scipy.optimize.least_squares数据在哪里？

Question

I'm trying to run a simple, multi-variate regression of the form

Y = b_1 * X_1 + b_2 * X_2 + b_3 * X_3 + e

with the constraints:

sum(beta) = 1
beta >= 0

I have my input data as below

df = pd.DataFrame(np.random.randint(low=0, high=10, size=(100,4)), 
          columns=['Historic Rate', 'Overnight', '1M','3M'])

Y = df['Historic Rate']
X = df['Overnight','1M','3M]

So i'm looking to use the function scipy.optimize.least_squares like so

scipy.optimize.least_squares(fun, bounds=(0,1),X)

where X = my independent variable data and with the function defined as

Y - B1*X1 - B2*X2 - B3*X3

I am unsure where the input data goes to estimate this OLS?

Answer 1

What is beta in your question? Assuming beta should be the vector containing b1,...,b3, it's just a constrained optimization problem that can be easily solved by scipy's minimize like this:

import pandas as pd
import numpy as np
from scipy.optimize import minimize

# Your Data
df = pd.DataFrame(np.random.randint(low=0, high=10, size=(100,4)), columns=['Historic Rate', 'Overnight', '1M','3M'])
Y = np.array(df['Historic Rate'])
X = np.array(df[['Overnight','1M','3M']])

# Define the Model
model = lambda b, X: b[0] * X[:,0] + b[1] * X[:,1] + b[2] * X[:,2]

# The objective Function to minimize (least-squares regression)
obj = lambda b, Y, X: np.sum(np.abs(Y-model(b, X))**2)

# Bounds: b[0], b[1], b[2] >= 0
bnds = [(0, None), (0, None), (0, None)]

# Constraint: b[0] + b[1] + b[2] - 1 = 0
cons = [{"type": "eq", "fun": lambda b: b[0]+b[1]+b[2] - 1}]

# Initial guess for b[1], b[2], b[3]:
xinit = np.array([0, 0, 1])

res = minimize(obj, args=(Y, X), x0=xinit, bounds=bnds, constraints=cons)
print(f"b1={res.x[0]}, b2={res.x[1]}, b3={res.x[2]}")