Various loss functions

Linear exponential (Python)

Why LINEX

Asset return application

Python set-up

library('reticulate')
use_condaenv(condaenv = 'STOCK_MASTER', required = TRUE)

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

Loss function

def linex(y, yhat, alpha = 0.5):
    error = y - yhat
    return np.exp(alpha * np.sign(y) * error) - (alpha * np.sign(y)) * error - 1

Plot

Note that ax.view_init(elev=30, azim=-60) are the defaults that set the angle and rotation of viewing.

elev: elevation, the angle above/below the x-y axis
azim: azimuth, rotation about the z axis

# Data
ys = np.linspace(-1.5, 1.5, 30)
yhats = np.linspace(-1.5, 1.5, 30) 
y, yhat = np.meshgrid(ys, yhats) 
z = linex(y, yhat)

# Plot
ax = plt.axes(projection='3d');
ax.plot_surface(y, yhat, z, rstride=1, cstride=1, cmap='viridis', edgecolor='none');
ax.set_xlabel('y');
ax.set_ylabel('yhat');
ax.set_zlabel('loss');
ax.set_title('Linear exponenial');
ax.view_init(10, -15);
ax.set_zlim(0, 3);
plt.show();

Plot (via function - experiment)

Per SO

Blog post

Subplots

# Function
def plot_fun(gr=1, ax=None, **kwargs):
    
    # Use the axes you have specified or gets the current axes from matplotlib
    #ax = ax or plt.gca()
    ax = plt.axes(projection='3d')
    
    # Data
    ys = np.linspace(gr*-1, gr, 30)
    yhats = ys 
    y, yhat = np.meshgrid(ys, yhats) 
    z = linex(y, yhat)
    ax.plot_surface(y, yhat, z, rstride=1, cstride=1, cmap='viridis', edgecolor='none')
    ax.set_xlabel('y')
    ax.set_ylabel('yhat')
    ax.set_zlabel('loss')
    ax.set_title('Linear exponenial')
    
    return ax


# Plot
plot_fun(gr=0.5);
plt.show();