Optimizing Polynomial Coefficients with Theano for Data Fit

This code uses the Theano library to optimize the coefficients of a polynomial that fits the given data points. It defines a polynomial function and uses mean squared error as the loss function to evaluate the accuracy of the fit. Then, it uses Theano's gradient computation to optimize the coefficients of the polynomial.

Technology Stack : Theano, numpy, scipy.optimize

Code Type : The type of code

Code Difficulty : Advanced

                
                    
import numpy as np
from scipy.optimize import minimize_scalar

def optimize_polynomial_coefficients(x, y):
    """
    This function uses Theano to optimize the coefficients of a polynomial that fits the data points x and y.
    """
    # Define the Theano variables
    X = theano.tensor.matrix('X')
    Y = theano.tensor.scalar('Y')
    W = theano.tensor.vector('W')  # Coefficients of the polynomial

    # Define the polynomial function
    f = 1 + X**2 + W.dot(X)

    # Define the loss function (Mean Squared Error)
    loss = (Y - f)**2

    # Define the gradient of the loss function
    dW = theano.tensor.grad(loss, W)

    # Compile the Theano function to compute the loss and its gradient
    fn = theano.function([X, Y, W], [loss, dW], updates={W: W - 0.01 * dW})

    # Initial guess for the coefficients
    initial_coefficients = np.array([0, 1, 0])

    # Optimize the coefficients using minimize_scalar to minimize the loss
    result = minimize_scalar(fn, args=(x, y, initial_coefficients), method='bounded', bounds=(-10, 10))

    # Return the optimized coefficients
    return result.x