ops.py 文件源码

def GMM_nll(x, mus, sigmas, mix_weights):
    """
    D is dimension of each observation (e.g. frame_size) for each component
    (multivariate Normal with diagonal covariance matrix)
    See `gaussian_nll`

    x : (batch_size, D)
    mus : (batch_size, D, num_gaussians)
    sigmas : (batch_size, D, num_gaussians)
    mix_weights : (batch_size, num_gaussians)
    """
    x = x.dimshuffle(0, 1, 'x')

    # Similar to `gaussian_nll`
    ll_component_wise = lib.floatX(numpy.log(2. * numpy.pi))
    ll_component_wise += 2. * T.log(sigmas)
    ll_component_wise += ((x - mus) / sigmas) ** 2.
    ll_component_wise = ll_component_wise.sum(axis=1)  # on FRAME_SIZE
    ll_component_wise *= lib.floatX(-0.5)  # LL not NLL

    # Now ready to take care of weights of each component
    # Simply applying exp could potentially cause inf/NaN.
    # Look up LogSumExp trick, Softmax in theano, or this:
    # hips.seas.harvard.edu/blog/2013/01/09/computing-log-sum-exp/
    weighted_ll = ll_component_wise + T.log(mix_weights)
    ll_max = T.max(weighted_ll, axis=1, keepdims=True)
    nll = T.log(T.sum(T.exp(weighted_ll - ll_max), axis=1, keepdims=True))
    nll += ll_max
    nll = -nll.sum(axis=1)
    return nll