  gp, gq = T.grad(cost=cost, wrt=[P_i, Q_j])
  train = theano.function(inputs=[i, j, x],
                          givens=[(P_i, P[i, :]), (Q_j, Q[:, j])],
                          updates=[(P, T.inc_subtensor(P[i, :], -gp * alpha)),
                                   (Q, T.inc_subtensor(Q[:, j], -gq * alpha))])
  for _ in xrange(steps):
    for (row, col), val in np.ndenumerate(D):
      if not getmask(D)[row, col]:
        train(row, col, val)
  return P.get_value(), Q.get_value()