AI Grounds
Open AI Grounds on a desktop
These interactive lessons need a larger screen. Please continue on a desktop or laptop computer.
AI Grounds
These interactive lessons need a larger screen. Please continue on a desktop or laptop computer.
Guided discovery
Move a weight. Trace the decision boundary.
Teal circles = actual Class A; orange squares = actual Class B. Indigo line = the decision cutoff. Each ring shows a prediction: solid for Class A, dashed for Class B. Editing parameters never moves these observations.
1x1 + 1x2 + 0 = 0.000000.
Contribution of x1 to the raw score. Use arrow keys on the slider. Press Enter or leave the number field to apply an exact edit.
Contribution of x2. Zero is allowed; it can produce a vertical boundary. Use arrow keys on the slider. Press Enter or leave the number field to apply an exact edit.
Constant added to every score. Use arrow keys on the slider. Press Enter or leave the number field to apply an exact edit.
Policy: choose Class A when sigmoid(score) ≥ cutoff. Changing it keeps scores fixed. Use arrow keys on the slider. Press Enter or leave the number field to apply an exact edit.
| Point | Score | Probability | Decision | Actual |
|---|---|---|---|---|
| A4 | 1.000000 | 0.731059 | Class A | Class A |
| Point | x1 | x2 | Actual | Score | Probability | Decision |
|---|---|---|---|---|---|---|
| A1 | 0 | 2 | A | 2.000000 | 0.880797 | A |
| A2 | 1 | 1 | A | 2.000000 | 0.880797 | A |
| A3 | 2 | 1 | A | 3.000000 | 0.952574 | A |
| A4 | 1 | 0 | A | 1.000000 | 0.731059 | A |
| B1 | -2 | 1 | B | -1.000000 | 0.268941 | B |
| B2 | -1 | 0 | B | -1.000000 | 0.268941 | B |
| B3 | -1 | -1 | B | -2.000000 | 0.119203 | B |
| B4 | -2 | -2 | B | -4.000000 | 0.017986 | B |
Both feature axes have equal scales. The line is clipped only to the visible −3..3 square. With nonzero weights and 0<cutoff<1, it solves w1x1+w2x2+Bias=ln(cutoff/(1−cutoff)). Cutoff endpoints have no finite logit. Finite scores here produce probabilities strictly between zero and one. Zero weights give a constant scorer; a tie everywhere is different from a separating line. This workbench directly edits parameters; it does not optimize them or estimate calibration from data.
Deep Learning · Logistic regression and decision rules