Add Gaussian negative log likelihood loss algorithm

@@ -1,3 +1,5 @@+# ruff: noqa: RUF002 -- ambiguous-unicode-character-docstring+ import numpy as np  @@ -302,6 +304,60 @@ def categorical_focal_cross_entropy(     return np.mean(cfce_loss)  +def gaussian_negative_log_likelihood_loss(+    y_true: np.ndarray,+    expectation_pred: np.ndarray,+    var_pred: np.ndarray,+    eps: float = 1e-6,+) -> float:+    """+    Calculate the negative log likelihood (NLL) loss between true labels and predicted+    Gaussian distributions.++    NLL = -Σ(ln(1/(σ√(2π))) - 0.5 * ((y_true - μ)/σ)^2)++    Reference: https://pytorch.org/docs/stable/generated/torch.nn.GaussianNLLLoss.html++    Parameters:+    - y_true: True labels+    - expectation_pred: Predicted expectation (μ) of the Gaussian distribution+    - var_pred: Predicted variance (σ^2) of the Gaussian distribution+    - eps: Small constant to avoid numerical instability++    Examples:+    >>> true_labels = np.array([1.0, 2.0, 3.0, 4.0, 5.0])+    >>> expectation = np.array([0.8, 2.1, 2.9, 4.2, 5.2])+    >>> variance = np.array([0.1, 0.2, 0.3, 0.4, 0.5])+    >>> loss = gaussian_negative_log_likelihood_loss(true_labels, expectation, variance)+    >>> bool(np.isclose(loss, -0.60621))+    True++    >>> true_labels = np.array([1.0, 2.0, 3.0, 4.0, 5.0])+    >>> expectation = np.array([0.8, 2.1, 2.9, 4.2, 5.2])+    >>> variance = np.array([0.1, 0.2, 0.3, 0.4])+    >>> gaussian_negative_log_likelihood_loss(true_labels, expectation, variance)+    Traceback (most recent call last):+        ...+    ValueError: Input arrays must have the same length.+    """++    if (+        len(y_true) != len(expectation_pred)+        or len(y_true) != len(var_pred)+        or len(expectation_pred) != len(var_pred)+    ):+        raise ValueError("Input arrays must have the same length.")++    # The constant term `0.5 * np.log(2 * np.pi)` is ignored since it doesn't affect the+    # optimization. PyTorch also ignores this term by default.+    # See https://pytorch.org/docs/stable/generated/torch.nn.GaussianNLLLoss.html+    loss_var = 0.5 * (np.log(np.maximum(var_pred, eps)))+    loss_exp = 0.5 * (np.square(y_true - expectation_pred) / np.maximum(var_pred, eps))+    loss = loss_var + loss_exp++    return np.mean(loss)++ def hinge_loss(y_true: np.ndarray, y_pred: np.ndarray) -> float:     """     Calculate the mean hinge loss for between true labels and predicted probabilities