🧠 Model internals
w₁ Glucose
0.0000w₂ BMI
0.0000w₃ Age
0.0000b Bias
0.0000Epoch 0 / 100Patient – / 20
Live calculations
1 SelectPick the next patient from the training set. SGD learns from one patient at a time.
2 ZCombine the patient's features with the current weights into a single score z.
3 σTurn the score z into a probability between 0 and 1 using the sigmoid function.
4 LossMeasure how wrong that probability is compared with the true label.
5 UpdateAdjust every weight a little in the direction that reduces the loss (gradient descent).
| RawThe patient's measurement in its original units (mg/dL, kg/m², years). | Scaled xThe raw value after standardising: (raw − training mean) ÷ training standard deviation. Puts all features on the same scale so training is stable. | WeightHow strongly this feature pushes the prediction toward diabetes (positive) or away from it (negative). This is what the model learns. | |
|---|---|---|---|
| Glucose | – | – | – |
| BMI | – | – | – |
| Age | – | – | – |
Weighted sum (z)iA linear score. Each scaled feature x is multiplied by its weight w, the results are added, then the bias b shifts the total. z > 0 leans "diabetes", z < 0 leans "no diabetes". z = 0 is the decision boundary.
Sigmoid (ŷ)iThe sigmoid σ squashes any score z into a probability between 0 and 1. Large positive z gives ŷ near 1, large negative z gives ŷ near 0, and z = 0 gives exactly 0.5. e is Euler's number (≈ 2.718).
Loss (log-loss)iBinary cross-entropy for one patient. If the true label y is 1 it reduces to −ln ŷ; if y is 0 it is −ln(1 − ŷ). Confident wrong answers get a huge loss, confident right answers get a tiny one. ln is the natural logarithm.
Gradient updateiOne step of gradient descent. The error (ŷ − y) says how far off we were; multiplying by the feature x says how much that feature is to blame. α (the learning rate) scales the step. The bias moves by α·error only.
Press Step or Play to begin training. The model starts with all weights at 0 (it predicts 50% for everyone).
Data and decision boundary
Blue region = model predicts no diabetes, red region = predicts diabetes (deeper colour = more confident). Dot size = age. The purple line is where the model is 50/50, drawn with Age held at its training average (a 3-feature model really has a plane; this is a 2-D slice of it).
Train vs test performance
Accuracy after every epoch. The test set is only measured here; the model never learns from it. If train keeps rising while test falls, the model is overfitting. With only 6 test patients the test line moves in big jumps.
Cost per epoch
Average log-loss over all 20 training patients, measured once at the end of every epoch (epoch 0 = untrained model, ln 2 ≈ 0.693).