#Maximum Likelihood Ranking



    # Initialize the weight vector

    # Run the maximum likelihood estimation

    # Normalize the weight vector

    # Sort the items based on the weight vector


# Example usage
    # Define your data matrix where each row represents an item and each column represents a feature

    # Run the maximum likelihood ranking

    # Print the results

if __name__ == '__main__':
    import numpy as np
    def maximum_likelihood_ranking(data):
        num_items = len(data)
        num_features = len(data[0])
        weights = np.ones(num_features)
        max_iterations = 1000  # Maximum number of iterations (adjust as needed)
        epsilon = 1e-6  # Convergence threshold (adjust as needed)
        for _ in range(max_iterations):
            old_weights = np.copy(weights)
            gradients = np.zeros(num_features)
            for i in range(num_items):
                xi = data[i]
                exp_sum = sum(np.exp(np.dot(weights, xj)) for j, xj in enumerate(data))
                for k in range(num_features):
                    gradients[k] += xi[k] * np.exp(np.dot(weights, xi)) / exp_sum
            weights += gradients
            if np.linalg.norm(weights - old_weights) < epsilon:
                break
        weights /= np.linalg.norm(weights)
        rankings = sorted(range(num_items), key=lambda i: np.dot(weights, data[i]), reverse=True)
        return rankings, weights
    if __name__ == '__main__':
        data = np.array([
            [1, 2, 3],
            [2, 1, 3],
            [3, 2, 1],
            [1, 3, 2]
        ])
        rankings, weights = maximum_likelihood_ranking(data)
        print("Rankings:", rankings)
        print("Weights:", weights)
