First I used R implementation quantile regression, and after that I used Sklearn implementation with the same quantile (tau) and alpha=0.0 (regularization constant). I am getting the same formulas! I tried many "solvers" and still the running time is much longer than that of R.
Running time: Scikit-learn model vs R model
For example:
In R model the default method is "br", and in Sklearn is "lasso". although I changed the method of R implementation to "lasso" the running time just shorter.
Import and create a Data:
import sklearn
print('sklearn version:', sklearn.__version__) # sklearn=1.0.1
import scipy
print('scipy version:', scipy.__version__) # scipy=1.7.2
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
import time
from sklearn.linear_model import QuantileRegressor
from sklearn.base import BaseEstimator, RegressorMixin
from sklearn.metrics import r2_score
from sklearn.ensemble import BaggingRegressor
from rpy2.robjects.packages import importr
from rpy2.robjects import numpy2ri, pandas2ri
pandas2ri.activate() #activate conversion of Python pandas to R data structures
numpy2ri.activate() #activate conversion of Python numpy to R data structures
n_samples, n_features = 10000, 1
X = np.linspace(start=0.0,stop=2.0,num=n_samples).reshape((n_samples,n_features))
y = X+X*np.random.rand(n_samples,n_features)+1
X = pd.DataFrame(data=X, columns=['X'])
y = pd.DataFrame(data=y, columns=['y'])
Function for plot the data (with or without a line):
from typing import NoReturn, List
import matplotlib.lines as mlines
def ScatterPlot(X : np.ndarray, Y : np.ndarray, title : str = "Default", line_coef : List[int] = None)->NoReturn:
print(line_coef)
fig, ax = plt.subplots(figsize=(6, 6))
ax.scatter(X, y, s=80, marker="P", c='green')
xmin, xmax = ax.get_xbound()
ymin, ymax = ax.get_ybound()
plt.title(title)
plt.xlabel("X")
plt.ylabel("Y")
ax.set(xlim=(xmin, xmax), ylim=(ymin, ymax))#, aspect='equal')
ax.grid()
if line_coef is not None:
p1, p2 = [0, line_coef[0]], [1, sum(line_coef)]
ymax = p1[1] + (p2[1] - p1[1]) / (p2[0] - p1[0]) * (xmax - p1[0])
ymin = p1[1] + (p2[1] - p1[1]) / (p2[0] - p1[0]) * (xmin - p1[0])
ax.add_line(mlines.Line2D([xmin,xmax], [ymin,ymax], color='red'))
plt.show()
ScatterPlot(X=X, Y=y)
Functions for getting the formulas:
def R_get_formula():
return (str(coef_R[0]) + ' + ' + ' + '.join(
['{} * [{}]'.format(str(a), str(b)) for a, b in zip(coef_R[1:].tolist(), ['X'])]))
def get_formula_from_sklearn(regressor):
return (str(regressor.intercept_) + ' + ' + ' + '.join(
['{} * [{}]'.format(str(a), str(b)) for a, b in zip(regressor.coef_.tolist(), regressor.feature_names_in_)]))
Fit the data and test the running time and the formulas:
tau=0.95
_quantreg = importr("quantreg") #import quantreg package from R
################# QuantileRegression R #################
start = time.time()
model_R = _quantreg.rq(formula='{} ~ .'.format(y.columns[0]), tau=tau, data=pd.concat(
[y.reset_index(drop=True), X.loc[y.index, :].reset_index(drop=True)], axis=1))
coef_R = numpy2ri.ri2py(model_R[0])
print('R tooks {} seconds to finish'.format(time.time()-start))
print("The formula is: {}".format(R_get_formula()))
print("Tau: {}".format(tau))
ScatterPlot(X=X, y=y, title="QuantileRegression - R",line_coef=coef_R)
################# QuantileRegression sklearn #################
start = time.time()
model_sklearn = QuantileRegressor(quantile=tau, alpha=0.0, solver='highs')
model_sklearn.fit(X, y)
print('Sklearn tooks {} seconds to finish'.format(time.time()-start))
print("The formula is: {}".format(get_formula_from_sklearn(model_sklearn)))
print("Tau: {}".format(tau))
ScatterPlot(X=X, y=y, title="QuantileRegression - sklearn",line_coef=[model_sklearn.intercept_] + list(model_sklearn.coef_))
Why its takes so much longer to fit model in sklearn then R model implementation?