Logistic Regression, Part 1: From a Line to a Probability

Logistic regression explained, part 1: from a straight line to a probability with the sigmoid function, for binary classification. Will this student pass: yes or no? A regression line answers "1.55", which is neither a yes nor a probability. In part one of logistic regression we see why a straight regression line is the wrong tool for a yes or no question, we draw a line that separates two classes, we find one with a simple nudging rule, and then we meet the sigmoid: the curve that turns the distance from that line into a probability. You will learn: Classification with two classes, written as 0 and 1 Why a regression line is a poor classifier: outputs below 0 and above 1, and one far point drags the cut (4.5 → 5.3 hours) The decision boundary w1·x1 + w2·x2 + b = 0, the score z, and its positive and negative side The perceptron rule: nudge the line towards a misclassified point; a real run that ends after five nudges Its two weaknesses: it stops at the first line with no mistakes, and it has no notion of confidence The sigmoid 1 / (1 + e^(−z)), built point by point: 0.02, 0.12, 0.5, 0.88, 0.98 How distance from the boundary becomes a probability, and why it is 0.5 on the boundary Reading a prediction as a probability, and choosing a threshold (0.3, 0.5, 0.8) Part two covers how the model is trained. Chapters 0:00 A yes or no question 0:36 Why a regression line is a poor classifier 2:11 The decision boundary and the score z 2:57 Nudging the line: the perceptron rule 3:47 Its two weaknesses 4:14 The sigmoid, built point by point 5:09 From distance to probability 5:44 Reading a prediction, choosing a threshold 6:18 Recap + try it yourself Try it yourself: compute the sigmoid of 2 (hint: e^(−2) ≈ 0.135) and the sigmoid of −2 (hint: e^2 ≈ 7.39). Add the two answers. What do you notice? Animations made with Manim Community Edition. The narration is a synthetic voice. All data in this video are simulated. #LogisticRegression #MachineLearning #AIEngineer More from Harban AI Labs: https://harban-ai-labs.vercel.app/