Which algorithm is used for binary classification by modeling the probability of an event using a sigmoid function?

• A. K-Means clustering
• B. Decision tree
• C. Linear regression
• D. Logistic regression

Answer: (D)

The idea here is to model the probability of a binary outcome using a sigmoid function. Logistic regression does exactly this: it takes the input features, forms a linear score z = w^T x + b, and maps that score through the sigmoid function to produce a probability between 0 and 1. This P(y=1|x) can then be compared to a threshold (often 0.5) to assign a class. The sigmoid output also lets us train the model using likelihood principles, typically with cross-entropy loss, which fits the weights to maximize the probability of the observed labels.

Other options don’t fit this specific approach. K-means clustering is unsupervised and groups data by similarity without estimating probabilities for a binary label. A decision tree can classify data but does not inherently model the probability with a smooth sigmoid. Linear regression predicts a continuous value rather than a probability, so it isn’t suited to delivering a probability of a binary event without additional transformation, and that transformation doesn’t preserve the straightforward probabilistic interpretation.