From 10a0274a1236b2e8f86e133aa08e52c1d3b82be7 Mon Sep 17 00:00:00 2001
From: somrita-banerjee <144698416+somrita-banerjee@users.noreply.github.com>
Date: Sun, 5 Oct 2025 16:32:38 +0530
Subject: [PATCH 01/17] Add naive and vectorized implementations of Linear
 Regression using Gradient Descent

---
 machine_learning/linear_regression_naive.py   | 138 ++++++++++++++++++
 .../linear_regression_vectorized.py           |  96 ++++++++++++
 2 files changed, 234 insertions(+)
 create mode 100644 machine_learning/linear_regression_naive.py
 create mode 100644 machine_learning/linear_regression_vectorized.py

diff --git a/machine_learning/linear_regression_naive.py b/machine_learning/linear_regression_naive.py
new file mode 100644
index 000000000000..ad4b408aa295
--- /dev/null
+++ b/machine_learning/linear_regression_naive.py
@@ -0,0 +1,138 @@
+"""
+Naive implementation of Linear Regression using Gradient Descent.
+
+This version is intentionally less optimized and more verbose,
+designed for educational clarity. It shows the step-by-step
+gradient descent update and error calculation.
+
+Dataset used: CSGO dataset (ADR vs Rating)
+"""
+
+# /// script
+# requires-python = ">=3.13"
+# dependencies = [
+#     "httpx",
+#     "numpy",
+# ]
+# ///
+
+import httpx
+import numpy as np
+
+
+def collect_dataset() -> np.ndarray:
+    """Collect dataset of CSGO (ADR vs Rating)
+
+    :return: dataset as numpy matrix
+    """
+    response = httpx.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
+    dataset = np.matrix(data)
+    return dataset
+
+
+def run_steep_gradient_descent(
+    data_x: np.ndarray, data_y: np.ndarray, len_data: int, alpha: float, theta: np.ndarray
+) -> np.ndarray:
+    """Run one step of steep gradient descent.
+
+    :param data_x: dataset features
+    :param data_y: dataset labels
+    :param len_data: number of samples
+    :param alpha: learning rate
+    :param theta: feature vector (weights)
+
+    :return: updated theta
+
+    >>> import numpy as np
+    >>> data_x = np.array([[1, 2], [3, 4]])
+    >>> data_y = np.array([5, 6])
+    >>> len_data = len(data_x)
+    >>> alpha = 0.01
+    >>> theta = np.array([0.1, 0.2])
+    >>> run_steep_gradient_descent(data_x, data_y, len_data, alpha, theta)
+    array([0.196, 0.343])
+    """
+    prod = np.dot(theta, data_x.T)
+    prod -= data_y.T
+    grad = np.dot(prod, data_x)
+    theta = theta - (alpha / len_data) * grad
+    return theta
+
+
+def sum_of_square_error(
+    data_x: np.ndarray, data_y: np.ndarray, len_data: int, theta: np.ndarray
+) -> float:
+    """Return sum of square error for error calculation.
+
+    >>> vc_x = np.array([[1.1], [2.1], [3.1]])
+    >>> vc_y = np.array([1.2, 2.2, 3.2])
+    >>> round(sum_of_square_error(vc_x, vc_y, 3, np.array([1])), 3)
+    0.005
+    """
+    prod = np.dot(theta, data_x.T)
+    prod -= data_y.T
+    error = np.sum(np.square(prod)) / (2 * len_data)
+    return float(error)
+
+
+def run_linear_regression(data_x: np.ndarray, data_y: np.ndarray) -> np.ndarray:
+    """Run linear regression using gradient descent.
+
+    :param data_x: dataset features
+    :param data_y: dataset labels
+    :return: learned feature vector theta
+    """
+    iterations = 100000
+    alpha = 0.000155
+
+    no_features = data_x.shape[1]
+    len_data = data_x.shape[0] - 1
+
+    theta = np.zeros((1, no_features))
+
+    for i in range(iterations):
+        theta = run_steep_gradient_descent(data_x, data_y, len_data, alpha, theta)
+        error = sum_of_square_error(data_x, data_y, len_data, theta)
+        print(f"Iteration {i + 1}: Error = {error:.5f}")
+
+    return theta
+
+
+def mean_absolute_error(predicted_y: np.ndarray, original_y: np.ndarray) -> float:
+    """Return mean absolute error.
+
+    >>> predicted_y = np.array([3, -0.5, 2, 7])
+    >>> original_y = np.array([2.5, 0.0, 2, 8])
+    >>> mean_absolute_error(predicted_y, original_y)
+    0.5
+    """
+    total = sum(abs(y - predicted_y[i]) for i, y in enumerate(original_y))
+    return total / len(original_y)
+
+
+def main() -> None:
+    """Driver function."""
+    data = collect_dataset()
+
+    len_data = data.shape[0]
+    data_x = np.c_[np.ones(len_data), data[:, :-1]].astype(float)
+    data_y = data[:, -1].astype(float)
+
+    theta = run_linear_regression(data_x, data_y)
+    print("Resultant Feature vector:")
+    for value in theta.ravel():
+        print(f"{value:.5f}")
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+    main()
diff --git a/machine_learning/linear_regression_vectorized.py b/machine_learning/linear_regression_vectorized.py
new file mode 100644
index 000000000000..60e75c01df48
--- /dev/null
+++ b/machine_learning/linear_regression_vectorized.py
@@ -0,0 +1,96 @@
+"""
+Vectorized implementation of Linear Regression using Gradient Descent.
+
+This version uses NumPy vectorization for efficiency.
+It is faster and cleaner than the naive version but assumes
+readers are familiar with matrix operations.
+
+Dataset used: CSGO dataset (ADR vs Rating)
+"""
+
+# /// script
+# requires-python = ">=3.13"
+# dependencies = [
+#     "httpx",
+#     "numpy",
+# ]
+# ///
+
+import httpx
+import numpy as np
+
+
+def collect_dataset() -> np.ndarray:
+    """Collect dataset of CSGO (ADR vs Rating).
+
+    :return: dataset as numpy array
+    """
+    response = httpx.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(
+    x: np.ndarray, y: np.ndarray, alpha: float = 0.000155, iterations: int = 100000
+) -> np.ndarray:
+    """Run gradient descent in a fully vectorized form.
+
+    :param x: dataset features
+    :param y: dataset labels
+    :param alpha: learning rate
+    :param iterations: number of iterations
+    :return: learned feature vector theta
+    """
+    m, n = x.shape
+    theta = np.zeros((n, 1))
+
+    for i in range(iterations):
+        predictions = x @ theta
+        errors = predictions - y
+        gradients = (x.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:
+    """Driver function."""
+    dataset = collect_dataset()
+
+    m = dataset.shape[0]
+    x = np.c_[np.ones(m), dataset[:, :-1]]  # add intercept term
+    y = dataset[:, -1].reshape(-1, 1)
+
+    theta = gradient_descent(x, y)
+    print("Resultant Feature vector:")
+    for value in theta.ravel():
+        print(f"{value:.5f}")
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+    main()
+

From 11fa072c4e84dd2f976a3f80d4cf24e22e06122c Mon Sep 17 00:00:00 2001
From: somrita-banerjee <144698416+somrita-banerjee@users.noreply.github.com>
Date: Sun, 5 Oct 2025 16:44:38 +0530
Subject: [PATCH 02/17] Add references section to docstrings in linear
 regression implementations

---
 machine_learning/linear_regression_naive.py      | 3 +++
 machine_learning/linear_regression_vectorized.py | 3 +++
 2 files changed, 6 insertions(+)

diff --git a/machine_learning/linear_regression_naive.py b/machine_learning/linear_regression_naive.py
index ad4b408aa295..80d89c1e5e97 100644
--- a/machine_learning/linear_regression_naive.py
+++ b/machine_learning/linear_regression_naive.py
@@ -6,6 +6,9 @@
 gradient descent update and error calculation.
 
 Dataset used: CSGO dataset (ADR vs Rating)
+
+References:
+https://en.wikipedia.org/wiki/Linear_regression
 """
 
 # /// script
diff --git a/machine_learning/linear_regression_vectorized.py b/machine_learning/linear_regression_vectorized.py
index 60e75c01df48..4000647faf17 100644
--- a/machine_learning/linear_regression_vectorized.py
+++ b/machine_learning/linear_regression_vectorized.py
@@ -6,6 +6,9 @@
 readers are familiar with matrix operations.
 
 Dataset used: CSGO dataset (ADR vs Rating)
+
+References:
+    https://en.wikipedia.org/wiki/Linear_regression
 """
 
 # /// script

From e879c47b74a5f0463949d5b2c71103ef9b8e71b7 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Sun, 5 Oct 2025 11:15:25 +0000
Subject: [PATCH 03/17] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 machine_learning/linear_regression_naive.py      | 6 +++++-
 machine_learning/linear_regression_vectorized.py | 3 +--
 2 files changed, 6 insertions(+), 3 deletions(-)

diff --git a/machine_learning/linear_regression_naive.py b/machine_learning/linear_regression_naive.py
index 80d89c1e5e97..c39fc7633b67 100644
--- a/machine_learning/linear_regression_naive.py
+++ b/machine_learning/linear_regression_naive.py
@@ -41,7 +41,11 @@ def collect_dataset() -> np.ndarray:
 
 
 def run_steep_gradient_descent(
-    data_x: np.ndarray, data_y: np.ndarray, len_data: int, alpha: float, theta: np.ndarray
+    data_x: np.ndarray,
+    data_y: np.ndarray,
+    len_data: int,
+    alpha: float,
+    theta: np.ndarray,
 ) -> np.ndarray:
     """Run one step of steep gradient descent.
 
diff --git a/machine_learning/linear_regression_vectorized.py b/machine_learning/linear_regression_vectorized.py
index 4000647faf17..b57db90ec49b 100644
--- a/machine_learning/linear_regression_vectorized.py
+++ b/machine_learning/linear_regression_vectorized.py
@@ -61,7 +61,7 @@ def gradient_descent(
 
         if i % (iterations // 10) == 0:  # log occasionally
             cost = np.sum(errors**2) / (2 * m)
-            print(f"Iteration {i+1}: Error = {cost:.5f}")
+            print(f"Iteration {i + 1}: Error = {cost:.5f}")
 
     return theta
 
@@ -96,4 +96,3 @@ def main() -> None:
 
     doctest.testmod()
     main()
-

From d868aba368eb7e0710b07e443c27981647c2ac49 Mon Sep 17 00:00:00 2001
From: somrita-banerjee <144698416+somrita-banerjee@users.noreply.github.com>
Date: Sun, 5 Oct 2025 16:49:37 +0530
Subject: [PATCH 04/17] Refactor function signatures for improved readability
 in linear regression implementation

---
 machine_learning/linear_regression_naive.py | 21 +++++++++++++++++----
 1 file changed, 17 insertions(+), 4 deletions(-)

diff --git a/machine_learning/linear_regression_naive.py b/machine_learning/linear_regression_naive.py
index 80d89c1e5e97..6173ba1cc55c 100644
--- a/machine_learning/linear_regression_naive.py
+++ b/machine_learning/linear_regression_naive.py
@@ -41,7 +41,11 @@ def collect_dataset() -> np.ndarray:
 
 
 def run_steep_gradient_descent(
-    data_x: np.ndarray, data_y: np.ndarray, len_data: int, alpha: float, theta: np.ndarray
+    data_x: np.ndarray,
+    data_y: np.ndarray,
+    len_data: int,
+    alpha: float,
+    theta: np.ndarray
 ) -> np.ndarray:
     """Run one step of steep gradient descent.
 
@@ -70,7 +74,10 @@ def run_steep_gradient_descent(
 
 
 def sum_of_square_error(
-    data_x: np.ndarray, data_y: np.ndarray, len_data: int, theta: np.ndarray
+    data_x: np.ndarray,
+    data_y: np.ndarray,
+    len_data: int,
+    theta: np.ndarray
 ) -> float:
     """Return sum of square error for error calculation.
 
@@ -85,7 +92,10 @@ def sum_of_square_error(
     return float(error)
 
 
-def run_linear_regression(data_x: np.ndarray, data_y: np.ndarray) -> np.ndarray:
+def run_linear_regression(
+    data_x: np.ndarray,
+    data_y: np.ndarray
+) -> np.ndarray:
     """Run linear regression using gradient descent.
 
     :param data_x: dataset features
@@ -108,7 +118,10 @@ def run_linear_regression(data_x: np.ndarray, data_y: np.ndarray) -> np.ndarray:
     return theta
 
 
-def mean_absolute_error(predicted_y: np.ndarray, original_y: np.ndarray) -> float:
+def mean_absolute_error(
+    predicted_y: np.ndarray,
+    original_y: np.ndarray
+) -> float:
     """Return mean absolute error.
 
     >>> predicted_y = np.array([3, -0.5, 2, 7])

From 260f5a6cc41be6558deb53da1504c5decb4438e1 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Sun, 5 Oct 2025 11:21:50 +0000
Subject: [PATCH 05/17] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 machine_learning/linear_regression_naive.py | 21 ++++++++-------------
 1 file changed, 8 insertions(+), 13 deletions(-)

diff --git a/machine_learning/linear_regression_naive.py b/machine_learning/linear_regression_naive.py
index 92b684eac4c8..c39fc7633b67 100644
--- a/machine_learning/linear_regression_naive.py
+++ b/machine_learning/linear_regression_naive.py
@@ -41,7 +41,11 @@ def collect_dataset() -> np.ndarray:
 
 
 def run_steep_gradient_descent(
-    data_x: np.ndarray, data_y: np.ndarray, len_data: int, alpha: float, theta: np.ndarray
+    data_x: np.ndarray,
+    data_y: np.ndarray,
+    len_data: int,
+    alpha: float,
+    theta: np.ndarray,
 ) -> np.ndarray:
     """Run one step of steep gradient descent.
 
@@ -70,10 +74,7 @@ def run_steep_gradient_descent(
 
 
 def sum_of_square_error(
-    data_x: np.ndarray,
-    data_y: np.ndarray,
-    len_data: int,
-    theta: np.ndarray
+    data_x: np.ndarray, data_y: np.ndarray, len_data: int, theta: np.ndarray
 ) -> float:
     """Return sum of square error for error calculation.
 
@@ -88,10 +89,7 @@ def sum_of_square_error(
     return float(error)
 
 
-def run_linear_regression(
-    data_x: np.ndarray,
-    data_y: np.ndarray
-) -> np.ndarray:
+def run_linear_regression(data_x: np.ndarray, data_y: np.ndarray) -> np.ndarray:
     """Run linear regression using gradient descent.
 
     :param data_x: dataset features
@@ -114,10 +112,7 @@ def run_linear_regression(
     return theta
 
 
-def mean_absolute_error(
-    predicted_y: np.ndarray,
-    original_y: np.ndarray
-) -> float:
+def mean_absolute_error(predicted_y: np.ndarray, original_y: np.ndarray) -> float:
     """Return mean absolute error.
 
     >>> predicted_y = np.array([3, -0.5, 2, 7])

From 80082fde9e39e6ee5fdc003368f5620906790c92 Mon Sep 17 00:00:00 2001
From: somrita-banerjee <144698416+somrita-banerjee@users.noreply.github.com>
Date: Sun, 5 Oct 2025 17:08:57 +0530
Subject: [PATCH 06/17] Refactor function signatures for improved readability
 in linear regression implementation

---
 machine_learning/linear_regression_naive.py | 21 ++++++++-------------
 1 file changed, 8 insertions(+), 13 deletions(-)

diff --git a/machine_learning/linear_regression_naive.py b/machine_learning/linear_regression_naive.py
index 92b684eac4c8..c39fc7633b67 100644
--- a/machine_learning/linear_regression_naive.py
+++ b/machine_learning/linear_regression_naive.py
@@ -41,7 +41,11 @@ def collect_dataset() -> np.ndarray:
 
 
 def run_steep_gradient_descent(
-    data_x: np.ndarray, data_y: np.ndarray, len_data: int, alpha: float, theta: np.ndarray
+    data_x: np.ndarray,
+    data_y: np.ndarray,
+    len_data: int,
+    alpha: float,
+    theta: np.ndarray,
 ) -> np.ndarray:
     """Run one step of steep gradient descent.
 
@@ -70,10 +74,7 @@ def run_steep_gradient_descent(
 
 
 def sum_of_square_error(
-    data_x: np.ndarray,
-    data_y: np.ndarray,
-    len_data: int,
-    theta: np.ndarray
+    data_x: np.ndarray, data_y: np.ndarray, len_data: int, theta: np.ndarray
 ) -> float:
     """Return sum of square error for error calculation.
 
@@ -88,10 +89,7 @@ def sum_of_square_error(
     return float(error)
 
 
-def run_linear_regression(
-    data_x: np.ndarray,
-    data_y: np.ndarray
-) -> np.ndarray:
+def run_linear_regression(data_x: np.ndarray, data_y: np.ndarray) -> np.ndarray:
     """Run linear regression using gradient descent.
 
     :param data_x: dataset features
@@ -114,10 +112,7 @@ def run_linear_regression(
     return theta
 
 
-def mean_absolute_error(
-    predicted_y: np.ndarray,
-    original_y: np.ndarray
-) -> float:
+def mean_absolute_error(predicted_y: np.ndarray, original_y: np.ndarray) -> float:
     """Return mean absolute error.
 
     >>> predicted_y = np.array([3, -0.5, 2, 7])

From ebf3ab20f94812ed215373dfc03094e02c7be127 Mon Sep 17 00:00:00 2001
From: somrita-banerjee <144698416+somrita-banerjee@users.noreply.github.com>
Date: Sun, 5 Oct 2025 17:26:14 +0530
Subject: [PATCH 07/17] Update README sections for dataset inputs and usage
 instructions in linear regression implementations

---
 machine_learning/linear_regression_naive.py    | 18 +++++++++++++++++-
 .../linear_regression_vectorized.py            | 16 ++++++++++++++++
 2 files changed, 33 insertions(+), 1 deletion(-)

diff --git a/machine_learning/linear_regression_naive.py b/machine_learning/linear_regression_naive.py
index c39fc7633b67..921d784a20ea 100644
--- a/machine_learning/linear_regression_naive.py
+++ b/machine_learning/linear_regression_naive.py
@@ -1,3 +1,19 @@
+"""README, Author - Somrita Banerjee(mailto:somritabanerjee126@gmail.com)
+Requirements:
+- Python >= 3.13
+- httpx
+- numpy
+
+Inputs:
+- Downloads a CSV dataset (ADR vs Rating) from a public GitHub URL.
+- The dataset should have features in all columns except the last, which is the label.
+
+Usage:
+- Run this script directly:
+    python linear_regression_naive.py
+- The script will fetch the dataset, run linear regression using gradient descent, and print the learned feature vector (theta) and error at each iteration.
+
+"""
 """
 Naive implementation of Linear Regression using Gradient Descent.
 
@@ -120,7 +136,7 @@ def mean_absolute_error(predicted_y: np.ndarray, original_y: np.ndarray) -> floa
     >>> mean_absolute_error(predicted_y, original_y)
     0.5
     """
-    total = sum(abs(y - predicted_y[i]) for i, y in enumerate(original_y))
+    total = sum(abs(predicted_y[i] - y) for i, y in enumerate(original_y))
     return total / len(original_y)
 
 
diff --git a/machine_learning/linear_regression_vectorized.py b/machine_learning/linear_regression_vectorized.py
index b57db90ec49b..5d274f08934a 100644
--- a/machine_learning/linear_regression_vectorized.py
+++ b/machine_learning/linear_regression_vectorized.py
@@ -1,3 +1,19 @@
+"""README, Author - Somrita Banerjee(mailto:somritabanerjee126@gmail.com)
+Requirements:
+- Python >= 3.13
+- httpx
+- numpy
+
+Inputs:
+- The script automatically downloads a CSV dataset (ADR vs Rating) from a public GitHub URL.
+- The dataset must have features in all columns except the last, which is the label (rating).
+
+Usage:
+- Run this script directly:
+    python linear_regression_vectorized.py
+- The script will fetch the dataset, run linear regression using gradient descent, and print the learned feature vector (theta) and error at intervals.
+
+"""
 """
 Vectorized implementation of Linear Regression using Gradient Descent.
 

From 7375f399e87515d54f88574c52a64deb3f879d0c Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Sun, 5 Oct 2025 11:56:37 +0000
Subject: [PATCH 08/17] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 machine_learning/linear_regression_naive.py      | 1 +
 machine_learning/linear_regression_vectorized.py | 1 +
 2 files changed, 2 insertions(+)

diff --git a/machine_learning/linear_regression_naive.py b/machine_learning/linear_regression_naive.py
index 921d784a20ea..c97b9933c760 100644
--- a/machine_learning/linear_regression_naive.py
+++ b/machine_learning/linear_regression_naive.py
@@ -14,6 +14,7 @@
 - The script will fetch the dataset, run linear regression using gradient descent, and print the learned feature vector (theta) and error at each iteration.
 
 """
+
 """
 Naive implementation of Linear Regression using Gradient Descent.
 
diff --git a/machine_learning/linear_regression_vectorized.py b/machine_learning/linear_regression_vectorized.py
index 5d274f08934a..31d69c551688 100644
--- a/machine_learning/linear_regression_vectorized.py
+++ b/machine_learning/linear_regression_vectorized.py
@@ -14,6 +14,7 @@
 - The script will fetch the dataset, run linear regression using gradient descent, and print the learned feature vector (theta) and error at intervals.
 
 """
+
 """
 Vectorized implementation of Linear Regression using Gradient Descent.
 

From 8d33d9042dc0b24f3f61fc556876e5cfe14c5e8d Mon Sep 17 00:00:00 2001
From: somrita-banerjee <144698416+somrita-banerjee@users.noreply.github.com>
Date: Sun, 5 Oct 2025 17:30:50 +0530
Subject: [PATCH 09/17] Add doctests for dataset collection and gradient
 descent functions

---
 machine_learning/linear_regression_naive.py   | 19 ++++++++
 .../linear_regression_vectorized.py           | 44 ++++++++++++++-----
 2 files changed, 52 insertions(+), 11 deletions(-)

diff --git a/machine_learning/linear_regression_naive.py b/machine_learning/linear_regression_naive.py
index 921d784a20ea..dd461a6b31cd 100644
--- a/machine_learning/linear_regression_naive.py
+++ b/machine_learning/linear_regression_naive.py
@@ -43,6 +43,12 @@ def collect_dataset() -> np.ndarray:
     """Collect dataset of CSGO (ADR vs Rating)
 
     :return: dataset as numpy matrix
+
+    >>> ds = collect_dataset()
+    >>> isinstance(ds, np.matrix)
+    True
+    >>> ds.shape[1] >= 2
+    True
     """
     response = httpx.get(
         "https://raw.githubusercontent.com/yashLadha/The_Math_of_Intelligence/"
@@ -111,6 +117,19 @@ def run_linear_regression(data_x: np.ndarray, data_y: np.ndarray) -> np.ndarray:
     :param data_x: dataset features
     :param data_y: dataset labels
     :return: learned feature vector theta
+
+    >>> import numpy as np
+    >>> x = np.array([[1, 1], [1, 2], [1, 3]])
+    >>> y = np.array([1, 2, 3])
+    >>> theta = run_linear_regression(x, y)
+    Iteration 1: Error = ...
+    ... # lots of output omitted
+    >>> theta.shape
+    (1, 2)
+    >>> abs(theta[0, 0] - 0) < 0.1  # intercept close to 0
+    True
+    >>> abs(theta[0, 1] - 1) < 0.1  # slope close to 1
+    True
     """
     iterations = 100000
     alpha = 0.000155
diff --git a/machine_learning/linear_regression_vectorized.py b/machine_learning/linear_regression_vectorized.py
index 5d274f08934a..c9c03bf23bf5 100644
--- a/machine_learning/linear_regression_vectorized.py
+++ b/machine_learning/linear_regression_vectorized.py
@@ -43,6 +43,12 @@ def collect_dataset() -> np.ndarray:
     """Collect dataset of CSGO (ADR vs Rating).
 
     :return: dataset as numpy array
+
+    >>> ds = collect_dataset()
+    >>> isinstance(ds, np.ndarray)
+    True
+    >>> ds.shape[1] >= 2
+    True
     """
     response = httpx.get(
         "https://raw.githubusercontent.com/yashLadha/The_Math_of_Intelligence/"
@@ -56,23 +62,36 @@ def collect_dataset() -> np.ndarray:
 
 
 def gradient_descent(
-    x: np.ndarray, y: np.ndarray, alpha: float = 0.000155, iterations: int = 100000
+    features: np.ndarray, labels: np.ndarray, alpha: float = 0.000155, iterations: int = 100000
 ) -> np.ndarray:
     """Run gradient descent in a fully vectorized form.
 
-    :param x: dataset features
-    :param y: dataset labels
+    :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)
+    Iteration 1: Error = ...
+    ... # output omitted
+    >>> theta.shape
+    (2, 1)
+    >>> abs(theta[0, 0] - 0) < 0.1  # intercept close to 0
+    True
+    >>> abs(theta[1, 0] - 1) < 0.1  # slope close to 1
+    True
     """
-    m, n = x.shape
+    m, n = features.shape
     theta = np.zeros((n, 1))
 
     for i in range(iterations):
-        predictions = x @ theta
-        errors = predictions - y
-        gradients = (x.T @ errors) / m
+        predictions = features @ theta
+        errors = predictions - labels
+        gradients = (features.T @ errors) / m
         theta -= alpha * gradients
 
         if i % (iterations // 10) == 0:  # log occasionally
@@ -94,14 +113,17 @@ def mean_absolute_error(predicted_y: np.ndarray, original_y: np.ndarray) -> floa
 
 
 def main() -> None:
-    """Driver function."""
+    """Driver function.
+
+    >>> main()  # doctest: +SKIP
+    """
     dataset = collect_dataset()
 
     m = dataset.shape[0]
-    x = np.c_[np.ones(m), dataset[:, :-1]]  # add intercept term
-    y = dataset[:, -1].reshape(-1, 1)
+    features = np.c_[np.ones(m), dataset[:, :-1]]  # add intercept term
+    labels = dataset[:, -1].reshape(-1, 1)
 
-    theta = gradient_descent(x, y)
+    theta = gradient_descent(features, labels)
     print("Resultant Feature vector:")
     for value in theta.ravel():
         print(f"{value:.5f}")

From 2e6804dbc293f3284e0c4dc36a9ba273e15ea380 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Sun, 5 Oct 2025 12:01:13 +0000
Subject: [PATCH 10/17] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 machine_learning/linear_regression_vectorized.py | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/machine_learning/linear_regression_vectorized.py b/machine_learning/linear_regression_vectorized.py
index c1ea222e8069..a47e1ac50182 100644
--- a/machine_learning/linear_regression_vectorized.py
+++ b/machine_learning/linear_regression_vectorized.py
@@ -63,7 +63,10 @@ def collect_dataset() -> np.ndarray:
 
 
 def gradient_descent(
-    features: np.ndarray, labels: np.ndarray, alpha: float = 0.000155, iterations: int = 100000
+    features: np.ndarray,
+    labels: np.ndarray,
+    alpha: float = 0.000155,
+    iterations: int = 100000,
 ) -> np.ndarray:
     """Run gradient descent in a fully vectorized form.
 

From 4db85f54d8cf8af7fcae41af60cf44eace47ad57 Mon Sep 17 00:00:00 2001
From: somrita-banerjee <144698416+somrita-banerjee@users.noreply.github.com>
Date: Sun, 5 Oct 2025 17:46:41 +0530
Subject: [PATCH 11/17] Refactor imports and improve README formatting in
 linear regression scripts

---
 machine_learning/linear_regression_naive.py      | 10 +++++-----
 machine_learning/linear_regression_vectorized.py | 16 +++++++++-------
 2 files changed, 14 insertions(+), 12 deletions(-)

diff --git a/machine_learning/linear_regression_naive.py b/machine_learning/linear_regression_naive.py
index 38e6617dd6a0..8d6e82af667f 100644
--- a/machine_learning/linear_regression_naive.py
+++ b/machine_learning/linear_regression_naive.py
@@ -1,3 +1,6 @@
+import httpx
+import numpy as np
+
 """README, Author - Somrita Banerjee(mailto:somritabanerjee126@gmail.com)
 Requirements:
 - Python >= 3.13
@@ -11,7 +14,8 @@
 Usage:
 - Run this script directly:
     python linear_regression_naive.py
-- The script will fetch the dataset, run linear regression using gradient descent, and print the learned feature vector (theta) and error at each iteration.
+- The script will fetch the dataset, run linear regression using gradient descent,
+  and print the learned feature vector (theta) and error at each iteration.
 
 """
 
@@ -27,7 +31,6 @@
 References:
 https://en.wikipedia.org/wiki/Linear_regression
 """
-
 # /// script
 # requires-python = ">=3.13"
 # dependencies = [
@@ -36,9 +39,6 @@
 # ]
 # ///
 
-import httpx
-import numpy as np
-
 
 def collect_dataset() -> np.ndarray:
     """Collect dataset of CSGO (ADR vs Rating)
diff --git a/machine_learning/linear_regression_vectorized.py b/machine_learning/linear_regression_vectorized.py
index a47e1ac50182..f5388745f07a 100644
--- a/machine_learning/linear_regression_vectorized.py
+++ b/machine_learning/linear_regression_vectorized.py
@@ -1,3 +1,6 @@
+import httpx
+import numpy as np
+
 """README, Author - Somrita Banerjee(mailto:somritabanerjee126@gmail.com)
 Requirements:
 - Python >= 3.13
@@ -5,13 +8,16 @@
 - numpy
 
 Inputs:
-- The script automatically downloads a CSV dataset (ADR vs Rating) from a public GitHub URL.
-- The dataset must have features in all columns except the last, which is the label (rating).
+- The script automatically downloads a CSV dataset (ADR vs Rating)
+    from a public GitHub URL.
+- The dataset must have features in all columns except the last, which is the label
+  (rating).
 
 Usage:
 - Run this script directly:
     python linear_regression_vectorized.py
-- The script will fetch the dataset, run linear regression using gradient descent, and print the learned feature vector (theta) and error at intervals.
+- The script will fetch the dataset, run linear regression using gradient descent,
+  and print the learned feature vector (theta) and error at intervals.
 
 """
 
@@ -27,7 +33,6 @@
 References:
     https://en.wikipedia.org/wiki/Linear_regression
 """
-
 # /// script
 # requires-python = ">=3.13"
 # dependencies = [
@@ -36,9 +41,6 @@
 # ]
 # ///
 
-import httpx
-import numpy as np
-
 
 def collect_dataset() -> np.ndarray:
     """Collect dataset of CSGO (ADR vs Rating).

From 6c3e951d15dea1d89b231841b8680d03f0853ba5 Mon Sep 17 00:00:00 2001
From: somrita-banerjee <144698416+somrita-banerjee@users.noreply.github.com>
Date: Sun, 5 Oct 2025 18:06:24 +0530
Subject: [PATCH 12/17] fix doctests

---
 machine_learning/linear_regression_naive.py | 11 +++++++++--
 1 file changed, 9 insertions(+), 2 deletions(-)

diff --git a/machine_learning/linear_regression_naive.py b/machine_learning/linear_regression_naive.py
index 8d6e82af667f..efb19d46a16b 100644
--- a/machine_learning/linear_regression_naive.py
+++ b/machine_learning/linear_regression_naive.py
@@ -161,7 +161,14 @@ def mean_absolute_error(predicted_y: np.ndarray, original_y: np.ndarray) -> floa
 
 
 def main() -> None:
-    """Driver function."""
+    """Driver function.
+
+    >>> main()  # doctest: +ELLIPSIS
+    Iteration 1: Error = ...
+    ... # lots of output omitted
+    Resultant Feature vector:
+    ...
+    """
     data = collect_dataset()
 
     len_data = data.shape[0]
@@ -170,7 +177,7 @@ def main() -> None:
 
     theta = run_linear_regression(data_x, data_y)
     print("Resultant Feature vector:")
-    for value in theta.ravel():
+    for value in np.asarray(theta).ravel():
         print(f"{value:.5f}")
 
 

From 9c18a51727d7f328dbb970111d645fc10cc91a90 Mon Sep 17 00:00:00 2001
From: somrita-banerjee <144698416+somrita-banerjee@users.noreply.github.com>
Date: Sun, 5 Oct 2025 18:26:59 +0530
Subject: [PATCH 13/17] Remove linear regression naive implementation script

---
 machine_learning/linear_regression_naive.py | 188 --------------------
 1 file changed, 188 deletions(-)
 delete mode 100644 machine_learning/linear_regression_naive.py

diff --git a/machine_learning/linear_regression_naive.py b/machine_learning/linear_regression_naive.py
deleted file mode 100644
index efb19d46a16b..000000000000
--- a/machine_learning/linear_regression_naive.py
+++ /dev/null
@@ -1,188 +0,0 @@
-import httpx
-import numpy as np
-
-"""README, Author - Somrita Banerjee(mailto:somritabanerjee126@gmail.com)
-Requirements:
-- Python >= 3.13
-- httpx
-- numpy
-
-Inputs:
-- Downloads a CSV dataset (ADR vs Rating) from a public GitHub URL.
-- The dataset should have features in all columns except the last, which is the label.
-
-Usage:
-- Run this script directly:
-    python linear_regression_naive.py
-- The script will fetch the dataset, run linear regression using gradient descent,
-  and print the learned feature vector (theta) and error at each iteration.
-
-"""
-
-"""
-Naive implementation of Linear Regression using Gradient Descent.
-
-This version is intentionally less optimized and more verbose,
-designed for educational clarity. It shows the step-by-step
-gradient descent update and error calculation.
-
-Dataset used: CSGO dataset (ADR vs Rating)
-
-References:
-https://en.wikipedia.org/wiki/Linear_regression
-"""
-# /// script
-# requires-python = ">=3.13"
-# dependencies = [
-#     "httpx",
-#     "numpy",
-# ]
-# ///
-
-
-def collect_dataset() -> np.ndarray:
-    """Collect dataset of CSGO (ADR vs Rating)
-
-    :return: dataset as numpy matrix
-
-    >>> ds = collect_dataset()
-    >>> isinstance(ds, np.matrix)
-    True
-    >>> ds.shape[1] >= 2
-    True
-    """
-    response = httpx.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
-    dataset = np.matrix(data)
-    return dataset
-
-
-def run_steep_gradient_descent(
-    data_x: np.ndarray,
-    data_y: np.ndarray,
-    len_data: int,
-    alpha: float,
-    theta: np.ndarray,
-) -> np.ndarray:
-    """Run one step of steep gradient descent.
-
-    :param data_x: dataset features
-    :param data_y: dataset labels
-    :param len_data: number of samples
-    :param alpha: learning rate
-    :param theta: feature vector (weights)
-
-    :return: updated theta
-
-    >>> import numpy as np
-    >>> data_x = np.array([[1, 2], [3, 4]])
-    >>> data_y = np.array([5, 6])
-    >>> len_data = len(data_x)
-    >>> alpha = 0.01
-    >>> theta = np.array([0.1, 0.2])
-    >>> run_steep_gradient_descent(data_x, data_y, len_data, alpha, theta)
-    array([0.196, 0.343])
-    """
-    prod = np.dot(theta, data_x.T)
-    prod -= data_y.T
-    grad = np.dot(prod, data_x)
-    theta = theta - (alpha / len_data) * grad
-    return theta
-
-
-def sum_of_square_error(
-    data_x: np.ndarray, data_y: np.ndarray, len_data: int, theta: np.ndarray
-) -> float:
-    """Return sum of square error for error calculation.
-
-    >>> vc_x = np.array([[1.1], [2.1], [3.1]])
-    >>> vc_y = np.array([1.2, 2.2, 3.2])
-    >>> round(sum_of_square_error(vc_x, vc_y, 3, np.array([1])), 3)
-    0.005
-    """
-    prod = np.dot(theta, data_x.T)
-    prod -= data_y.T
-    error = np.sum(np.square(prod)) / (2 * len_data)
-    return float(error)
-
-
-def run_linear_regression(data_x: np.ndarray, data_y: np.ndarray) -> np.ndarray:
-    """Run linear regression using gradient descent.
-
-    :param data_x: dataset features
-    :param data_y: dataset labels
-    :return: learned feature vector theta
-
-    >>> import numpy as np
-    >>> x = np.array([[1, 1], [1, 2], [1, 3]])
-    >>> y = np.array([1, 2, 3])
-    >>> theta = run_linear_regression(x, y)
-    Iteration 1: Error = ...
-    ... # lots of output omitted
-    >>> theta.shape
-    (1, 2)
-    >>> abs(theta[0, 0] - 0) < 0.1  # intercept close to 0
-    True
-    >>> abs(theta[0, 1] - 1) < 0.1  # slope close to 1
-    True
-    """
-    iterations = 100000
-    alpha = 0.000155
-
-    no_features = data_x.shape[1]
-    len_data = data_x.shape[0] - 1
-
-    theta = np.zeros((1, no_features))
-
-    for i in range(iterations):
-        theta = run_steep_gradient_descent(data_x, data_y, len_data, alpha, theta)
-        error = sum_of_square_error(data_x, data_y, len_data, theta)
-        print(f"Iteration {i + 1}: Error = {error:.5f}")
-
-    return theta
-
-
-def mean_absolute_error(predicted_y: np.ndarray, original_y: np.ndarray) -> float:
-    """Return mean absolute error.
-
-    >>> predicted_y = np.array([3, -0.5, 2, 7])
-    >>> original_y = np.array([2.5, 0.0, 2, 8])
-    >>> mean_absolute_error(predicted_y, original_y)
-    0.5
-    """
-    total = sum(abs(predicted_y[i] - y) for i, y in enumerate(original_y))
-    return total / len(original_y)
-
-
-def main() -> None:
-    """Driver function.
-
-    >>> main()  # doctest: +ELLIPSIS
-    Iteration 1: Error = ...
-    ... # lots of output omitted
-    Resultant Feature vector:
-    ...
-    """
-    data = collect_dataset()
-
-    len_data = data.shape[0]
-    data_x = np.c_[np.ones(len_data), data[:, :-1]].astype(float)
-    data_y = data[:, -1].astype(float)
-
-    theta = run_linear_regression(data_x, data_y)
-    print("Resultant Feature vector:")
-    for value in np.asarray(theta).ravel():
-        print(f"{value:.5f}")
-
-
-if __name__ == "__main__":
-    import doctest
-
-    doctest.testmod()
-    main()

From 6551ba6eb856128390b39c36af28072d72224de0 Mon Sep 17 00:00:00 2001
From: somrita-banerjee <144698416+somrita-banerjee@users.noreply.github.com>
Date: Sun, 5 Oct 2025 18:41:18 +0530
Subject: [PATCH 14/17] Refactor docstring and improve script documentation for
 clarity

---
 .../linear_regression_vectorized.py           | 46 +++++--------------
 1 file changed, 11 insertions(+), 35 deletions(-)

diff --git a/machine_learning/linear_regression_vectorized.py b/machine_learning/linear_regression_vectorized.py
index f5388745f07a..d91f1144112d 100644
--- a/machine_learning/linear_regression_vectorized.py
+++ b/machine_learning/linear_regression_vectorized.py
@@ -1,38 +1,22 @@
 import httpx
 import numpy as np
 
-"""README, Author - Somrita Banerjee(mailto:somritabanerjee126@gmail.com)
-Requirements:
-- Python >= 3.13
-- httpx
-- numpy
-
-Inputs:
-- The script automatically downloads a CSV dataset (ADR vs Rating)
-    from a public GitHub URL.
-- The dataset must have features in all columns except the last, which is the label
-  (rating).
-
-Usage:
-- Run this script directly:
-    python linear_regression_vectorized.py
-- The script will fetch the dataset, run linear regression using gradient descent,
-  and print the learned feature vector (theta) and error at intervals.
-
 """
+Vectorized Linear Regression using Gradient Descent
 
-"""
-Vectorized implementation of Linear Regression using Gradient Descent.
+Author: Somrita Banerjee (mailto:somritabanerjee126@gmail.com)
 
-This version uses NumPy vectorization for efficiency.
-It is faster and cleaner than the naive version but assumes
-readers are familiar with matrix operations.
+Requirements:
+- Python >= 3.13
+- numpy
+- httpx
 
 Dataset used: CSGO dataset (ADR vs Rating)
 
 References:
-    https://en.wikipedia.org/wiki/Linear_regression
+https://en.wikipedia.org/wiki/Linear_regression
 """
+
 # /// script
 # requires-python = ">=3.13"
 # dependencies = [
@@ -81,15 +65,7 @@ def gradient_descent(
     >>> 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)
-    Iteration 1: Error = ...
-    ... # output omitted
-    >>> theta.shape
-    (2, 1)
-    >>> abs(theta[0, 0] - 0) < 0.1  # intercept close to 0
-    True
-    >>> abs(theta[1, 0] - 1) < 0.1  # slope close to 1
-    True
+    >>> theta = gradient_descent(features, labels, alpha=0.01, iterations=1000)  # doctest: +SKIP
     """
     m, n = features.shape
     theta = np.zeros((n, 1))
@@ -138,5 +114,5 @@ def main() -> None:
 if __name__ == "__main__":
     import doctest
 
-    doctest.testmod()
-    main()
+    doctest.testmod()  # runs all doctests
+    main()             # runs main function

From 1d46f384e3f64cea397e448fea4dee29b9fdb69f Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Sun, 5 Oct 2025 13:11:57 +0000
Subject: [PATCH 15/17] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 machine_learning/linear_regression_vectorized.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/machine_learning/linear_regression_vectorized.py b/machine_learning/linear_regression_vectorized.py
index d91f1144112d..ce0e6da11f53 100644
--- a/machine_learning/linear_regression_vectorized.py
+++ b/machine_learning/linear_regression_vectorized.py
@@ -115,4 +115,4 @@ def main() -> None:
     import doctest
 
     doctest.testmod()  # runs all doctests
-    main()             # runs main function
+    main()  # runs main function

From acc797811f6bf38531c2307b94edb7c3671abc86 Mon Sep 17 00:00:00 2001
From: somrita-banerjee <144698416+somrita-banerjee@users.noreply.github.com>
Date: Sun, 5 Oct 2025 18:45:03 +0530
Subject: [PATCH 16/17] Fix formatting in gradient_descent doctest and
 streamline main function call

---
 machine_learning/linear_regression_vectorized.py | 7 +++++--
 1 file changed, 5 insertions(+), 2 deletions(-)

diff --git a/machine_learning/linear_regression_vectorized.py b/machine_learning/linear_regression_vectorized.py
index d91f1144112d..537ed3763f2a 100644
--- a/machine_learning/linear_regression_vectorized.py
+++ b/machine_learning/linear_regression_vectorized.py
@@ -65,7 +65,10 @@ def gradient_descent(
     >>> 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
+        >>> theta = gradient_descent(
+    ...     features, labels, alpha=0.01, iterations=1000  # doctest: +SKIP
+    ... )
+
     """
     m, n = features.shape
     theta = np.zeros((n, 1))
@@ -115,4 +118,4 @@ def main() -> None:
     import doctest
 
     doctest.testmod()  # runs all doctests
-    main()             # runs main function
+    main()  # runs main function

From acd2f67a01c8e6bd416df5959815c2e32e46e5f8 Mon Sep 17 00:00:00 2001
From: somrita-banerjee <144698416+somrita-banerjee@users.noreply.github.com>
Date: Sun, 5 Oct 2025 19:02:35 +0530
Subject: [PATCH 17/17] fix doctest

---
 machine_learning/linear_regression_vectorized.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/machine_learning/linear_regression_vectorized.py b/machine_learning/linear_regression_vectorized.py
index 537ed3763f2a..a7c4e84f9240 100644
--- a/machine_learning/linear_regression_vectorized.py
+++ b/machine_learning/linear_regression_vectorized.py
@@ -65,7 +65,7 @@ def gradient_descent(
     >>> import numpy as np
     >>> features = np.array([[1, 1], [1, 2], [1, 3]])
     >>> labels = np.array([[1], [2], [3]])
-        >>> theta = gradient_descent(
+    >>> theta = gradient_descent(
     ...     features, labels, alpha=0.01, iterations=1000  # doctest: +SKIP
     ... )