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estimation logistic regression using newton Raphson

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Nurmalitasari nurmalitasari
Nurmalitasari nurmalitasari 2022년 3월 3일
답변: Sudarsanan A K 2023년 12월 15일
How can I solve logistic regression model using newton raphson?

답변 (1개)

Sudarsanan A K
Sudarsanan A K 2023년 12월 15일
Hi Nurmalitasari,
To solve a logistic regression model using the Newton-Raphson method in MATLAB, you will need to follow these steps:
  1. Define the logistic regression function.
  2. Implement the gradient and Hessian computation for logistic regression.
  3. Apply the Newton-Raphson iterative update until convergence.
Below is a MATLAB example that demonstrates how to solve a logistic regression model using the Newton-Raphson method. This example includes a simple synthetic dataset for illustration purposes and visualizations of the decision boundary.
%% Example MATLAB code for solving logistic regression using Newton-Raphson method
% Create a synthetic dataset
rng(0); % Seed for reproducibility
n = 100; % Number of samples
x = linspace(-5, 5, n)'; % Feature values
y = double((x + randn(n, 1)) > 0); % Labels with some noise
% Visualize the dataset
figure;
scatter(x(y==0), zeros(sum(y==0), 1), 'r', 'filled'); hold on;
scatter(x(y==1), zeros(sum(y==1), 1), 'b', 'filled');
xlabel('Feature x');
ylabel('Probability');
title('Synthetic dataset');
legend('Class 0', 'Class 1');
% Logistic regression function
sigmoid = @(z) 1 ./ (1 + exp(-z));
% Initialize weights
w = [0; 0]; % [intercept; slope]
% Add intercept term to feature matrix
X = [ones(n, 1), x];
% Newton-Raphson iterations
max_iter = 10;
for iter = 1:max_iter
% Compute the predicted probabilities
p = sigmoid(X * w);
% Compute the gradient of the log-likelihood
gradient = X' * (y - p);
% Compute the Hessian matrix
W = diag(p .* (1 - p));
Hessian = -X' * W * X;
% Update weights using Newton-Raphson update rule
w = w - Hessian \ gradient;
% Visualize the decision boundary during iterations
% Define a range of x values for plotting the decision boundary
x_range = linspace(min(x), max(x), 100);
% Compute the corresponding y values using the vectorized function
y_range = sigmoid([ones(size(x_range')), x_range'] * w);
% Plot the decision boundary
plot(x_range, y_range, 'LineWidth', 1); drawnow;
end
% Final visualization with decision boundary
figure;
scatter(x(y==0), zeros(sum(y==0), 1), 'r', 'filled'); hold on;
scatter(x(y==1), zeros(sum(y==1), 1), 'b', 'filled');
% Define a range of x values for plotting the decision boundary
x_range = linspace(min(x), max(x), 100);
% Compute the corresponding y values using the vectorized function
y_range = sigmoid([ones(size(x_range')), x_range'] * w);
% Plot the decision boundary
plot(x_range, y_range, 'k', 'LineWidth', 2);
xlabel('Feature x');
ylabel('Probability');
title('Logistic Regression with Newton-Raphson');
legend('Class 0', 'Class 1', 'Decision Boundary');
Below are the documentation links for the important MATLAB functions utilized in the logistic regression example:
I hope this helps!

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