def generate_information_weight_matrix(expert_predictions, average_distribution, eps=1e-14, KL_weight = 1.0, cross_entropy_weight=1.0, expert_weights=None):
    pdf = utils.cdf_to_pdf(expert_predictions)
    average_pdf = utils.cdf_to_pdf(average_distribution)
    average_pdf[average_pdf<=0] = np.min(average_pdf[average_pdf>0])/2  # KL is not defined when Q=0 and P is not
    inside = pdf * (np.log(pdf) - np.log(average_pdf[None,None,:]))
    inside[pdf<=0] = 0  # (xlog(x) of zero is zero)
    KL_distance_from_average = np.sum(inside, axis=2)  # (NUM_EXPERTS, NUM_VALIDATIONS)
    assert np.isfinite(KL_distance_from_average).all()

    clipped_predictions = np.clip(expert_predictions, 0.0, 1.0)
    cross_entropy_per_sample = - (    average_distribution[None,None,:]  * np.log(   clipped_predictions+eps) +\
                                  (1.-average_distribution[None,None,:]) * np.log(1.-clipped_predictions+eps) )

    cross_entropy_per_sample[cross_entropy_per_sample<0] = 0  # (NUM_EXPERTS, NUM_VALIDATIONS, 600)
    assert np.isfinite(cross_entropy_per_sample).all()
    if expert_weights is None:
        weights = cross_entropy_weight*cross_entropy_per_sample + KL_weight*KL_distance_from_average[:,:,None]  #+  # <- is too big?
    else:
        weights = (cross_entropy_weight*cross_entropy_per_sample + KL_weight*KL_distance_from_average[:,:,None]) * expert_weights[:,None,None]  #+  # <- is too big?

    #make sure the ones without predictions don't get weight, unless absolutely necessary
    weights[np.where((expert_predictions == average_distribution[None,None,:]).all(axis=2))] = 1e-14
    return weights

def weighted_geom_method(prediction_matrix, average, eps=1e-14, expert_weights=None, *args, **kwargs):
    if len(prediction_matrix.flatten()) == 0:
        return np.zeros(600)
    weights = generate_information_weight_matrix(prediction_matrix, average, expert_weights=expert_weights, *args, **kwargs)
    assert np.isfinite(weights).all()
    pdf = utils.cdf_to_pdf(prediction_matrix)
    x_log = np.log(pdf)
    x_log[pdf<=0] = np.log(eps)
    # Compute the mean
    geom_av_log = np.sum(x_log * weights, axis=(0,1)) / (np.sum(weights, axis=(0,1)) + eps)
    geom_av_log = geom_av_log - np.max(geom_av_log)  # stabilizes rounding errors?

    geom_av = np.exp(geom_av_log)
    res = np.cumsum(geom_av/np.sum(geom_av))
    return res

def prodav(x, **kwargs):
    if len(x) == 0:
        return np.zeros(600)
    return np.cumsum(utils.norm_prod(utils.cdf_to_pdf(x)))

def geomav(x, **kwargs):
    if len(x) == 0:
        return np.zeros(600)
    res = np.cumsum(utils.norm_geometric_average(utils.cdf_to_pdf(x)))
    return res

}

# Objective
l2_weight = 0.000
l2_weight_out = 0.000
def build_objective(interface_layers):
    # l2 regu on certain layers
    l2_penalty = nn.regularization.regularize_layer_params_weighted(
        interface_layers["regularizable"], nn.regularization.l2)
    # build objective
    return objectives.KaggleObjective(interface_layers["outputs"], penalty=l2_penalty)

# Testing
postprocess = postprocess.postprocess
test_time_augmentations = 100  # More augmentations since a we only use single slices
tta_average_method = lambda x: np.cumsum(utils.norm_geometric_average(utils.cdf_to_pdf(x)))


# nonlinearity putting a lower bound on it's output
def lb_softplus(lb):
    return lambda x: nn.nonlinearities.softplus(x) + lb


init = nn.init.Orthogonal()

rnn_layer = functools.partial(nn.layers.RecurrentLayer,
    W_in_to_hid=init,
    W_hid_to_hid=init,
    b=nn.init.Constant(0.1),
    nonlinearity=nn.nonlinearities.rectify,
    hid_init=nn.init.Constant(0.),

def make_monotone_distribution_fast(distributions):
    return utils.pdf_to_cdf(np.clip(utils.cdf_to_pdf(distributions), 0.0, 1.0))

def optimize_expert_weights(expert_predictions,
                            average_distribution,
                            mask_matrix=None,
                            targets=None,
                            num_cross_validation_masks=2,
                            num_folds=1,
                            eps=1e-14,
                            cutoff=0.01,
                            do_optimization=True,
                            expert_weights=None,
                            optimal_params=None,
                            special_average=False,
                            *args, **kwargs):
    """
    :param expert_predictions: experts x validation_samples x 600 x
    :param mask_matrix: experts x validation_samples x
    :param targets: validation_samples x 600 x
    :param average_distribution: 600 x
    :param eps:
    :return:
    """
    if expert_weights is not None:
        mask_matrix = mask_matrix[expert_weights>cutoff,:]  # remove
        expert_predictions = expert_predictions[expert_weights>cutoff,:,:]  # remove

    NUM_EXPERTS = expert_predictions.shape[0]
    NUM_FILTER_PARAMETERS = 2
    WINDOW_SIZE = 599

    # optimizing weights
    X = theano.shared(expert_predictions.astype('float32'))  # source predictions = (NUM_EXPERTS, NUM_VALIDATIONS, 600)
    x_coor = theano.shared(np.linspace(-(WINDOW_SIZE-1)/2, (WINDOW_SIZE-1)/2, num=WINDOW_SIZE, dtype='float32'))  # targets = (NUM_VALIDATIONS, 600)

    NUM_VALIDATIONS = expert_predictions.shape[1]
    ind = theano.shared(np.zeros((NUM_VALIDATIONS,), dtype='int32'))  # targets = (NUM_VALIDATIONS, 600)

    if optimal_params is None:
        params_init = np.concatenate([ np.ones((NUM_EXPERTS,), dtype='float32'),
                                       np.ones((NUM_FILTER_PARAMETERS,), dtype='float32') ])
    else:
        params_init = optimal_params.astype('float32')

    params = theano.shared(params_init.astype('float32'))
    #params = T.vector('params', dtype='float32')  # expert weights = (NUM_EXPERTS,)

    C = 0.0001
    if not special_average:
        # Create theano expression
        # inputs:
        W = params[:NUM_EXPERTS]
        weights = T.nnet.softmax(W.dimshuffle('x',0)).dimshuffle(1, 0)
        preds = X.take(ind, axis=1)
        mask = theano.shared(mask_matrix.astype('float32')).take(ind, axis=1)
        # expression
        masked_weights = mask * weights
        tot_masked_weights = T.clip(masked_weights.sum(axis=0), 1e-7, utils.maxfloat)
        preds_weighted_masked = preds * masked_weights.dimshuffle(0, 1, 'x')
        cumulative_distribution = preds_weighted_masked.sum(axis=0) / tot_masked_weights.dimshuffle(0, 'x')
        # loss
        l1_loss = weights.sum()
    else:
        # calculate the weighted average for each of these experts
        weights = generate_information_weight_matrix(expert_predictions, average_distribution)  # = (NUM_EXPERTS, NUM_VALIDATIONS, 600)
        weight_matrix = theano.shared((mask_matrix[:,:,None]*weights).astype('float32'))
        pdf = utils.cdf_to_pdf(expert_predictions)
        x_log = np.log(pdf)
        x_log[pdf<=0] = np.log(eps)
        # Compute the mean
        X_log = theano.shared(x_log.astype('float32'))  # source predictions = (NUM_EXPERTS, NUM_VALIDATIONS, 600)
        X_log_i = X_log.take(ind, axis=1)
        w_i = weight_matrix.take(ind, axis=1)

        W = params[:NUM_EXPERTS]
        w_i = w_i * T.nnet.softmax(W.dimshuffle('x',0)).dimshuffle(1, 0, 'x')

        #the different predictions, are the experts
        geom_av_log = T.sum(X_log_i * w_i, axis=0) / (T.sum(w_i, axis=0) + eps)
        geom_av_log = geom_av_log - T.max(geom_av_log,axis=-1).dimshuffle(0,'x')  # stabilizes rounding errors?

        geom_av = T.exp(geom_av_log)

        geom_pdf = geom_av/T.sum(geom_av,axis=-1).dimshuffle(0,'x')
        l1_loss = 0
        cumulative_distribution = T.cumsum(geom_pdf, axis=-1)

    if not do_optimization:
        ind.set_value(range(NUM_VALIDATIONS))
        f_eval = theano.function([], cumulative_distribution)
        cumulative_distribution = f_eval()
        return cumulative_distribution[0]
    else:
        # convert to theano_values (for regularization)
        t_valid = theano.shared(targets.astype('float32'))  # targets = (NUM_VALIDATIONS, 600)
        t_train = theano.shared(targets.astype('float32'))  # targets = (NUM_VALIDATIONS, 600)

    CRPS_train = T.mean((cumulative_distribution - t_train.take(ind, axis=0))**2) + C * l1_loss
    CRPS_valid = T.mean((cumulative_distribution - t_valid.take(ind, axis=0))**2)

    iter_optimize = theano.function([], CRPS_train, on_unused_input="ignore", updates=lasagne.updates.adam(CRPS_train, [params], 1.0))
    f_val = theano.function([], CRPS_valid)
#.........这里部分代码省略.........