人口预测的Logistic模型的matlab代码

这是一个简单的人口预测的logistic模型的matlab代码：

%清空环境变量
clear;

%加载数据
data = load('population.csv');
x = data(:, 1);
y = data(:, 2);

%绘制散点图
figure;
scatter(x, y);
xlabel('Year');
ylabel('Population');

%初始化参数
theta = [0; 0];
alpha = 0.01;
num_iters = 400;

%添加偏置项
X = [ones(length(x), 1), x];

%定义sigmoid函数
function g = sigmoid(z)
    g = 1 ./ (1 + exp(-z));
end

%定义损失函数
function J = costFunction(X, y, theta)
    m = length(y);
    h = sigmoid(X * theta);
    J = -(1 / m) * sum(y .* log(h) + (1 - y) .* log(1 - h));
end

%定义梯度下降函数
function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters)
    m = length(y);
    J_history = zeros(num_iters, 1);
    for iter = 1:num_iters
        h = sigmoid(X * theta);
        theta = theta - (alpha / m) * X' * (h - y);
        J_history(iter) = costFunction(X, y, theta);
    end
end

%运行梯度下降
[theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters);

%输出最终权重值
fprintf('Theta found by gradient descent: ');
fprintf('%f %f \n', theta(1), theta(2));

%绘制预测结果
hold on;
plot(x, sigmoid(X * theta), '-');
legend('Training data', 'Logistic regression');
hold off;

其中，数据文件`population.csv`包含了年份和人口数量两列数据。运行此代码将会输出最终的权重值，并绘制出预测结果的曲线。