Understanding the Decision Boundary for Logistic Regression

Understanding the Decision Boundary for Logistic Regression For binary classification issues, logistic regression is a popular approach in machine learning. The input features are mapped to a probability of the positive class using a logistic function. We shall examine the computation of predictions via logistic regression and the representation of the decision boundary in more detail in this article. Logistic Regression Review A value termed z, which is equal to the dot product of the input features and weights plus a bias component, is calculated as the first step in logistic regression. The anticipated probability of the positive class is then obtained by passing the value z through the Sigmoid function, g(z). The Sigmoid function's formula is as follows: 𝑔(𝑧) = 1 −𝑧 1+𝑒 Then, using a threshold, the final forecast, y hat, is generated. The most common threshold is 0.5, with y hat being adjusted to 1 if 𝑔(𝑧) ≥ 0. 5 and 0 otherwise. Making Sense of the Decision Boundary Logistic regression establishes a decision boundary to distinguish between the positive and negative samples in a two-feature classification problem. Depending on the quantity of characteristics, the equation of a line or a curve determines the decision boundary. Set g(z) = 0.5 and solve for one feature in terms of the other to obtain the equation of the decision boundary. The decision boundary, where 𝑤1 and 𝑤2 are the weights for the two features and b is the bias term, occurs when 𝑤1 · 𝑥1 + 𝑤2𝑥2 + 𝑏 = 0. We can plot the affirmative and negative examples and depict the boundary between them by drawing a line or curve. The positive class is represented by the side of the line or curve where 𝑔(𝑧) =≥ 0. 5, and the negative class is represented by the side where 𝑔(𝑧) < 0. 5. Using the Decision Boundary to Interpret The decision border is a handy tool for deciphering the predictions made by the logistic regression model. We may learn more about the relative weights of each characteristic in establishing the class labels by examining the coefficients of the weights and the bias term. For instance, if a feature's weight is high and positive, it suggests that a feature's value is correlated with a higher likelihood of belonging to the positive class. A larger value of that attribute is connected to a reduced probability of the positive class, however, if the weight is large and negative. The decision border is moved up or down by the bias term, but its slope is unaffected. The decision boundary is shifted upward by a significant positive bias term, which makes it simpler for samples to fall into the positive category. A significant negative bias term lowers the decision limit, making it more difficult for samples to fall inside the positive category.