Deep Learning 101: Lesson 3: Loss and Metric
This article is part of the “Deep Learning 101” series. Explore the full series for more insights and in-depth learning here.
In machine learning, evaluating and improving model performance depends on understanding loss and metrics. This section explains the importance of loss functions for regression (such as Mean Squared Error) and classification (such as Cross-Entropy Loss). Metrics like accuracy, precision, and recall also play a critical role, and we’ll explore why they’re necessary. We’ll talk about how loss functions guide the training process by measuring the model’s errors, and how metrics help interpret model performance in a practical way. These concepts are essential to building efficient machine learning models because they provide the feedback needed to tune models and make informed decisions about their implementation.
Consider the dataset presented in the table below, consisting of columns x, y, and y’:
Upon performing a linear regression analysis, we hypothesize the relationship between x and y’ to be:
y’ = 1 + 2x
Here, y’ represents the predicted values, while y denotes the true output values.
In evaluating the performance of our regression model, we’ll look at four key metrics: Mean Square Error (MSE), Mean Absolute Error (MAE), Cosine Proximity, and Cosine Distance. Notably, MSE and MAE fall into the category of loss functions, while Cosine Proximity and Cosine Distance are considered evaluation metrics.
Changing the y-values in the table will affect the calculated values for our loss functions and metrics accordingly.
The formulas to compute these four metrics are as follows:
Mean Square Error (MSE): This calculates the average squared difference between the predicted and actual values.
Mean Absolute Error (MAE): This computes the average absolute difference between the predicted and actual values.
Cosine Proximity: This metric measures the similarity between two vectors by determining the cosine of the angle between them. In machine learning, it provides insight into the closeness of two samples or feature vectors.
Cosine Distance: Essentially the inverse of cosine proximity, it quantifies the dissimilarity between two vectors.
Using the above formulas, we calculate the values of these quantities as below:
Mean Square Error = 2.00
Mean Absolute Error = 1.33
Cosine Proximity = 0.99
Cosine Distance = 0.01
To better understand the loss function, we can look at a scatterplot comparing our data set to the regression line. This gives you a clear idea of how close (or far) the actual data points are to the regression line.
By comparing the actual data points to this regression line, we can see how well our model fits the data. Data points that are close to the regression line indicate that the model’s predictions are accurate, while points that are far from the line highlight errors in the model’s predictions. This visual analysis helps in understanding the extent of deviation and provides insights into the performance of the regression model. The closer the data points are to the regression line, the lower the error, which aligns with lower values in our loss functions like Mean Squared Error (MSE) and Mean Absolute Error (MAE).
Summary
Understanding loss functions and metrics is crucial for evaluating and improving machine learning models. Loss functions like Mean Squared Error (MSE) and Mean Absolute Error (MAE) guide the training process by measuring the model’s errors. Metrics such as accuracy, precision, and recall help interpret the model’s performance in practical terms. This feedback is essential for tuning models and making informed decisions about their implementation. In this discussion, we explored key metrics and their importance, demonstrated how changing dataset values affects these metrics, and provided formulas to compute them. A visual scatter plot further illustrated the relationship between actual data points and the regression line.
4 Ways to Learn
1. Read the article: Loss and Metric
2. Play with the visual tool: Loss and Metric
3. Watch the video: Loss and Metric
4. Practice with the code: Loss and Metric
Previous Article: Linear Regression
Next Article: Gradient Descent
