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lda committed 2025-05-06 04:22:13 +07:00
1 parent c70a62fd69
commit 3bf9133dfd
4 files changed
+146 -69
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1/gradient.py
+34 -55
View File
@@ -1,57 +1,21 @@
import numpy as np
# Hypothesis function
def hypothesis(X, theta):
"""
Compute the hypothesis (predictions) for the given input and parameters.
"""
result = np.dot(X, theta).reshape(-1, 1)
# print("Shape of X:", X.shape)
# print("Shape of theta:", theta.shape)
# print("Shape of hypothesis output:", result.shape)
return result
# Cost function (Mean Squared Error)
def compute_cost(X, y, theta):
"""
Compute the cost (Mean Squared Error) for the given input, target, and parameters.
"""
m = len(y)
predictions = hypothesis(X, theta)
errors = predictions - y
cost = (1 / (2 * m)) * np.sum(errors**2)
# # print(f"Max error: {np.max(errors):.4f}, Cost: {cost:.4f}") # Debugging
return cost
# Compute gradients
def compute_gradients(theta, X, y):
"""
Compute gradients for gradient descent.
Parameters:
theta (numpy.ndarray): Model parameters (n,).
X (numpy.ndarray): Feature matrix (m, n).
y (numpy.ndarray): Target values (m, 1).
Returns:
numpy.ndarray: Gradients (n,).
"""
# print("Shape of theta, X, y:", theta.shape, X.shape, y.shape)
m = len(y)
errors = hypothesis(X, theta) - y # Compute prediction errors
# print("Shape of errors:", errors.shape) # Debugging
gradients = (1 / m) * np.dot(X.T, errors) # Compute gradients
# print("Shape of gradients:", gradients.shape) # Debugging
return gradients.flatten()
# from question import hypothesis
from regulations import compute_cost, compute_gradients # type: ignore
# Gradient Descent function (Batch)
def gradient_descent(X, y, theta, learning_rate, iterations, return_cost: bool = False):
def gradient_descent(
X,
y,
theta,
learning_rate=0.01,
iterations=1000,
lambda_=0.1,
return_cost: bool = False,
):
"""
Perform batch gradient descent to optimize theta.
"""
@@ -61,13 +25,13 @@ def gradient_descent(X, y, theta, learning_rate, iterations, return_cost: bool =
# print("Shape of X:", X.shape) # Should be (200, 4)
# print("Shape of y:", y.shape) # Should be (200, 1)
# print("Shape of theta:", theta.shape) # Should be (4,)
gradients = compute_gradients(theta, X, y) # Compute gradients
gradients = compute_gradients(theta, X, y, lambda_) # Compute gradients
# print(f"Iteration {i + 1}:")
# print(f" Shape of theta: {theta.shape}")
# print(f" Shape of gradients: {gradients.shape}")
theta -= learning_rate * gradients # Update theta
if return_cost:
cost = compute_cost(X, y, theta)
cost = compute_cost(X, y, theta, lambda_)
costs.append(cost) # Track cost
# print(f" Cost: {cost:.4f}")
return (theta, costs) if return_cost else theta
@@ -75,7 +39,14 @@ def gradient_descent(X, y, theta, learning_rate, iterations, return_cost: bool =
# Mini-batch Gradient Descent function
def mini_batch_gradient_descent(
X, y, theta, learning_rate, iterations, batch_size, return_cost: bool = False
X,
y,
theta,
learning_rate=0.01,
iterations=1000,
batch_size=32,
lambda_=0.1,
return_cost: bool = False,
):
"""
Perform mini-batch gradient descent to optimize theta.
@@ -91,10 +62,12 @@ def mini_batch_gradient_descent(
for j in range(0, m, batch_size):
X_batch = X_shuffled[j : j + batch_size]
y_batch = y_shuffled[j : j + batch_size]
gradients = compute_gradients(theta, X_batch, y_batch) # Compute gradients
gradients = compute_gradients(
theta, X_batch, y_batch, lambda_
) # Compute gradients
theta -= learning_rate * gradients # Update theta
if return_cost:
cost = compute_cost(X, y, theta)
cost = compute_cost(X, y, theta, lambda_)
costs.append(cost) # Track cost
# print(f"Iteration {i + 1}/{iterations}, Cost: {cost:.4f}") # Debugging
return (theta, costs) if return_cost else theta
@@ -102,7 +75,13 @@ def mini_batch_gradient_descent(
# Stochastic Gradient Descent function
def stochastic_gradient_descent(
X, y, theta, learning_rate, iterations, return_cost: bool = False
X,
y,
theta,
learning_rate=0.01,
iterations=1000,
lambda_=0.1,
return_cost: bool = False,
):
"""
Perform stochastic gradient descent to optimize theta.
@@ -115,11 +94,11 @@ def stochastic_gradient_descent(
X_sample = X[j : j + 1]
y_sample = y[j : j + 1]
gradients = compute_gradients(
theta, X_sample, y_sample
theta, X_sample, y_sample, lambda_
) # Compute gradients
theta -= learning_rate * gradients # Update theta
if return_cost:
cost = compute_cost(X, y, theta)
cost = compute_cost(X, y, theta, lambda_)
costs.append(cost) # Track cost
# print(f"Iteration {i + 1}/{iterations}, Cost: {cost:.4f}") # Debugging
return (theta, costs) if return_cost else theta
1/main.ipynb
+14 -14
View File
@@ -10,7 +10,7 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 1,
"id": "fa275d88",
"metadata": {},
"outputs": [],
@@ -22,7 +22,7 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 2,
"id": "0d63f004",
"metadata": {},
"outputs": [
@@ -96,14 +96,14 @@
"# theta = theta.reshape(-1, 1)\n",
"print(\"Shape of theta:\", theta.shape)\n",
"\n",
"learning_rate = 0.001\n",
"learning_rate = 0.01\n",
"iterations = 1000\n",
"batch_size = 32 # For mini-batch gradient descent"
]
},
{
"cell_type": "code",
"execution_count": 8,
"execution_count": 4,
"id": "8d5bf6a6",
"metadata": {},
"outputs": [
@@ -111,9 +111,9 @@
"name": "stdout",
"output_type": "stream",
"text": [
"Theta batch: [ 1.40204919e+01 3.91562216e+00 2.79885945e+00 -1.09326135e-02]\n",
"Theta (mini_batch): [ 1.40204919e+01 3.91562216e+00 2.79885945e+00 -1.09326135e-02]\n",
"Theta (stochastic): [ 1.40204919e+01 3.91562216e+00 2.79885945e+00 -1.09326135e-02]\n"
"Theta batch: [14.0103694 3.51501145 2.60914121 0.19570495]\n",
"Theta (mini_batch): [14.0103694 3.51501145 2.60914121 0.19570495]\n",
"Theta (stochastic): [14.0103694 3.51501145 2.60914121 0.19570495]\n"
]
}
],
@@ -176,7 +176,7 @@
"outputs": [
{
"data": {
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truncated
"image/png": 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truncated
"text/plain": [
"<Figure size 800x600 with 1 Axes>"
]
@@ -186,7 +186,7 @@
},
{
"data": {
"image/png": 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truncated
"image/png": 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truncated
"text/plain": [
"<Figure size 800x600 with 1 Axes>"
]
@@ -196,7 +196,7 @@
},
{
"data": {
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truncated
"image/png": "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 truncated
"text/plain": [
"<Figure size 800x600 with 1 Axes>"
]
@@ -206,7 +206,7 @@
},
{
"data": {
"image/png": 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truncated
"image/png": "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 truncated
"text/plain": [
"<Figure size 800x600 with 1 Axes>"
]
@@ -216,7 +216,7 @@
},
{
"data": {
"image/png": 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truncated
"image/png": 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truncated
"text/plain": [
"<Figure size 800x600 with 1 Axes>"
]
@@ -226,7 +226,7 @@
},
{
"data": {
"image/png": 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truncated
"image/png": 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truncated
"text/plain": [
"<Figure size 800x600 with 1 Axes>"
]
@@ -236,7 +236,7 @@
},
{
"data": {
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truncated
"image/png": 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truncated
"text/plain": [
"<Figure size 800x600 with 1 Axes>"
]
1/question.py
+50
View File
@@ -0,0 +1,50 @@
import numpy as np
# Hypothesis function
def hypothesis(X, theta):
"""
Compute the hypothesis (predictions) for the given input and parameters.
"""
result = np.dot(X, theta).reshape(-1, 1)
# print("Shape of X:", X.shape)
# print("Shape of theta:", theta.shape)
# print("Shape of hypothesis output:", result.shape)
return result
# Cost function (Mean Squared Error)
def compute_cost(X, y, theta, _lambda=0):
"""
Compute the cost (Mean Squared Error) for the given input, target, and parameters.
"""
m = len(y)
predictions = hypothesis(X, theta)
errors = predictions - y
cost = (1 / (2 * m)) * np.sum(errors**2)
# # print(f"Max error: {np.max(errors):.4f}, Cost: {cost:.4f}") # Debugging
return cost
# Compute gradients
def compute_gradients(theta, X, y, _lambda=0):
"""
Compute gradients for gradient descent.
Parameters:
theta (numpy.ndarray): Model parameters (n,).
X (numpy.ndarray): Feature matrix (m, n).
y (numpy.ndarray): Target values (m, 1).
Returns:
numpy.ndarray: Gradients (n,).
"""
# print("Shape of theta, X, y:", theta.shape, X.shape, y.shape)
m = len(y)
errors = hypothesis(X, theta) - y # Compute prediction errors
# print("Shape of errors:", errors.shape) # Debugging
gradients = (1 / m) * np.dot(X.T, errors) # Compute gradients
# print("Shape of gradients:", gradients.shape) # Debugging
return gradients.flatten()
1/regulations.py
+48
View File
@@ -27,3 +27,51 @@ def standardize(X):
mean = np.mean(X, axis=0)
std = np.std(X, axis=0)
return (X - mean) / std
from question import hypothesis
# Cost function (Mean Squared Error)
def compute_cost(X, y, theta, lambda_):
"""
Compute the cost (Mean Squared Error) with L2 regularization.
Parameters:
X (numpy.ndarray): Feature matrix (m, n).
y (numpy.ndarray): Target values (m, 1).
theta (numpy.ndarray): Model parameters (n,).
lambda_ (float): Regularization parameter.
Returns:
float: Regularized cost.
"""
m = len(y)
predictions = hypothesis(X, theta)
errors = predictions - y
reg_comp = (lambda_ / (2 * m)) * np.sum(theta[1:]**2) # Exclude theta[0]
cost = (1 / (2 * m)) * np.sum(errors**2) + reg_comp
return cost
# Compute gradients
def compute_gradients(theta, X, y, lambda_):
"""
Compute gradients for gradient descent with L2 regularization.
Parameters:
theta (numpy.ndarray): Model parameters (n,).
X (numpy.ndarray): Feature matrix (m, n).
y (numpy.ndarray): Target values (m, 1).
lambda_ (float): Regularization parameter.
Returns:
numpy.ndarray: Gradients (n,).
"""
m = len(y)
errors = hypothesis(X, theta) - y # Compute prediction errors
gradients = (1 / m) * np.dot(X.T, errors) # Compute gradients
reg_term = (lambda_ / m) * theta # Regularization term
reg_term = reg_term.reshape(-1, 1)
reg_term[0] = 0 # Do not regularize the bias term (theta[0])
gradients += reg_term # Add regularization term to gradients
return gradients.flatten()