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MSVR.py
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"""
Multi-output Support Vector Regression
https://github.com/Analytics-for-Forecasting/msvr
"""
# Copyright (C) 2020 Xinze Zhang, Kaishuai Xu, Siyue Yang, Yukun Bao
# This program is free software: you can redistribute it and/or modify
# it under the terms of the Apache.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# Apache License for more details.
import numpy as np
from sklearn.metrics.pairwise import pairwise_kernels
class MSVR():
def __init__(self, kernel='rbf', degree=3, gamma=None, coef0=0.0, tol=0.001, C=1.0, epsilon=0.1):
super(MSVR, self).__init__()
self.kernel = kernel
self.degree = degree
self.gamma = gamma
self.coef0 = coef0
self.tol = tol
self.C = C
self.epsilon = epsilon
self.Beta = None
self.NSV = None
self.xTrain = None
def fit(self, x, y):
self.xTrain = x.copy()
C = self.C
epsi = self.epsilon
tol = self.tol
n_m = np.shape(x)[0] # num of samples
n_d = np.shape(x)[1] # input data dimensionality
n_k = np.shape(y)[1] # output data dimensionality (output variables)
# H = kernelmatrix(ker, x, x, par)
H = pairwise_kernels(x, x, metric=self.kernel, filter_params=True,
degree=self.degree, gamma=self.gamma, coef0=self.coef0)
self.Beta = np.zeros((n_m, n_k))
#E = prediction error per output (n_m * n_k)
E = y - np.dot(H, self.Beta)
#RSE
u = np.sqrt(np.sum(E**2, 1, keepdims=True))
#RMSE
RMSE = []
RMSE_0 = np.sqrt(np.mean(u**2))
RMSE.append(RMSE_0)
#points for which prediction error is larger than epsilon
i1 = np.where(u > epsi)[0]
#set initial values of alphas a (n_m * 1)
a = 2 * C * (u - epsi) / u
#L (n_m * 1)
L = np.zeros(u.shape)
# we modify only entries for which u > epsi. with the sq slack
L[i1] = u[i1]**2 - 2 * epsi * u[i1] + epsi**2
#Lp is the quantity to minimize (sq norm of parameters + slacks)
Lp = []
BetaH = np.dot(np.dot(self.Beta.T, H), self.Beta)
Lp_0 = np.sum(np.diag(BetaH), 0) / 2 + C * np.sum(L)/2
Lp.append(Lp_0)
eta = 1
k = 1
hacer = 1
val = 1
while(hacer):
Beta_a = self.Beta.copy()
E_a = E.copy()
u_a = u.copy()
i1_a = i1.copy()
M1 = H[i1][:, i1] + \
np.diagflat(1/a[i1]) + 1e-10 * np.eye(len(a[i1]))
#compute betas
# sal1 = np.dot(np.linalg.pinv(M1),y[i1]) #求逆or广义逆（M-P逆）无法保证M1一定是可逆的？
sal1 = np.dot(np.linalg.inv(M1), y[i1])
eta = 1
self.Beta = np.zeros(self.Beta.shape)
self.Beta[i1] = sal1.copy()
#error
E = y - np.dot(H, self.Beta)
#RSE
u = np.sqrt(np.sum(E**2, 1)).reshape(n_m, 1)
i1 = np.where(u >= epsi)[0]
L = np.zeros(u.shape)
L[i1] = u[i1]**2 - 2 * epsi * u[i1] + epsi**2
#%recompute the loss function
BetaH = np.dot(np.dot(self.Beta.T, H), self.Beta)
Lp_k = np.sum(np.diag(BetaH), 0) / 2 + C * np.sum(L)/2
Lp.append(Lp_k)
#Loop where we keep alphas and modify betas
while(Lp[k] > Lp[k-1]):
eta = eta/10
i1 = i1_a.copy()
self.Beta = np.zeros(self.Beta.shape)
#%the new betas are a combination of the current (sal1)
#and of the previous iteration (Beta_a)
self.Beta[i1] = eta*sal1 + (1-eta)*Beta_a[i1]
E = y - np.dot(H, self.Beta)
u = np.sqrt(np.sum(E**2, 1)).reshape(n_m, 1)
i1 = np.where(u >= epsi)[0]
L = np.zeros(u.shape)
L[i1] = u[i1]**2 - 2 * epsi * u[i1] + epsi**2
BetaH = np.dot(np.dot(self.Beta.T, H), self.Beta)
Lp_k = np.sum(np.diag(BetaH), 0) / 2 + C * np.sum(L)/2
Lp[k] = Lp_k
#stopping criterion 1
if(eta < 1e-16):
Lp[k] = Lp[k-1] - 1e-15
self.Beta = Beta_a.copy()
u = u_a.copy()
i1 = i1_a.copy()
hacer = 0
#here we modify the alphas and keep betas
a_a = a.copy()
a = 2 * C * (u - epsi) / u
RMSE_k = np.sqrt(np.mean(u**2))
RMSE.append(RMSE_k)
if((Lp[k-1]-Lp[k])/Lp[k-1] < tol):
hacer = 0
k = k + 1
#stopping criterion #algorithm does not converge. (val = -1)
if(len(i1) == 0):
hacer = 0
self.Beta = np.zeros(self.Beta.shape)
val = -1
self.NSV = len(i1)
def predict(self, x):
H = pairwise_kernels(x, self.xTrain, metric=self.kernel, filter_params=True,
degree=self.degree, gamma=self.gamma, coef0=self.coef0)
yPred = np.dot(H, self.Beta)
return yPred
# def score(self,x):