def fit(self, X: Union[pd.DataFrame, np.ndarray], y: Union[pd.DataFrame, np.ndarray, Iterable]) \
-> skbase.ClassifierMixin:
X, y = self._check_X_y_fit(X, y)
self.classes_ = np.unique(y)
self.nfeatures_ = X.shape[1]
bw = np.full(self.nfeatures_, self.bw) if isinstance(self.bw, float) else self.bw
self.model_ = smkernel.KernelReg(endog=y * 2 - 1, exog=X, var_type='c' * self.nfeatures_,
reg_type=self.reg_type, bw=bw,
defaults=smkernelbase.EstimatorSettings(efficient=False))
return self
def justfit(W,X,name,title):
ngoods = W.shape[1]
order = np.argsort(X)
f, (ax) = plt.subplots(ngoods, sharex=True, sharey=False)
f.set_size_inches(20.,50.)
ax[0].set_title(title)
for i in range(ngoods):
for item in ([ax[i].title, ax[i].xaxis.label, ax[i].yaxis.label] +
ax[i].get_xticklabels() + ax[i].get_yticklabels()):
item.set_fontsize(20)
model = kreg.KernelReg(endog=W.T[i], exog=X, var_type='c')
sm_mean, sm_mfx = model.fit()
ax[i].plot( X[order], sm_mean[order], '-r', alpha=1)
ax[i].set_ylabel(goods[i])
f.savefig(name + '.png')
def term2(x, y, z, gamma, kz, h):
n = len(x)
xps = []
for i in range(n):
Wi = (x[i], y[i], z[i])
xp1 = phi_i(Wi, gamma)
xps.append(xp1)
nw = kr.KernelReg(xps, [z], 'c', reg_type='lc', bw='aic')
means, marginals = nw.fit([z])
for i in range(n):
xp2 = Kh(h, kz, z[i])
means[i] *= xp2
mean = means[i].mean()
result = mean
print('E(phi(X|Z)*pdf(Z)) = ', result)
return result
################################################## # Now consider that the quadratic model may not be quite right. # Maybe it is some other nonlinear function. # A nonparametric approach can estimate the relationship # flexibly to determine what functional form should be used. # For kernel regression, we will pass the prices and horsepower # as separate arrays. y = tractors['log_saleprice'] X = tractors['horsepower'] # Initialize the model object. kde_reg = npreg.KernelReg(endog=y, exog=X, var_type='c') # Fit the predictions to a grid of values. X_grid = np.arange(0, 500, 10) kde_pred = kde_reg.fit(data_predict=X_grid) # Plot the fitted curve with a scattergraph of the data. fig, ax = plt.subplots() ax.plot(tractors['horsepower'], tractors['log_saleprice'], '.', alpha=0.5) ax.plot(X_grid, kde_pred[0], '-', color='tab:blue', alpha=0.9) plt.show() #-------------------------------------------------- # Tuning the bandwidth #--------------------------------------------------
def iterative_wls(x, y, tol=1e-6, max_iter=100):
"""Run a weighted least squares linear regression with
iterative refinement of variance. (This is computationally intensive!)
Parameters
----------
x : float
predictor vector of size n*1
y : float
target variable of size n*1
max_iter : int
Maximum number of iterations for IWLS. Default is 100
tol: float
tolerance level for norm of difference of successive estimates for
coefficients of linear regression and robust estimates of spread
of residuals. Defaults to 1e-6
Returns
-------
coefs : float
2*1 vector of coefficients of linear regression.
"""
x = np.c_[np.ones(len(x)), x] # append column vector of 1's
iteration = 0
old_coefs = None
#----------------------------------------
# Run an OLS to get initial estimates
#----------------------------------------
regression = smf.WLS(y, sm.add_constant(x)).fit()
coefs = regression.params
while old_coefs is None or (np.max(abs(coefs - old_coefs)) > tol and
iteration < max_iter):
#----------------------------------------------------------------------
# Construct the log-squared residuals and use a non-parametric
# method (kernel regression) to estimate the conditonal mean.
# Residual can be 0 in which case log-squared residual is not defined.
# Ignore the warning and put a small value for log-squared residual and
# proceed.
# Exponentiate to predict the variance and take inverse of the variance
# as weights.
#----------------------------------------------------------------------
with np.errstate(divide='ignore', invalid='ignore'):
old_coefs = coefs
log_squared_residuals = np.where(regression.resid**2 > 0,
np.log(regression.resid**2),
1e-12)
model = nparam_kreg.KernelReg(endog=y,
exog=log_squared_residuals,
var_type='c')
weights = np.exp(model.fit()[0])**-1
#-------------------------------
# Update regression coefficients
#-------------------------------
regression = sm.WLS(y, sm.add_constant(x), weights=weights).fit()
coefs = regression.params
iteration += 1
return coefs
SE = []
for i in range(len(X)):
X_1 = np.delete(X, i)
Y_1 = np.delete(Y, i)
X_pre, Y_pre = main(X_1, Y_1, h)
Y_p = Y_pre[find_nearest(X_pre, X[i])]
SE.append((Y_p - Y[i]) ** 2)
MSE.append(np.mean(SE))
print(MSE.index(min(MSE)))
# So the best h is 0.686
X_pre, Y_pre = main(X, Y, 0.686)
plt.figure(figsize=(10,6))
plt.plot(X, Y, 'og')
plt.plot(X_pre, Y_pre, color='blue')
plt.xlabel('Crime Rate')
plt.ylabel('Price')
plt.legend(['Data','Pred'])
plt.show()
# 或者使用python的kernel regression包
model = kernel_regression.KernelReg(endog = Y, exog = [X],var_type = 'c',reg_type = "ll",bw = 'cv_ls',ckertype='gaussian')
pred = model.fit(X)[0]
plt.figure(figsize=(10,6))
plt.scatter(X,Y,color = 'green')
plt.scatter(X,pred,color = 'blue')
plt.xlabel('Crime Rate')
plt.ylabel('Price')
plt.legend(['Data','Pred'])
plt.show()