loss_functions.py

import numpy as np


def mean_square_error(y_true: np.ndarray, y_pred: np.ndarray) -> float:
    """
    Calculate MSE loss

    Parameters
    ----------
    y_true: ndarray of shape (n_samples, )
        True response values
    y_pred: ndarray of shape (n_samples, )
        Predicted response values

    Returns
    -------
    MSE of given predictions
    """
    return np.mean((y_true - y_pred)**2)


def misclassification_error(y_true: np.ndarray, y_pred: np.ndarray, normalize: bool = True) -> float:
    """
    Calculate misclassification loss

    Parameters
    ----------
    y_true: ndarray of shape (n_samples, )
        True response values
    y_pred: ndarray of shape (n_samples, )
        Predicted response values
    normalize: bool, default = True
        Normalize by number of samples or not

    Returns
    -------
    Misclassification of given predictions
    """
    score = np.sum(y_true != y_pred)
    return score / len(y_true) if normalize else score


def accuracy(y_true: np.ndarray, y_pred: np.ndarray) -> float:
    """
    Calculate accuracy of given predictions

    Parameters
    ----------
    y_true: ndarray of shape (n_samples, )
        True response values
    y_pred: ndarray of shape (n_samples, )
        Predicted response values

    Returns
    -------
    Accuracy of given predictions
    """
    score = np.sum(y_true == y_pred)
    return score / len(y_true)


def cross_entropy(y_true: np.ndarray, y_pred: np.ndarray) -> float:
    """
    Calculate the cross entropy of given predictions

    Parameters
    ----------
    y_true: ndarray of shape (n_samples, )
        True response values
    y_pred: ndarray of shape (n_samples, )
        Predicted response values

    Returns
    -------
    Cross entropy of given predictions
    """
    if len(y_true.shape) == 2:
        correct_class_prob = (y_pred * y_true).sum(axis=1)
    else:
        correct_class_prob = y_pred[np.arange(len(y_true)), y_true]

    return -np.log(correct_class_prob + 1e-10).mean()


def softmax(X: np.ndarray) -> np.ndarray:
    """
    Compute the Softmax function for each sample in given data

    Parameters:
    -----------
    X: ndarray of shape (n_samples, n_features)

    Returns:
    --------
    output: ndarray of shape (n_samples, n_features)
        Softmax(x) for every sample x in given data X
    """
    exp_X = np.exp(X)
    return exp_X / exp_X.sum(axis=1, keepdims=True)