def sym_logdensity(self, x):
""" x is a matrix of column datapoints (VxB) V = n_visible, B = batch size """
def density_given_previous_a_and_x(x, w, V_alpha, b_alpha, V_mu, b_mu, V_sigma, b_sigma, activations_factor, p_prev, a_prev, x_prev):
a = a_prev + T.dot(T.shape_padright(x_prev, 1), T.shape_padleft(w, 1))
h = self.nonlinearity(a * activations_factor) # BxH
Alpha = T.nnet.softmax(T.dot(h, V_alpha) + T.shape_padleft(b_alpha)) # BxC
Mu = T.dot(h, V_mu) + T.shape_padleft(b_mu) # BxC
Sigma = T.exp((T.dot(h, V_sigma) + T.shape_padleft(b_sigma))) # BxC
p = p_prev + log_sum_exp(-constantX(0.5) * T.sqr((Mu - T.shape_padright(x, 1)) / Sigma) - T.log(Sigma) - constantX(0.5 * np.log(2 * np.pi)) + T.log(Alpha))
return (p, a, x)
# First element is different (it is predicted from the bias only)
a0 = T.zeros_like(T.dot(x.T, self.W)) # BxH
p0 = T.zeros_like(x[0])
x0 = T.ones_like(x[0])
([ps, _as, _xs], updates) = theano.scan(density_given_previous_a_and_x,
sequences=[x, self.W, self.V_alpha, self.b_alpha, self.V_mu, self.b_mu, self.V_sigma, self.b_sigma, self.activation_rescaling],
outputs_info=[p0, a0, x0])
return (ps[-1], updates)
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