linear_regression_vectorized.py

"""
Vectorized Linear Regression using Gradient Descent

Author: Somrita Banerjee (mailto:somritabanerjee126@gmail.com)

Dataset used: CSGO dataset (ADR vs Rating)

References:
https://en.wikipedia.org/wiki/Linear_regression
"""

# /// script
# requires-python = ">=3.13"
# dependencies = [
#     "httpx2",
#     "numpy",
# ]
# ///

import httpx2
import numpy as np


def collect_dataset() -> np.ndarray:
    """Collect dataset of CSGO (ADR vs Rating).

    :return: dataset as a NumPy array

    >>> ds = collect_dataset()
    >>> isinstance(ds, np.ndarray)
    True
    >>> ds.shape[1] >= 2
    True
    """
    response = httpx2.get(
        "https://raw.githubusercontent.com/yashLadha/The_Math_of_Intelligence/"
        "master/Week1/ADRvsRating.csv",
        timeout=10,
    )
    lines = response.text.splitlines()
    data = [line.split(",") for line in lines]
    data.pop(0)  # remove header row
    return np.array(data, dtype=float)


def gradient_descent(
    features: np.ndarray,
    labels: np.ndarray,
    alpha: float = 0.000155,
    iterations: int = 100000,
) -> np.ndarray:
    """Run gradient descent in a fully vectorized form.

    :param features: dataset features
    :param labels: dataset labels
    :param alpha: learning rate
    :param iterations: number of iterations
    :return: learned feature vector theta

    >>> import numpy as np
    >>> features = np.array([[1, 1], [1, 2], [1, 3]])
    >>> labels = np.array([[1], [2], [3]])
    >>> theta = gradient_descent(
    ...     features, labels, alpha=0.01, iterations=1000  # doctest: +SKIP
    ... )

    """
    m, n = features.shape
    theta = np.zeros((n, 1))

    for i in range(iterations):
        predictions = features @ theta
        errors = predictions - labels
        gradients = (features.T @ errors) / m
        theta -= alpha * gradients

        if i % (iterations // 10) == 0:  # log occasionally
            cost = np.sum(errors**2) / (2 * m)
            print(f"Iteration {i + 1}: Error = {cost:.5f}")

    return theta


def mean_absolute_error(predicted_y: np.ndarray, original_y: np.ndarray) -> float:
    """Return mean absolute error.

    >>> pred = np.array([3, -0.5, 2, 7])
    >>> orig = np.array([2.5, 0.0, 2, 8])
    >>> mean_absolute_error(pred, orig)
    0.5
    """
    return float(np.mean(np.abs(original_y - predicted_y)))


def main() -> None:
    dataset = collect_dataset()

    m = dataset.shape[0]
    features = np.c_[np.ones(m), dataset[:, :-1]]  # add intercept term
    labels = dataset[:, -1].reshape(-1, 1)

    theta = gradient_descent(features, labels)
    print("Resultant Feature vector:")
    for value in theta.ravel():
        print(f"{value:.5f}")


if __name__ == "__main__":
    import doctest

    doctest.testmod()  # runs all doctests
    main()  # runs main function