The 1958 Model Behind Your Credit Card: How Logistic Regression Learns

When you apply for a credit card, the model deciding your fate probably isn't a giant neural network. There's a good chance it's logistic regression, first published in 1958 and still the benchmark in retail banking. In this episode we go slowly and visually through two questions: what is logistic regression, and how does it learn its numbers? ✅ why a straight line is the natural first try, and why it breaks ✅ the sigmoid: a straight line, squashed into a probability ✅ the weighted sum: what a coefficient really is (an "exchange rate" for evidence) ✅ log loss / binary cross-entropy and maximum likelihood, explained term by term ✅ gradient descent step by step: start with a guess → measure the loss → follow the gradient → step → repeat ✅ the learning rate: what it means and what happens when it's too small or too big ✅ standardizing inputs, momentum, Adam, L-BFGS and SGD ✅ why this same loop, with backpropagation, trains neural networks and LLMs ✅ the whole thing in scikit-learn and in six lines of NumPy Every number on screen comes from real code on simulated credit data: our hand-written gradient descent and scikit-learn land on the same coefficients. ⏱️ Chapters 0:00 Intro 0:44 Where training fits 1:35 Why logistic regression? 2:12 The problem: yes or no 2:58 From a line to an S-curve 4:51 The score: a weighted sum 6:41 Measuring how wrong we are 9:15 Step 1: start with a guess 10:04 Step 2: the gradient 11:45 Step 3: step and repeat 13:37 Smarter ways down the hill 15:03 The foundation of neural networks 16:13 In Python 17:00 Recap & what's next 📺 Episode 1, Data Science in the Credit Card Domain:    • How Credit Card Companies use AI on You (D...   🔔 Next on Gradient Room: reading the model (coefficients, odds, standard errors, p-values), correlated inputs & VIF, overfitting & regularization, the assumptions, and what we do after training. Like, share and subscribe so you don't miss them.