def fit(data, labels, label_size, alpha=1.0):
'''
Train standard naive bayes model.
Args:
data(Expr): documents to be trained.
labels(Expr): the correct labels of the training data.
label_size(int): the number of different labels.
alpha(float): alpha parameter of naive bayes model.
'''
# calc document freq
df = expr.reduce(data,
axis=0,
dtype_fn=lambda input: input.dtype,
local_reduce_fn=lambda ex, data, axis: (data > 0).sum(axis),
accumulate_fn=np.add)
idf = expr.log(data.shape[0] * 1.0 / (df + 1)) + 1
# Normalized Frequency for a feature in a document is calculated by dividing the feature frequency
# by the root mean square of features frequencies in that document
square_sum = expr.reduce(data,
axis=1,
dtype_fn=lambda input: input.dtype,
local_reduce_fn=lambda ex, data, axis: np.square(data).sum(axis),
accumulate_fn=np.add)
rms = expr.sqrt(square_sum * 1.0 / data.shape[1])
# calculate weight normalized Tf-Idf
data = data / rms.reshape((data.shape[0], 1)) * idf.reshape((1, data.shape[1]))
# add up all the feature vectors with the same labels
#weights_per_label_and_feature = expr.ndarray((label_size, data.shape[1]), dtype=np.float64)
#for i in range(label_size):
# i_mask = (labels == i)
# weights_per_label_and_feature = expr.assign(weights_per_label_and_feature, np.s_[i, :], expr.sum(data[i_mask, :], axis=0))
weights_per_label_and_feature = expr.shuffle(expr.retile(data, tile_hint=util.calc_tile_hint(data, axis=0)),
_sum_instance_by_label_mapper,
target=expr.ndarray((label_size, data.shape[1]), dtype=np.float64, reduce_fn=np.add),
kw={'labels': labels, 'label_size': label_size},
cost_hint={hash(labels):{'00':0, '01':np.prod(labels.shape)}})
# sum up all the weights for each label from the previous step
weights_per_label = expr.sum(weights_per_label_and_feature, axis=1)
# generate naive bayes per_label_and_feature weights
weights_per_label_and_feature = expr.log((weights_per_label_and_feature + alpha) /
(weights_per_label.reshape((weights_per_label.shape[0], 1)) +
alpha * weights_per_label_and_feature.shape[1]))
return {'scores_per_label_and_feature': weights_per_label_and_feature.optimized().force(),
'scores_per_label': weights_per_label.optimized().force(),
}
def black_scholes(current, strike, maturity, rate, volatility):
d1 = 1.0 / (volatility * sqrt(maturity)) * (
log(current / strike) + (rate + volatility ** 2 / 2) * (maturity)
)
d2 = 1.0 / (volatility * sqrt(maturity)) * (
log(current / strike) + (rate + volatility ** 2 / 2) * (maturity)
) - volatility * maturity
call = norm_cdf(d1) * current - \
norm_cdf(d2) * strike * exp(-rate * maturity)
put = norm_cdf(-d2) * strike * exp(-rate * maturity) - \
norm_cdf(-d1) * current
return put, call
def fit(data, labels, label_size, alpha=1.0):
'''
Train standard naive bayes model.
Args:
data(Expr): documents to be trained.
labels(Expr): the correct labels of the training data.
label_size(int): the number of different labels.
alpha(float): alpha parameter of naive bayes model.
'''
labels = expr.force(labels)
# calc document freq
df = expr.reduce(data,
axis=0,
dtype_fn=lambda input: input.dtype,
local_reduce_fn=lambda ex, data, axis: (data > 0).sum(axis),
accumulate_fn=np.add,
tile_hint=(data.shape[1],))
idf = expr.log(data.shape[0] * 1.0 / (df + 1)) + 1
# Normalized Frequency for a feature in a document is calculated by dividing the feature frequency
# by the root mean square of features frequencies in that document
square_sum = expr.reduce(data,
axis=1,
dtype_fn=lambda input: input.dtype,
local_reduce_fn=lambda ex, data, axis: np.square(data).sum(axis),
accumulate_fn=np.add,
tile_hint=(data.shape[0],))
rms = expr.sqrt(square_sum * 1.0 / data.shape[1])
# calculate weight normalized Tf-Idf
data = data / rms.reshape((data.shape[0], 1)) * idf.reshape((1, data.shape[1]))
# add up all the feature vectors with the same labels
sum_instance_by_label = expr.ndarray((label_size, data.shape[1]),
dtype=np.float64,
reduce_fn=np.add,
tile_hint=(label_size / len(labels.tiles), data.shape[1]))
sum_instance_by_label = expr.shuffle(data,
_sum_instance_by_label_mapper,
target=sum_instance_by_label,
kw={'labels': labels, 'label_size': label_size})
# sum up all the weights for each label from the previous step
weights_per_label = expr.sum(sum_instance_by_label, axis=1, tile_hint=(label_size,))
# generate naive bayes per_label_and_feature weights
weights_per_label_and_feature = expr.shuffle(sum_instance_by_label,
_naive_bayes_mapper,
kw={'weights_per_label': weights_per_label,
'alpha':alpha})
return {'scores_per_label_and_feature': weights_per_label_and_feature.force(),
'scores_per_label': weights_per_label.force(),
}
def fit(data, labels, label_size, alpha=1.0):
'''
Train standard naive bayes model.
Args:
data(Expr): documents to be trained.
labels(Expr): the correct labels of the training data.
label_size(int): the number of different labels.
alpha(float): alpha parameter of naive bayes model.
'''
# calc document freq
df = expr.reduce(data,
axis=0,
dtype_fn=lambda input: input.dtype,
local_reduce_fn=lambda ex, data, axis:
(data > 0).sum(axis),
accumulate_fn=np.add)
idf = expr.log(data.shape[0] * 1.0 / (df + 1)) + 1
# Normalized Frequency for a feature in a document is calculated by dividing the feature frequency
# by the root mean square of features frequencies in that document
square_sum = expr.reduce(
data,
axis=1,
dtype_fn=lambda input: input.dtype,
local_reduce_fn=lambda ex, data, axis: np.square(data).sum(axis),
accumulate_fn=np.add)
rms = expr.sqrt(square_sum * 1.0 / data.shape[1])
# calculate weight normalized Tf-Idf
data = data / rms.reshape((data.shape[0], 1)) * idf.reshape(
(1, data.shape[1]))
# add up all the feature vectors with the same labels
#weights_per_label_and_feature = expr.ndarray((label_size, data.shape[1]), dtype=np.float64)
#for i in range(label_size):
# i_mask = (labels == i)
# weights_per_label_and_feature = expr.assign(weights_per_label_and_feature, np.s_[i, :], expr.sum(data[i_mask, :], axis=0))
weights_per_label_and_feature = expr.shuffle(
expr.retile(data, tile_hint=util.calc_tile_hint(data, axis=0)),
_sum_instance_by_label_mapper,
target=expr.ndarray((label_size, data.shape[1]),
dtype=np.float64,
reduce_fn=np.add),
kw={
'labels': labels,
'label_size': label_size
},
cost_hint={hash(labels): {
'00': 0,
'01': np.prod(labels.shape)
}})
# sum up all the weights for each label from the previous step
weights_per_label = expr.sum(weights_per_label_and_feature, axis=1)
# generate naive bayes per_label_and_feature weights
weights_per_label_and_feature = expr.log(
(weights_per_label_and_feature + alpha) /
(weights_per_label.reshape((weights_per_label.shape[0], 1)) +
alpha * weights_per_label_and_feature.shape[1]))
return {
'scores_per_label_and_feature':
weights_per_label_and_feature.optimized().force(),
'scores_per_label':
weights_per_label.optimized().force(),
}
