Loss Functions: MSE, MAE and Cross-Entropy

A loss function turns a model's mistakes into one number to minimize. Implement compute_loss(kind, predictions, targets) for three common losses, where n is the number of predictions:

• "mse" (mean squared error): average of (p - t)²
• "mae" (mean absolute error): average of |p - t|
• "binary_cross_entropy": -average of [t × ln(p) + (1 - t) × ln(1 - p)]. First clip each prediction p to the range [0.0000001, 0.9999999] so the logarithm is never ln(0).

Input

kind: "mse", "mae" or "binary_cross_entropy".

predictions: The model's predictions.

targets: The correct values (same length). For cross-entropy they are 0 or 1 and predictions are between 0 and 1.

Output

Return the loss as a decimal number.

Constraints

1 ≤ length ≤ 1,000

-1,000 ≤ each value ≤ 1,000 (0 ≤ p ≤ 1 and t ∈ {0, 1} for cross-entropy)

Examples

Input:
kind = "mse"
targets = [3.0, -0.5, 2.0]
predictions = [2.5, 0.0, 2.0]

Expected output:
expected = 0.166667

Input:
std::string kind = "mse";
std::vector<double> targets = {3.0, -0.5, 2.0};
std::vector<double> predictions = {2.5, 0.0, 2.0};

Expected output:
double expected = 0.166667;

Input:
string kind = "mse";
double[] targets = new double[] {3.0, -0.5, 2.0};
double[] predictions = new double[] {2.5, 0.0, 2.0};

Expected output:
double expected = 0.166667;

Input:
kind = "binary_cross_entropy"
targets = [1.0, 0.0]
predictions = [0.9, 0.2]

Expected output:
expected = 0.164252

Input:
std::string kind = "binary_cross_entropy";
std::vector<double> targets = {1.0, 0.0};
std::vector<double> predictions = {0.9, 0.2};

Expected output:
double expected = 0.164252;

Input:
string kind = "binary_cross_entropy";
double[] targets = new double[] {1.0, 0.0};
double[] predictions = new double[] {0.9, 0.2};

Expected output:
double expected = 0.164252;

References

This challenge is adapted for CodeUtility. Follow the statement and constraints above.

• Goodfellow, Bengio and Courville, Deep Learning
• Michael Nielsen, Neural Networks and Deep Learning