Funzioni di loss personalizzate

Machine Learning per la finanza in Python

Nathan George

Data Science Professor

mancata corrispondenza di direzione

MSE con penalità di direzione

Se predizione e target hanno la stessa direzione:

$ \sum(y - \hat{y})^2$

Se no:

$\sum (y - \hat{y})^2 * \text{penalty} $

Implementare funzioni di loss personalizzate

import tensorflow as tf

Creare una funzione

import tensorflow as tf

# create loss function
def mean_squared_error(y_true, y_pred):

Loss MSE (mean squared error)

import tensorflow as tf

# create loss function
def mean_squared_error(y_true, y_pred):

    loss = tf.square(y_true - y_pred)
    return tf.reduce_mean(loss, axis=-1)

Aggiungi la loss personalizzata a keras

import tensorflow as tf

# create loss function
def mean_squared_error(y_true, y_pred):
    loss = tf.square(y_true - y_pred)
    return tf.reduce_mean(loss, axis=-1)

# enable use of loss with keras
import keras.losses
keras.losses.mean_squared_error = mean_squared_error

# fit the model with our mse loss function
model.compile(optimizer='adam', loss=mean_squared_error)
history = model.fit(scaled_train_features, train_targets, epochs=50)

Verificare la direzione corretta

tf.less(y_true * y_pred, 0)

Direzione corretta:

neg * neg = pos
pos * pos = pos

Direzione errata:

neg * pos = neg
pos * neg = neg

Usare tf.where()

# create loss function
def sign_penalty(y_true, y_pred):
    penalty = 10.
    loss = tf.where(tf.less(y_true * y_pred, 0), 
                    penalty * tf.square(y_true - y_pred), 
                    tf.square(y_true - y_pred))

Mettere tutto insieme

# create loss function
def sign_penalty(y_true, y_pred):
    penalty = 100.
    loss = tf.where(tf.less(y_true * y_pred, 0),
                    penalty * tf.square(y_true - y_pred), 
                    tf.square(y_true - y_pred))

    return tf.reduce_mean(loss, axis=-1)

# enable use of loss with keras
keras.losses.sign_penalty = sign_penalty

Usare la loss personalizzata

# create the model
model = Sequential()
model.add(Dense(50,
                input_dim=scaled_train_features.shape[1],
                activation='relu'))
model.add(Dense(10, activation='relu'))
model.add(Dense(1, activation='linear'))

# fit the model with our custom 'sign_penalty' loss function
model.compile(optimizer='adam', loss=sign_penalty)
history = model.fit(scaled_train_features, train_targets, epochs=50)

La forma a farfalla

train_preds = model.predict(scaled_train_features)
# scatter the predictions vs actual
plt.scatter(train_preds, train_targets)
plt.xlabel('predictions')
plt.ylabel('actual')
plt.show()

grafico a farfalla

Crea la tua funzione di loss!

Machine Learning per la finanza in Python