main.py

# Task 1b
import numpy as np
import pandas as pd

# This task is about linear regression: given an input vector x, your goal is to
# predict a value y as a linear function of a set of feature transformations, phi(x)

df = pd.read_csv('C:/Users/Lannan Jiang/PycharmProjects/IML_Task1b/train.csv')

X_train = np.asarray(df.loc[:, 'x1':'x5'])
y_train = np.asarray(df.loc[:, 'y']).reshape(X_train.shape[0], 1)
Id = np.asarray(df.loc[:, 'Id'])

# Step 1: compute phi
# Step 2: use the transformed features to fit the model to find the weight vector


# quadratic
def generate_quadratic(X, degree=2):
    X = X ** degree
    return X


# Exponential
def generate_exponential(X):
    X = np.exp(X)
    return X


# Cosine
def generate_cosine(X):
    X = np.cos(X)
    return X


# linear is just linear

# phi size: 700x21
phi = np.zeros((X_train.shape[0], 21))

# compute phi
for j in range(0, phi.shape[0]):
    if j < 5:
        phi[:, j] = X_train[:, j]
    elif 5 <= j < 10:
        phi[:, j] = generate_quadratic(X_train[:, j-5])
    elif 10 <= j < 15:
        phi[:, j] = generate_exponential(X_train[:, j-10])
    elif 15 <= j < 20:
        phi[:, j] = generate_cosine(X_train[:, j-15])
    elif j == 20:
        phi[:, j] = np.ones(X_train.shape[0])

weights = np.linalg.solve(np.dot(phi.T, phi), np.dot(phi.T, y_train))

# write to csv
temp_df = pd.DataFrame(weights)
file = 'C:/Users/Lannan Jiang/PycharmProjects/IML_Task1b/submission.csv'
pd.DataFrame(temp_df).to_csv(file, index=False, header=False)