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XGBoost Algorithm Pseudocode

This example provides a pseudocode description of the key functions and tasks in the XGBoost algorithm.

1. Regularized Learning Objective

Function CalculateObjective(predictions, targets, trees):
    total_loss = 0
    for i in range(len(targets)):
        prediction_error = loss_function(predictions[i], targets[i])
        regularization_term = sum(Ω(tree) for tree in trees)
        total_loss += prediction_error + regularization_term
    return total_loss

2. Gradient Tree Boosting

Function GradientBoosting(data, num_trees):
    model = initialize_model()
    for t in range(num_trees):
        residuals = calculate_residuals(model.predict(data), data.targets)
        tree = build_tree(data.features, residuals)
        model.add_tree(tree, learning_rate)
    return model

3. Tree Structure Calculation

Function CalculateOptimalWeights(gradients, hessians, lambda):
    for each leaf j:
        numerator = sum(gradients[i] for i in leaf j)
        denominator = sum(hessians[i] for i in leaf j) + lambda
        leaf_weight = -numerator / denominator
        set_weight(leaf j, leaf_weight)

4. Split Finding

4.1 Exact Greedy Algorithm

Function ExactGreedySplit(data, gradients, hessians):
    best_gain = 0
    best_split = None
    for feature in data.features:
        for split_point in possible_split_points:
            gain = calculate_split_gain(split_point, gradients, hessians)
            if gain > best_gain:
                best_gain = gain
                best_split = split_point
    return best_split

4.2 Approximate Algorithm

Function ApproximateSplit(data, gradients, hessians, num_buckets):
    candidate_splits = generate_candidate_splits(data, num_buckets)
    best_gain = 0
    best_split = None
    for split in candidate_splits:
        gain = calculate_split_gain(split, gradients, hessians)
        if gain > best_gain:
            best_gain = gain
            best_split = split
    return best_split

5. Sparsity-aware Split Finding

Function SparsityAwareSplit(data, gradients, hessians, default_direction):
    best_gain = 0
    best_split = None
    for feature in data.features:
        for direction in ["left", "right"]:
            set_default_direction(feature, direction)
            gain = calculate_split_gain_with_default(data, gradients, hessians)
            if gain > best_gain:
                best_gain = gain
                best_split = (feature, direction)
    return best_split

6. Tree Pruning and Growing Criteria

Function ShouldContinueSplit(current_depth, max_depth, min_loss_reduction):
    if current_depth >= max_depth or min_loss_reduction <= 0:
        return False
    return True

7. Column (Feature) Subsampling

Function FeatureSubsampling(features, subsample_ratio):
    num_features_to_select = int(len(features) * subsample_ratio)
    selected_features = random_sample(features, num_features_to_select)
    return selected_features

8. Shrinkage (Learning Rate)

Function UpdateTreeWeights(trees, shrinkage_rate):
    for tree in trees:
        for leaf in tree.leaves:
            leaf.weight *= shrinkage_rate

9. Regularization Techniques

plaintext CalculateRegularization(tree, gamma, lambda):
    regularization_cost = gamma * number_of_leaves(tree) + lambda * sum(leaf.weight^2 for leaf in tree.leaves)
    return regularization_cost

10. Out-of-core Computing

Function LoadDataInChunks(file_path, chunk_size):
    while more_data_available(file_path):
        chunk = read_next_chunk(file_path, chunk_size)
        yield chunk

This pseudocode gives a structured representation of each major aspect of the XGBoost algorithm based on the subtasks and functions outlined in the paper.

Adjustments might be necessary based on specific implementation details or optimizations.

Refer to the XGBoost paper and source code for a more complete description.

See Also