Regression with asymmetric loss function

RegressionAsymmetricLossFunction.py

import numpy as np
import pylab as pl
from lmfit import minimize, Parameters

# Creating some data with some strong random factor
x = np.linspace(0, 10, 50)
y = (x-3)**2 + np.random.rand( 50 )*5

# Defining residuals using an asymmetric loss function
def residual(params, x, data, eps_data):
    alpha = params['alpha']
    beta = params['beta']
    delta = params['delta']

    model = alpha*x + beta*x**2 + delta
    dy = (model - data)
    return dy**2*(np.sign(dy) + 0.8)**2/eps_data


# Setting up the optimization environment
params = Parameters()
params.add('alpha', value=0.1)
params.add('beta', value=0.05)
params.add('delta', value=1000.)
eps_data = 1.0

# Running the optimzation and grabbibg the resulting 
# parameters back
out = minimize(residual, params, args=(x, y, eps_data))
resultparams = out.params.valuesdict()
alpha = resultparams['alpha']
beta  = resultparams['beta']
delta = resultparams['delta']


# Plotting the results
pl.figure()
pl.plot( x, y, 'ko' )
pl.plot( x, alpha*x + beta*x**2 + delta, 'r-' )
pl.show()