Comparing various online solvers in Scikit Learn

Scikit Learn is a popular Python library that provides a wide range of machine-learning algorithms and tools. One of the key features of Scikit Learn is the ability to solve optimization problems using various online solvers. In this article, we will compare some of the most commonly used online solvers in Scikit Learn.

What is an Online Solver?

An online solver is a type of optimization algorithm that updates its parameters incrementally as it processes each data point. This approach is often used in large-scale machine learning applications, where it is not feasible to process all the data at once due to memory or computational constraints.

There are two types of online solvers: 

• Stochastic: Stochastic solvers update the parameters for each data point.
• Batch: batch solvers update the parameters after processing a batch of data points. 

Scikit Learn provides several online solvers for different machine learning algorithms, including linear regression, logistic regression, and support vector machines.

Online Solvers in Scikit Learn:

1. Stochastic Gradient Descent (SGD): Stochastic Gradient Descent is a popular online solver for linear and logistic regression in Scikit Learn. It updates the parameters for each data point based on the gradient of the loss function. SGD is fast and efficient for large datasets, but it may require careful tuning of hyperparameters to achieve good performance.
2. Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS): L-BFGS is a batch solver that is commonly used for optimization problems in machine learning. It approximates the Hessian matrix of the loss function to update the parameters. L-BFGS is efficient for problems with a large number of parameters, but it may not be suitable for large datasets due to memory constraints.
3. Adam: Adam is a popular stochastic solver that is commonly used for deep learning applications. It adapts the learning rate based on the gradients and previous updates to the parameters. Adam is efficient for problems with large datasets and high-dimensional data, but it may require careful tuning of hyper-parameters to achieve good performance.
4. Stochastic Average Gradient (SAG): SAG is a stochastic solver that is commonly used for linear regression in Scikit Learn. It updates the parameters based on the average of the gradients for each data point. SAG is efficient for problems with large datasets, but it may require more iterations to converge than other solvers.
5. Stochastic Average Gradient Descent (SAGA): SAGA is an extension of SAG that is commonly used for logistic regression in Scikit Learn. It updates the parameters based on the average of the gradients for each data point, but it also includes a correction term to improve convergence. SAGA is efficient for problems with large datasets and high-dimensional data, but it may require careful tuning of hyper-parameters to achieve good performance.

Implementations

Here is an example of how to use L-BFGS for logistic regression:

In this example, we first load the MNIST dataset and split it into training and test sets.

Python3

# Import the necessary libraries
from sklearn.linear_model import LogisticRegression
from sklearn.datasets import load_digits
from sklearn.model_selection import train_test_split

# Load the MNIST dataset
digits = load_digits()

# Split the data into training and test sets
X_train, X_test, y_train, y_test = train_test_split(digits.data,
                                                    digits.target,
                                                    test_size=0.2,
                                                    random_state=42)

# Create an instance of LogisticRegression
# with the 'lbfgs' solver and L2 penalty
clf = LogisticRegression(solver='lbfgs',
                         penalty='l2',
                         max_iter=10000)

# Fit the model to the training data
clf.fit(X_train, y_train)

# Evaluate the model on the test data
accuracy = clf.score(X_test, y_test)

print("Logistic regression Accuracy:", accuracy)

Output:

Logistic regression Accuracy: 0.9722222222222222

Applying various online solvers and computing the accuracy

Python3

# Import the necessary libraries
from sklearn.datasets import load_digits
from sklearn.linear_model import LogisticRegression, SGDClassifier
from sklearn.linear_model import PassiveAggressiveClassifier, Perceptron
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score

# load digits dataset
digits = load_digits()

# split data into train and test sets
X_train, X_test, y_train, y_test = train_test_split(
    digits.data, digits.target, test_size=0.3)

# define solvers to compare
solvers = [
    ('SAG', LogisticRegression(penalty='l2',
                               solver='sag',
                               max_iter=100)),
    ('SAGA', LogisticRegression(penalty='l1',
                                solver='saga',
                                max_iter=100)),
    ('L-BFGS', LogisticRegression(penalty='l2',
                                  solver='lbfgs',
                                  max_iter=100)),
    ('liblinear', LogisticRegression(penalty='l1',
                                     solver='liblinear',
                                     max_iter=100)),
    ('SGD', SGDClassifier(loss='log', max_iter=100)),
    ('Passive-Aggressive', PassiveAggressiveClassifier(max_iter=100)),
    ('Perceptron', Perceptron(max_iter=100))
]

# train and evaluate each solver
for name, clf in solvers:
    clf.fit(X_train, y_train)
    y_pred = clf.predict(X_test)
    acc = accuracy_score(y_test, y_pred)
    print(f"{name} accuracy: {acc}")

Output:

SAG accuracy: 0.9648148148148148
SAGA accuracy: 0.9703703703703703
L-BFGS accuracy: 0.9592592592592593
liblinear accuracy: 0.9648148148148148
SGD accuracy: 0.9518518518518518
Passive-Aggressive accuracy: 0.9574074074074074
Perceptron accuracy: 0.937037037037037