Loss Functions and Multilayer Perceptrons (MLP): A Comprehensive Analysis of Evaluation Metrics, Selecting the Optimal Function to Enhance Model Accuracy

# Loss Functions and Multilayer Perceptrons (MLP): A Comprehensive Guide to Evaluation Metrics, Choosing the Optimal Function, and Enhancing Model Accuracy

## 1. Introduction to Loss Functions

A loss function is a measure of how well a machine learning model's predictions match up with the actual values. It quantifies the model'***mon loss functions include Mean Squared Error (MSE), Mean Absolute Error (MAE), and Cross-Entropy Loss. The theoretical foundations and practical applications of these functions will be discussed in detail in subsequent sections.

## 2. Loss Functions in Multilayer Perceptrons (MLP)

In Multilayer Perceptrons (MLP), the loss function measures the difference between the model's output and the true labels, serving as the key optimization goal during model training. This article will introduce three commonly used loss functions in MLP: Mean Squared Error (MSE), Mean Absolute Error (MAE), and Cross-Entropy Loss.

### 2.1 MSE (Mean Squared Error)

#### 2.1.1 Theoretical Basis

Mean Squared Error (MSE) is the most commonly used loss function for regression tasks. It measures the average of the squared differences between the predicted values and the actual values. The formula is as follows:

MSE = (1/n) * ∑(y_i - y_hat_i)^2

Where:

* n is the number of samples
* y_i is the true label
* y_hat_i is the model's predicted value

#### 2.1.2 Practical Application

MSE is suitable for predicting continuous target variables such as house prices or temperature. It is sensitive to outliers, so when extreme values are present in the data, it may yield misleading results.

### 2.2 MAE (Mean Absolute Error)

#### 2.2.1 Theoretical Basis

Mean Absolute Error (MAE) is another loss function used for regression tasks. It measures the average of the absolute differences between the predicted values and the actual values. The formula is as follows:

MAE = (1/n) * ∑|y_i - y_hat_i|

Where:

* n is the number of samples
* y_i is the true label
* y_hat_i is the model's predicted value

#### 2.2.2 Practical Application

MAE is not sensitive to outliers, making it more stable than MSE when extreme values are present in the data. It is suitable for predicting continuous target variables such as customer churn rates or sales figures.

### 2.3 Cross-Entropy Loss

#### 2.3.1 Theoretical Basis

Cross-Entropy Loss is a commonly used loss function for classification tasks. It measures the difference between the predicted probability distribution and the actual probability distribution. For binary classification problems, the formula is:

Cross-Entropy Loss = - (y_i * log(y_hat_i) + (1 - y_i) * log(1 - y_hat_i))

Where:

* y_i is the true label (0 or 1)
* y_hat_i is the model's predicted probability

#### 2.3.2 Practical Application

Cross-Entropy Loss is suitable for predicting discrete target variables such as image classification or text classification. It is sensitive to differences in probability distributions, so it generates larger loss values when there is a significant difference between the model's predicted probabilities and the actual probabilities.

## 3. Evaluation Metrics for Loss Functions

### 3.1 Accuracy

**3.1.1 Definition and Calculation Method**

Accuracy is the most basic metric for measuring the performance of a classification model. It represents the proportion of correct predictions over all samples. The formula for calculating accuracy is:

Accuracy = Numb