functions.py

# Copyright 2019 Mycroft AI Inc.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""
Mathematical functions used to customize
computation in various places
"""
frommathimportexp, log, sqrt, pi
importnumpyasnp
fromtypingimport*

LOSS_BIAS=0.9# [0..1] where 1 is inf bias


defset_loss_bias(bias: float):
"""
 Changes the loss bias

 This allows customizing the acceptable tolerance between
 false negatives and false positives

 Near 1.0 reduces false positives
 Near 0.0 reduces false negatives
 """
globalLOSS_BIAS
LOSS_BIAS=bias


defweighted_log_loss(yt, yp) ->Any:
"""
 Binary crossentropy with a bias towards false negatives
 yt: Target
 yp: Prediction
 """
fromkerasimportbackendasK

pos_loss=-(0+yt) *K.log(0+yp+K.epsilon())
neg_loss=-(1-yt) *K.log(1-yp+K.epsilon())

returnLOSS_BIAS*K.mean(neg_loss) + (1.-LOSS_BIAS) *K.mean(pos_loss)


defweighted_mse_loss(yt, yp) ->Any:
"""Standard mse loss with a weighting between false negatives and positives"""
fromkerasimportbackendasK

total=K.sum(K.ones_like(yt))
neg_loss=total*K.sum(K.square(yp* (1-yt))) /K.sum(1-yt)
pos_loss=total*K.sum(K.square(1.- (yp*yt))) /K.sum(yt)

returnLOSS_BIAS*neg_loss+ (1.-LOSS_BIAS) *pos_loss


deffalse_pos(yt, yp) ->Any:
"""
 Metric for Keras that *estimates* false positives while training
 This will not be completely accurate because it weights batches
 equally
 """
fromkerasimportbackendasK
returnK.sum(K.cast(yp* (1-yt) >0.5, 'float')) /K.maximum(1.0, K.sum(1-yt))


deffalse_neg(yt, yp) ->Any:
"""
 Metric for Keras that *estimates* false negatives while training
 This will not be completely accurate because it weights batches
 equally
 """
fromkerasimportbackendasK
returnK.sum(K.cast((1-yp) * (0+yt) >0.5, 'float')) /K.maximum(1.0, K.sum(0+yt))


defload_keras() ->Any:
"""Imports Keras injecting custom functions to prevent exceptions"""
importkeras
keras.losses.weighted_log_loss=weighted_log_loss
keras.metrics.false_pos=false_pos
keras.metrics.false_positives=false_pos
keras.metrics.false_neg=false_neg
returnkeras


defsigmoid(x):
"""Sigmoid squashing function for scalars"""
return1/ (1+exp(-x))


defasigmoid(x):
"""Inverse sigmoid (logit) for scalars"""
return-log(1/x-1)


defpdf(x, mu, std):
"""Probability density function (normal distribution)"""
ifstd==0:
return0
return (1.0/ (std*sqrt(2*pi))) *np.exp(-(x-mu) **2/ (2*std**2))