In-depth Logistic Regression

This presentation offers a visually intuitive and mathematically grounded exploration of logistic regression, designed to bridge conceptual understanding and practical implementation. It begins by illustrating how disparate numerical features, such as age and salary, influence binary decision outcomes and highlights the critical challenge that unscaled data can lead to numerical instability and model failure. The narrative then introduces normalisation as a fundamental preprocessing step, demonstrating how standardisation aligns features onto a common scale to ensure mathematical stability. Building upon this, the presentation explains the linear model that combines weighted inputs into a single score (z), representing aggregated evidence. This score is transformed using the sigmoid function to produce interpretable probabilities bounded between 0 and 1, which are then converted into actionable decisions through thresholding. The learning process is rigorously defined by the log loss function, which captures the cost of incorrect predictions and guides optimisation. The risks of overfitting are clearly depicted, contrasting memorisation with true pattern learning, followed by the introduction of regularisation to enforce simplicity and generalisation. The concept of the decision boundary is visualised geometrically as a separator between classes in feature space, and model performance is validated using a confusion matrix, which shows perfect classification in this example. The presentation culminates in a holistic architectural view of the logistic regression pipeline and connects theory to implementation through Jupyter-based workflows, making the model transparent and reproducible.