我正在研究一个分位数回归神经网络 (QRNN)，它可以作为风力发电的预测器以及虚假数据注入攻击的检测器。
我几乎完成了它，但我试图通过取中位数分位数（tau = 0.5）并使用 RMSE 将其与实际风能进行比较来量化它的准确性（同时还试图绘制实际风能与中位数分位数的关系） . 但是，我一直遇到问题。
因为 q_hat（预测的中位数）是一个 numpy 数组，而 y_test（实际风力测试数据）是一个 pandas 数据框，所以我必须将 y_test 转换为 numpy，但它给了我这个错误：
“AttributeError：‘numpy.ndarray’对象没有属性‘index’”
这是此代码所需的 pinball_loss.py 文件：
import numpy as np
import tensorflow as tf
from keras import backend as K
K.set_floatx('float64')
# pinball loss function with penalty
def pinball_loss(y, q, tau, alpha = 0.001, kappa = 0, margin = 0):
"""
:param y: target
:param q: predicted quantile
:param tau: coverage level
:param alpha: smoothing parameter
:param kappa: penalty term
:param margin: margin for quantile cross-over
:return: quantile loss
"""
# calculate smooth pinball loss function
error = (y - q)
quantile_loss = K.mean(tau * error + alpha * K.softplus(-error / alpha) )
# calculate smooth cross-over penalty
diff = q[:, 1:] - q[:, :-1]
penalty = kappa * K.mean(tf.square(K.maximum(tf.Variable(tf.zeros([1], dtype=tf.float64)), margin - diff)))
return quantile_loss + penalty
这是我在 Jupyter Notebook 中的代码（为方便起见，我用虚线分隔单元格）：
import warnings
warnings.filterwarnings("ignore")
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from sklearn.model_selection import train_test_split
import tensorflow as tf
from tensorflow.keras import regularizers
from tensorflow.keras.models import Sequential
from tensorflow.keras.callbacks import EarlyStopping
from tensorflow.keras.layers import Dense
from tensorflow.keras import backend as K
---------------------------------------------------------------------------------------------------------
data = pd.read_csv('2018 - Lillgrund (Sweden) Offshore Wind Farm Data.csv', header = [0,1])
data = pd.DataFrame(data, columns= [['local_time','output','windspeed'],['Europe/Copenhagen','kW','m/s']])
#Combine local time with Europe/Copenhagen and output with kW as one header.
data.columns = data.columns.map('_'.join)
---------------------------------------------------------------------------------------------------------
#Use the date column as the index.
data['local_time_Europe/Copenhagen'] = pd.to_datetime(data['local_time_Europe/Copenhagen'])
#Two weeks of data from 1/1/18 to 2/1/18 indexed hourly (744 total data points).
date_rng = (data['local_time_Europe/Copenhagen'] >= '2018-1-01') & (data['local_time_Europe/Copenhagen'] <= '2018-2-1 00:00:00')
data = data.loc[date_rng]
#Sets array as dates instead of row number
data.set_index('local_time_Europe/Copenhagen', inplace=True)
#Check to see index
# data.index
---------------------------------------------------------------------------------------------------------
# create lagged time series features
lags = range(1, 6)
df = pd.DataFrame(data= data['output_kW'], index=data.index)
df = df.assign(**{'{} (t-{})'.format("Windspeed", t): data["windspeed_m/s"].shift(t) for t in lags}).dropna()
#Windspeeds are taken from hour before. i.e. original windspeed @ 6am was 10.124 m/s, windspeed @ t-1 (5am) is 9.596 m/s.
---------------------------------------------------------------------------------------------------------
# create training and testing data
X = df.drop(columns=["output_kW"])
Y = df['output_kW']
X_train, X_test, y_train, y_test = train_test_split(X, Y, test_size=0.2, shuffle=False)
---------------------------------------------------------------------------------------------------------
#tau = np.arange(0.05, 1.0, 0.05) Original tau with multiple quantiles that I've already plotted
tau = 0.5 #Single point Quantile prediction
#N_tau = len(tau) #tau starts from 0.05 to 1, incremented by 0.05, which is 19 points.
N_tau = 1
N_features = 5 #Windspeed is the feature for X.
hidden_dim = 40 # number of hidden nodes
Lambda = 0.001 # L2 regularization
# loss function parameters (no need to modify)
loss_param={
'tau': tau,
'alpha': 0.01,
}
---------------------------------------------------------------------------------------------------------
def pinball_loss(y, q, tau, alpha):
"""
:param y: target
:param q: predicted quantile
:param tau: coverage level
:param alpha: smoothing parameter
:param kappa: penalty term
:param margin: margin for quantile cross-over
:return: quantile loss
"""
# calculate smooth pinball loss function
error = (y - q)
quantile_loss = K.mean(tau * error + alpha * K.softplus(-error / alpha) )
return quantile_loss
---------------------------------------------------------------------------------------------------------
# add first layer to a sequential model
model = Sequential()
model.add(Dense(hidden_dim,
input_dim=N_features,
kernel_regularizer=regularizers.l2(Lambda),
activation='relu'))
# add output layer
model.add(Dense(N_tau))
# compile model
model.compile(loss=lambda Y, Q: pinball_loss(y = Y, q = Q, **loss_param), optimizer='Adam')
# fit the model
history = model.fit(X_train, y_train, epochs=1000, verbose=0, batch_size=32, validation_split=0.1);
---------------------------------------------------------------------------------------------------------
plt.plot(history.history['loss']);
plt.plot(history.history['val_loss']);
plt.legend(('Loss', 'Val Loss'))
plt.ylabel('Loss');
plt.xlabel('Epoch');
plt.title("Training Loss");
---------------------------------------------------------------------------------------------------------
# estimate quantiles of testing data
q_hat = model.predict(X_test)
q_hat = pd.DataFrame(q_hat, index = X_test.index)
---------------------------------------------------------------------------------------------------------
N_PI = int(N_tau/2)
#y3 = y_test.to_numpy() #THIS ISN'T WORKING EITHER
y3 = np.array(y_test)
plt.figure(figsize=(12,6))
plt.plot(y3, color='red')
x = y3.index.values
for i in range(N_PI):
y1 = q_hat.iloc[:,i]
y2 = q_hat.iloc[:,-1-i]
plt.fill_between(x, y1, y2, color='blue', alpha=str(1/N_PI))
plt.title('RMSE: %.2f'% np.sqrt(sum((q_hat-y3)**2)/len(y3)));
plt.ylabel('Wind Power')
plt.xlabel('Time (hour)');
上面的最后一个单元格是我收到以下错误的地方：
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
<ipython-input-20-338503ab24ea> in <module>
4 plt.figure(figsize=(12,6))
5 plt.plot(y3, color='red')
----> 6 x = y3.index.values
7 for i in range(N_PI):
8 y1 = q_hat.iloc[:,i]
AttributeError: 'numpy.ndarray' object has no attribute 'index'
当我尝试使用 RMSE 绘制中位数分位数与实际风力功率（红线）时，出现上述“属性误差”后会发生以下情况
我还尝试使用我对建立 tau 的单元格和最后一个单元格的代码进行编辑的代码执行以下操作：
tau = np.arange(0.49, 0.51, 0.01) #Single point Quantile prediction
N_tau = len(tau) #tau starts from 0.05 to 1, incremented by 0.05, which is 19 points.
N_features = 5 #Windspeed is the feature for X.
hidden_dim = 40 # number of hidden nodes
Lambda = 0.001 # L2 regularization
# loss function parameters (no need to modify)
loss_param={
'tau': tau,
'alpha': 0.01,
}
---------------------------------------------------------------------------------------------------------
N_PI = int(N_tau/2)
plt.figure(figsize=(12,6))
plt.plot(y_test, color='red')
x = y_test.index.values
for i in range(N_PI):
y1 = q_hat.iloc[:,i]
y2 = q_hat.iloc[:,-1-i]
plt.fill_between(x, y1, y2, color='blue', alpha=str(1/N_PI))
y3 = (y2.values+y1.values)/2
#y3 is averaging the upper and lower quantiles, which is technically wrong since it isn't the median...
plt.title('RMSE: %.2f'% np.sqrt(sum((y3-y_test)**2)/len(y_test)));
plt.ylabel('Wind Power')
plt.xlabel('Time (hour)');
我得到以下情节： 这是当我做 tau = np.arange(0.49, 0.51, 0.01) 和 N_tau = len(tau)
虽然这看起来是正确的并且几乎是我想要的，但还有另一个问题！每次我重新启动整个内核时，RMSE 都会不断变化（每次都会变小一点，即从 15,000 到 14950 到 14830 等）。
我非常接近完成这个，我只想通过比较中位数与实际风力来验证我的 QRNN 的准确性，但这部分（这可能是一个简单的修复）给我带来了很多麻烦. 请帮忙！