You will be able to
- Convert a binary logit into probability.
- Calculate binary cross-entropy and distinguish probability from a decision threshold.
A score becomes a probability
A binary model can output a real-valued logit z. The sigmoid maps z to p, interpreted as the model probability of class 1. A chosen threshold turns probability into a decision; changing threshold changes false-positive/false-negative trade-offs, not the fitted probability itself.
A loss that sees confidence
For y in {0,1}, binary cross-entropy is −y log p−(1−y) log(1−p). Natural logarithms produce loss in nats. A confidently wrong prediction incurs a large loss. Stable implementations operate on logits to avoid taking logs of probabilities rounded to zero or one.
Worked example
At z=0, p=0.5 and either target gives loss ln 2≈0.693. For y=1, p=0.9 gives loss≈0.105, whereas p=0.1 gives≈2.303.
A common trap
A probability of 0.9 is not proof the model is calibrated; that must be assessed across relevant held-out outcomes.
Predict, then experiment
For target 1, does increasing the logit raise or lower the loss? Before touching the controls, say or write your prediction.
Try it yourself
From a logit to probability
How does confidence affect cross-entropy?
Curve is sigmoid(z). The circle marks the adjustable logit; target is 0 or 1. Binary cross-entropy uses natural logarithms and a numerically stable logit formula.
Your experiment
Set target 1 and compare logits −4,0,+4. Repeat for target 0. Observe the same probability curve but a different loss for the changed label.
Change one parameter at a time. Compare what you observed with your prediction and record an explanation in your notes.
Check your understanding
Try from memory first. Hints and feedback are part of learning, not a penalty. These checks are for self-study, not a graded qualification.
Reference answers (after your attempt)
- the decision policy — Correct: the same scores can produce different decisions.
- 0.5 — 1/(1+exp(0))=1/2.
Apply it: Choose a decision threshold responsibly
Use paper, your notes, or a local notebook/editor. Code examples are Python 3 starting points to run yourself; this page does not execute code or automatically assess the practical task.
- Name a binary task and the cost of each error type.
- Describe how to select a threshold on validation data.
- Specify a held-out calibration and decision-metric check.
Reference solution & review criteria
For costly false negatives, a lower threshold may increase recall at the cost of more false positives. Select by an explicit validation objective, then report held-out confusion counts and calibration; avoid tuning on final test results.
Your notebook
Notes and progress stay in this browser. They are not sent to the server; ordinary web-server request logs still operate. Export a backup from the course page.
Completion requires both correct checks and your practical-task acknowledgement.
Go deeper
Sources support further study; the worked examples and questions here are original. Browser experiments are small, disclosed models—not evidence of production-model quality or hardware performance.