Identify the incorrect numerical functions in the various function representation of machine learning.

In the context of machine learning, different numerical functions are used for various purposes, such as loss functions, activation functions, and evaluation metrics. Here are some common functions and examples of potential incorrect representations that could occur:

1. Loss Functions:

   • Mean Squared Error (MSE): Correctly defined as $\text{MSE} = \frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2$ An incorrect representation might omit the square or the averaging factor.

   • Cross-Entropy Loss: Defined as $\text{Loss} = -\frac{1}{n} \sum_{i=1}^{n} [y_i \log(\hat{y}_i) + (1 - y_i) \log(1 - \hat{y}_i)]$ An incorrect function might mix up the terms or forget the negative sign.

2. Activation Functions:

   • Sigmoid Function: $\sigma(x) = \frac{1}{1 + e^{-x}}$ A common error could be using $\sigma(x) = e^{-x}$ instead.

   • ReLU (Rectified Linear Unit): Correctly defined as $\text{ReLU}(x) = \max(0, x)$ An incorrect version might define it as $\text{ReLU}(x) = x$ without the $\max(0, x)$.

3. Evaluation Metrics:

   • Accuracy: $\text{Accuracy} = \frac{\text{Number of Correct Predictions}}{\text{Total Predictions}}$ An incorrect representation might count false positives instead of just correct predictions.

4. Regularization:

   • L2 Regularization: $\text{L2} = \lambda \sum_{i=1}^{n} w_i^2$ An incorrect interpretation may confuse it with L1 regularization.

Identifying the incorrect functions typically involves a careful review of how they are defined and ensuring they adhere to the established mathematical representations crucial for effective machine learning practices.