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lazzy_decomposion.py
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lazzy_decomposion.py
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# -*- coding: utf-8 -*-
"""
Created on Sat Jun 03 13:53:45 2017
@author: Young
"""
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
"""
=======================================
Lazzy learning
=======================================
Input: training set D
query point x_q, or validation set
Kmax - the maximum number of neighbors
Output: y_q - the prediction of the vectorial output of the query point x_q
Steps:
1. Sort increaingly the set vectors {xi} with respect to the diatance to x_1
2. [j] will designate the index of the jth closest neighbor of x_q
3. for k in {2,...,Kmax} do:
y_qk = sum(y[j])/k
# where using [j] collects all the k closest neighbor of x_q
E_look = e_look.mean()
# where e_look = e_k.mean(), e_k = k*(y[j]-y_qk)/(k-1)
end
4. K* = arg min{E_look}
5. y_q = y_qK*
"""
def elu_distance(x_q, X):
"""
计算查询点x_q与训练样本X中各店的欧拉距离
"""
return ((x_q - X)**2).sum(axis = 1)
def abs_distance(x_q, X):
"""
计算查询点x_q与训练样本X中各店的绝对距离
"""
return (abs(x_q - X)).sum(axis = 1)
def err_evaluation(y_pred,y,err = 'abs'):
if err == 'square':
return ((y_pred-y)**2).mean()
else:
return (abs(y_pred-y)).mean()
def lazzy_loo(x_q, X, y, Kmax = 50, dis = elu_distance):
"""
留一法求给定最大邻居数下,所有备选模型:(误差,邻居数);
默认欧拉距离
"""
l = len(y)
if dis == elu_distance:
distance = elu_distance(x_q, X)
else:
distance = abs_distance(x_q, X)
neighbors = distance.argsort()
models = [] # 用模型记录误差及相应的邻居数
for k in xrange(2, Kmax+1):
e_look = 0.0
k_neighbors_idx = neighbors[0:k]
y_qk = y[k_neighbors_idx].mean(axis = 0)
for j in k_neighbors_idx:
# e_loo_kj = 0.0
# e_loo_kj = k * (y[j] - y_qk) / (k - 1)
# e_look += sum(e_loo_kj**2)
# square err
e_look += sum((k * (y[j] - y_qk) / (k - 1))**2)
# # absolute err
# e_look += sum(abs(k * (y[j] - y_qk) / (k - 1)))
models.append((e_look/k/l, k))
return models
def lazzy_prediction(x, X, Y, models, method = 'WIN', dis = elu_distance):
"""
根据学习的models = lazzy_loo(x, X, Y, Kmax),进行预测
method = 'M'为多模型平均
method = 'WM'为加权平均
method = 'WIN'为选择最佳模型
"""
if dis == elu_distance:
distance = elu_distance(x, X)
else:
distance = abs_distance(x, X)
neighbors_idx = distance.argsort()
if method == 'WIN':
models.sort()
num_neighbors = models[0][1]
y_pred = Y[neighbors_idx[0:num_neighbors]].mean(axis = 0)
return y_pred
if method == 'M':
n = len(models)
y_pred = 0.0
for err,num_neighbors in models:
y_pred += Y[neighbors_idx[0:num_neighbors]].mean(axis =0)
return y_pred/n
if method == 'WM':
y_pred = 0.0
total_err = 0.0
models.sort()
err_sorted = sorted([err for err, k in models],reverse = True)
# print err_sorted
i = 0
for err,num_neighbors in models:
y_pred += err_sorted[i] * Y[neighbors_idx[0:num_neighbors]].mean(axis =0)
total_err += err
i += 1
return y_pred/total_err
def create_dataset(seq, input_lags, pre_period):
"""
功能:根据时间序列,及给定的输入时滞及预测时长,构建训数据集(X,Y)
"""
X = []; Y = []
n = len(seq)
window = input_lags + pre_period
for i in xrange(n - window + 1):
# # if do like this, you need to pay attention
x = seq[i: input_lags + i]
#or y = seq[input_lags + i: input_lags + pre_period + i]
y = seq[input_lags + i: window + i]
# # easy to understand
# x_y = seq[i:i+window]
# x = x_y[0:input_lags]
# y = x_y[input_lags:window]
X.append(x)
Y.append(y)
return np.array(X), np.array(Y)
from sklearn.preprocessing import StandardScaler
from sklearn.preprocessing import RobustScaler
def choose_best_lag(seq, pre_period, lags = range(1,30), Kmax = 200):
"""
选择最佳lazzy model,及输入时滞
模型:(误差,延时,邻居数)
"""
models = []
# 标准化
std_sca = StandardScaler().fit(np.array(seq).reshape(-1,1))
# rob_sca = RobustScaler().fit(np.array(seq).reshape(-1,1))
seq = std_sca.transform(np.array(seq).reshape(-1,1))
# 根据时滞及序列创建数据集,并进行交叉验证
from sklearn.model_selection import train_test_split
for input_lag in lags:
# window = input_lag + pre_period
X, Y = create_dataset(seq.flatten(), input_lag, pre_period)
# lazzy_models = lazzy_loo(X[-1], X[0:-1], Y[:-1], Kmax)
# y_pred = lazzy_prediction(X[-1], X[0:-1], Y[:-1], lazzy_models)
# err = err_evaluation(y_pred.flatten(), Y[-1])
#
# lazzy_models.sort()
# models.append((err, input_lag, lazzy_models[0][1]))
# do more cv
# for state in range(0,3):
err = 0.0
X_train, X_test, y_train, y_test = train_test_split(X, Y, test_size=0.01, random_state=0)
for x_q,y_q in zip(X_test,y_test):
lazzy_models = lazzy_loo(x_q, X_train, y_train, Kmax)
y_pred = lazzy_prediction(x_q, X_train, y_train, lazzy_models)
err += err_evaluation(y_pred.flatten(), y_q)
lazzy_models.sort()
models.append((err/len(X_test), input_lag, lazzy_models[0][1]))
models.sort()
best_lag = models[0][1]
best_k = models[0][2]
# fig, ax = plt.subplots()
# ax.plot(y_pred.flatten(),label='prediction')
# ax.plot(Y[-1],label='real')
# ax.set_title('best cv lags')
return models, best_lag, best_k
if __name__ == '__main__':
# df for dataframe, s for series
df = pd.read_csv('Tianchi_power.csv')
df['record_date'] = pd.to_datetime(df['record_date'])
# total power consumption
# 先要把record_date格式转换
s_power_consumption = df.groupby('record_date')['power_consumption'].sum()
# seq = s_power_consumption.values
power = s_power_consumption.values
from statsmodels.tsa.seasonal import seasonal_decompose
decomposition = seasonal_decompose(s_power_consumption.values,freq=7)
trend = decomposition.trend
seasonal = decomposition.seasonal
residual = decomposition.resid
# print 'Ok'
trend = np.concatenate((np.tile(trend[3],3),trend[3:-3],np.tile(trend[-4],3))) # 首尾需要合理填充
residual = power - trend - seasonal
trend_residual = power - seasonal
# for trend
seq = trend_residual
pre_period = 30
seq_test = seq[-pre_period:]
seq_train_cv = seq[:-pre_period]
lag_models, best_trend_lag, best_k = choose_best_lag(seq_train_cv, pre_period,
lags = range(1,120), Kmax = 200)
input_lags = best_trend_lag
# input_lags = 30
window = input_lags + pre_period
std_sca = StandardScaler().fit(np.array(seq).reshape(-1,1)) # fit all seq
seq_train_cv = std_sca.transform(np.array(seq_train_cv).reshape(-1,1))
X, Y = create_dataset(seq_train_cv.flatten(), input_lags, pre_period)
# testing lazzy_prediction()
# 新的样本输入
x = seq[-window:-window+input_lags]
# print 'x1',x
x = std_sca.transform(np.array(x).reshape(-1,1)).flatten()
# print 'x2',x
# drawing
fig, ax = plt.subplots()
ax.plot(seq_test,label='real')
# 真正预测时充分利用cv的数据,重新训练
models = lazzy_loo(x, X, Y, Kmax = 200) # 对于趋势Kmax可以作为一个参数调节
# print 'x3',x
methods = ['WIN','M','WM']
# methods = ['WM','M','WIN']
for method in methods:
y_pred = lazzy_prediction(x, X, Y, models=models, method = method)
y_pred = std_sca.inverse_transform(y_pred.reshape(-1,1))
if method == 'WIN':
err = (abs(y_pred-seq_test)/seq_test).mean()
ax.plot(y_pred,label='%s - %s neighbors with err %.2f%%'%(method,models[0][1],100*err))
else:
err = (abs(y_pred-seq_test)/seq_test).mean()
ax.plot(y_pred,label='%s - %s models with err %.2f%%'%(method,len(models),100*err))
ax.legend()
ax.set_title('trend')
y_trend = y_pred
err = 100*(abs(y_pred.flatten()-seq_test)/seq_test).mean()
print 'trend testing err: %.2f%%'% err
# # for residual
# seq = residual
#
# pre_period = 30
# seq_test = seq[-pre_period:]
# seq_train_cv = seq[:-pre_period]
#
# lag_models, best_resi_lag, best_k = choose_best_lag(seq_train_cv, pre_period, lags = range(1,120), Kmax = 200)
# input_lags = best_resi_lag
## input_lags = 86
# window = input_lags + pre_period
#
# std_sca = StandardScaler().fit(np.array(seq_train_cv).reshape(-1,1))
# seq_train_cv = std_sca.transform(np.array(seq_train_cv).reshape(-1,1))
#
# X, Y = create_dataset(seq_train_cv.flatten(), input_lags, pre_period)
#
# # testing lazzy_prediction()
# # 新的样本输入
# x = seq[-window:-window+input_lags]
# x = std_sca.transform(np.array(x).reshape(-1,1)).flatten()
#
# # drawing
# fig, ax = plt.subplots()
# ax.plot(seq_test,label='real')
# # 真正预测时充分利用cv的数据,重新训练
# models = lazzy_loo(x, X, Y, Kmax = 100)
#
# methods = ['WIN','WM','M']
# methods = ['M','WM','WIN']
# for method in methods:
# y_pred = lazzy_prediction(x, X, Y, models=models, method = method)
# y_pred = std_sca.inverse_transform(y_pred.reshape(-1,1))
# if method == 'WIN':
# err = (abs(y_pred-seq_test)).mean()
# ax.plot(y_pred,label='%s - %s neighbors with err %.2f'%(method,models[0][1],err))
# else:
# err = (abs(y_pred-seq_test)).mean()
# ax.plot(y_pred,label='%s - %s models with err %.2f'%(method,len(models),err))
# ax.legend()
# ax.set_title('residual')
#
# y_resi = y_pred
#
# err = (abs(y_pred-seq_test)).mean()
# print 'residual testing err: %.2f'% err
#
# # restore the predictions
# y_pred = y_resi + y_trend + seasonal[-pre_period:].reshape(-1,1)
# # drawing
# fig, ax = plt.subplots()
# ax.plot(power[-pre_period:],label='real')
# ax.plot(y_pred,label='prediction')
# ax.legend()
#
# err = (abs(y_pred-power[-pre_period:])/power[-pre_period:]).mean()
# print 'testing err: %s'% err
# print 'WM + M'
# """
# ======================================================
# Prediction
# ======================================================
# """
# # for trend
# seq = trend
#
# pre_period = 30
#
## input_lags = best_trend_lag
# input_lags = 3
# window = input_lags + pre_period
#
# std_sca = StandardScaler().fit(np.array(seq).reshape(-1,1))
# seq = std_sca.transform(np.array(seq).reshape(-1,1))
#
# X, Y = create_dataset(seq.flatten(), input_lags, pre_period)
#
# # testing lazzy_prediction()
# # 新的样本输入
# x = seq[-window:-window+input_lags] # or X[-1]
# x = std_sca.transform(np.array(x).reshape(-1,1)).flatten()
#
# # drawing
# fig, ax = plt.subplots()
## ax.plot(seq_test,label='real')
# # 真正预测时充分利用cv的数据,重新训练
# models = lazzy_loo(x, X, Y, Kmax = 200)
# methods = ['WIN','M','WM']
# for method in methods:
# y_pred = lazzy_prediction(x, X, Y, models=models, method = method)
# y_pred = std_sca.inverse_transform(y_pred.reshape(-1,1))
# if method == 'WIN':
# ax.plot(y_pred,label='%s - %s neighbors'%(method,models[0][1]))
# else:
# ax.plot(y_pred,label='%s - %s models'%(method,len(models)))
# ax.legend()
# ax.set_title('Trend Prediction')
#
# y_trend = y_pred
#
# # for residual
# seq = residual
#
## input_lags = best_resi_lag
# input_lags = 86
# window = input_lags + pre_period
#
# std_sca = StandardScaler().fit(np.array(seq).reshape(-1,1))
# seq = std_sca.transform(np.array(seq).reshape(-1,1))
#
# X, Y = create_dataset(seq.flatten(), input_lags, pre_period)
#
# # testing lazzy_prediction()
# # 新的样本输入
# x = seq[-window:-window+input_lags] # or X[-1]
# x = std_sca.transform(np.array(x).reshape(-1,1)).flatten()
#
# # drawing
# fig, ax = plt.subplots()
## ax.plot(seq_test,label='real')
# # 真正预测时充分利用cv的数据,重新训练
# models = lazzy_loo(x, X, Y, Kmax = 200)
# methods = ['M','WM','WIN']
# for method in methods:
# y_pred = lazzy_prediction(x, X, Y, models=models, method = method)
# y_pred = std_sca.inverse_transform(y_pred.reshape(-1,1))
# if method == 'WIN':
# ax.plot(y_pred,label='%s - %s neighbors'%(method,models[0][1]))
# else:
# ax.plot(y_pred,label='%s - %s models'%(method,len(models)))
# ax.legend()
# ax.set_title('Residual Prediction')
#
# y_resi = y_pred
#
# # restoring, final prediction
# y_pred = y_resi + y_trend + seasonal[0:30].reshape(-1,1)
# # drawing
# fig, ax = plt.subplots()
# ax.plot(y_pred,label='prediction')
# ax.legend()
# ax.set_title('Final Prediction')
#
### power9 = y_pred
###
### # write to file
### fr = open('Tianchi_power_predict_table.csv','w')
### fr.write('record_date,power_consumption\n')
### for i,power in enumerate(power9):
### if i+1 < 10:
### fr.write('2016090%s,'%(i+1)+str(int(power))+'\n')
### else:
### fr.write('201609%s,'%(i+1)+str(int(power))+'\n')
### fr.close()
###
### plt.plot(power9)
##