Multiclass Sparse Logistic Regression

Introduction

In this lab, we will explore how to use Multiclass Sparse Logistic Regression on the 20newsgroups dataset using scikit-learn. We will compare the performance of Multinomial logistic regression with one-versus-rest L1 logistic regression.

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Skills Graph

Import Libraries

We begin by importing the necessary libraries and modules that we will use in this lab.

import timeit
import warnings

import matplotlib.pyplot as plt
import numpy as np

from sklearn.datasets import fetch_20newsgroups_vectorized
from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import train_test_split
from sklearn.exceptions import ConvergenceWarning

warnings.filterwarnings("ignore", category=ConvergenceWarning, module="sklearn")

Load and Prepare Data

Next, we load the 20newsgroups dataset and prepare the data for training and testing.

## We use SAGA solver
solver = "saga"

## Turn down for faster run time
n_samples = 5000

X, y = fetch_20newsgroups_vectorized(subset="all", return_X_y=True)
X = X[:n_samples]
y = y[:n_samples]

X_train, X_test, y_train, y_test = train_test_split(
    X, y, random_state=42, stratify=y, test_size=0.1
)
train_samples, n_features = X_train.shape
n_classes = np.unique(y).shape[0]

print(
    "Dataset 20newsgroup, train_samples=%i, n_features=%i, n_classes=%i"
    % (train_samples, n_features, n_classes)
)

Define and Train Models

We will define two models, Multinomial and One-vs-Rest L1 Logistic Regression, and train them with different number of epochs.

models = {
    "ovr": {"name": "One versus Rest", "iters": [1, 2, 3]},
    "multinomial": {"name": "Multinomial", "iters": [1, 2, 5]},
}

for model in models:
    ## Add initial chance-level values for plotting purpose
    accuracies = [1 / n_classes]
    times = [0]
    densities = [1]

    model_params = models[model]

    ## Small number of epochs for fast runtime
    for this_max_iter in model_params["iters"]:
        print(
            "[model=%s, solver=%s] Number of epochs: %s"
            % (model_params["name"], solver, this_max_iter)
        )
        lr = LogisticRegression(
            solver=solver,
            multi_class=model,
            penalty="l1",
            max_iter=this_max_iter,
            random_state=42,
        )
        t1 = timeit.default_timer()
        lr.fit(X_train, y_train)
        train_time = timeit.default_timer() - t1

        y_pred = lr.predict(X_test)
        accuracy = np.sum(y_pred == y_test) / y_test.shape[0]
        density = np.mean(lr.coef_ != 0, axis=1) * 100
        accuracies.append(accuracy)
        densities.append(density)
        times.append(train_time)
    models[model]["times"] = times
    models[model]["densities"] = densities
    models[model]["accuracies"] = accuracies
    print("Test accuracy for model %s: %.4f" % (model, accuracies[-1]))
    print(
        "%% non-zero coefficients for model %s, per class:\n %s"
        % (model, densities[-1])
    )
    print(
        "Run time (%i epochs) for model %s:%.2f"
        % (model_params["iters"][-1], model, times[-1])
    )

Visualize Results

Finally, we will visualize the results of the trained models using a line graph.

fig = plt.figure()
ax = fig.add_subplot(111)

for model in models:
    name = models[model]["name"]
    times = models[model]["times"]
    accuracies = models[model]["accuracies"]
    ax.plot(times, accuracies, marker="o", label="Model: %s" % name)
    ax.set_xlabel("Train time (s)")
    ax.set_ylabel("Test accuracy")
ax.legend()
fig.suptitle("Multinomial vs One-vs-Rest Logistic L1\nDataset %s" % "20newsgroups")
fig.tight_layout()
fig.subplots_adjust(top=0.85)
run_time = timeit.default_timer() - t0
print("Example run in %.3f s" % run_time)
plt.show()

Summary

In this lab, we used scikit-learn to perform Multiclass Sparse Logistic Regression on the 20newsgroups dataset. We compared the performance of Multinomial logistic regression with one-versus-rest L1 logistic regression, and visualized the results using a line graph.