AI Algorithm: Mathematics

Now, it's time to write a computer program to execute this algorithm using the C language. This example assumes a basic understanding of C and focuses on the core logic:

#include ＜stdio.h>
#include ＜math.h>

// Function to calculate mean squared error (MSE) loss
double calculate_loss(int n, double *x, double *y, double m, double b) {
    double loss = 0.0;
    for (int i = 0; i < n; i++) {
        double y_pred = m * x[i] + b;
        loss += (y[i] - y_pred) * (y[i] - y_pred);
    }
    return loss / n;
}

// Function to perform gradient descent and update parameters
void gradient_descent(int n, double *x, double *y, double *m, double *b, double learning_rate) {
    double dm = 0.0, db = 0.0;
    for (int i = 0; i < n; i++) {
        double y_pred = (*m) * x[i] + (*b);
        dm += -2 * x[i] * (y[i] - y_pred);
        db += -2 * (y[i] - y_pred);
    }
    *m = *m - learning_rate * (dm / n);
    *b = *b - learning_rate * (db / n);
}

// Function to normalize the input features
void normalize(int n, double *x) {
    double max_x = x[0];
    for (int i = 1; i < n; i++) {
        if (x[i] > max_x) {
            max_x = x[i];
        }
    }
    for (int i = 0; i < n; i++) {
        x[i] /= max_x;
    }
}

int main() {
    // Example dataset
    int n = 5;
    double x[] = {1400, 1600, 1700, 1875, 1100};
    double y[] = {180000, 200000, 220000, 240000, 150000};

    // Normalize the input features
    normalize(n, x);

    // Initial parameters
    double m = 0.5;
    double b = 100000;

    // Hyperparameter: learning rate
    double learning_rate = 0.000001;

    // Number of iterations
    int num_iterations = 1000;

    // Training loop
    for (int i = 0; i < num_iterations; i++) {
        // Calculate mean squared error loss
        double loss = calculate_loss(n, x, y, m, b);

        // Print loss for monitoring purposes
        if (i % 100 == 0) {
            printf("Iteration %d, Loss: %lf\n", i, loss);
        }

        // Update parameters using gradient descent
        gradient_descent(n, x, y, &m, &b, learning_rate);
    }

    // Print the final learned parameters
    printf("Final Parameters: m = %lf, b = %lf\n", m, b);

    // Example: Predict the price for a new house size (e.g., 1500 sq. ft.)
    double new_size = 1500;
    double predicted_price = m * new_size + b;
    printf("Predicted Price for %lf sq. ft.: %lf\n", new_size, predicted_price);

    return 0;
}

Iteration 0, Loss: 10579915360.172594  
Iteration 100, Loss: 10573210482.516537
Iteration 200, Loss: 10566510102.789234
Iteration 300, Loss: 10559814217.972036
Iteration 400, Loss: 10553122825.048319
Iteration 500, Loss: 10546435921.003483
Iteration 600, Loss: 10539753502.824955
Iteration 700, Loss: 10533075567.502178
Iteration 800, Loss: 10526402112.026602
Iteration 900, Loss: 10519733133.391729
Final Parameters: m = 169.502571, b = 100195.665306
Predicted Price for 1500.000000 sq. ft.: 354449.521177

This C program includes functions for calculating the mean squared error loss and performing gradient descent to update the parameters 'm' and 'b'. The main function initializes the dataset, hyperparameters, and runs the training loop. The learned parameters are printed at the end, and a prediction is made for a new house size.

Remember: Keep in mind that this is a simplified example, and in practice, libraries like math.h and additional error handling may be used.

This is a basic example, and real-world scenarios involve more complex algorithms and features, but the fundamental principles remain similar.