Python：我们如何使用移动平均来平滑噪声信号？

Question

对于随机森林回归的评估，我尝试使用moving average filter为this link RandomForestRegressor改进结果>

import pandas as pd
import math
import matplotlib
import matplotlib.pyplot as plt
import numpy as np
from sklearn.ensemble import RandomForestRegressor, GradientBoostingRegressor
from sklearn.model_selection import GridSearchCV
from sklearn.metrics import r2_score, mean_squared_error, make_scorer
from sklearn.model_selection import train_test_split
from math import sqrt
from sklearn.cross_validation import train_test_split


n_features=3000

df = pd.read_csv('cubic32.csv')

for i in range(1,n_features):
    df['X_t'+str(i)] = df['X'].shift(i)

print(df)

df.dropna(inplace=True)


X = df.drop('Y', axis=1)
y = df['Y']

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.40)

X_train = X_train.drop('time', axis=1)
X_test = X_test.drop('time', axis=1)


parameters = {'n_estimators': [10]}
clf_rf = RandomForestRegressor(random_state=1)
clf = GridSearchCV(clf_rf, parameters, cv=5, scoring='neg_mean_squared_error', n_jobs=-1)
model = clf.fit(X_train, y_train)
model.cv_results_['params'][model.best_index_]
math.sqrt(model.best_score_*-1)
model.grid_scores_

#####
print()
print(model.grid_scores_)
print("The best score: ",model.best_score_)

print("RMSE:",math.sqrt(model.best_score_*-1))

clf_rf.fit(X_train,y_train)
modelPrediction = clf_rf.predict(X_test)
print(modelPrediction)

print("Number of predictions:",len(modelPrediction))

meanSquaredError=mean_squared_error(y_test, modelPrediction)
print("Mean Square Error (MSE):", meanSquaredError)
rootMeanSquaredError = sqrt(meanSquaredError)
print("Root-Mean-Square Error (RMSE):", rootMeanSquaredError)

fig, ax = plt.subplots()
index_values=range(0,len(y_test))

y_test.sort_index(inplace=True)
X_test.sort_index(inplace=True)

modelPred_test = clf_rf.predict(X_test)
ax.plot(pd.Series(index_values), y_test.values)

smoothed = np.convolve(modelPred_test, np.ones(10)/10)
PlotInOne=pd.DataFrame(pd.concat([pd.Series(smoothed), pd.Series(y_test.values)], axis=1))
plt.figure(); PlotInOne.plot(); plt.legend(loc='best')

但是，预测值的图表看起来（如下所示）非常粗糙（蓝线），即使我正在平滑预测值，如下所示

smoothed = np.convolve(modelPred_test, np.ones(10)/10)

橙色线是实际值的图表。

有没有什么方法可以惩罚预测误差（或使用移动平均或其他平滑技术平滑信号的噪声），以便我们得到更接近实际值的图？我也试图增加随机森林树（n_estimators）的估算量，但它似乎没有多大改善。如果我们单独绘制实际值，它看起来如下。