Scores and Boundaries

Threshold Equality Is a Policy

The threshold rule includes an equality choice. This lesson pins the row whose score equals the threshold and shows why it becomes class 1 under the stated policy.

highlighted = computed this step

Pin the equality policy

Use exact scores -1, 0, and 1 with threshold 0. The stated policy is score >= threshold -> class 1.

scores=(−1,0,1),t=0\text{scores}=(-1,0,1),\quad t=0
Threshold Equality Is a PolicyThe exact equality row follows the stated comparison rule.threshold equality policyscore >= threshold -> class 1scorecomparison to 0decisionwhy-1score < threshold0below threshold0score = threshold1equality included1score > threshold1above thresholdscore=0 equals threshold -> class 1a stated 'score > threshold' policy would put only the equality row onthe other sidethreshold equality is a stated decision policy; not a claim of accuracy,calibration, training, generalization, or probability

Apply it row by row

The score -1 is below the threshold, so it gets class 0. The scores 0 and 1 are at or above the threshold, so they get class 1.

(−1,0,1)⇒(0,1,1)(-1,0,1)\Rightarrow(0,1,1)
Threshold Equality Is a PolicyThe exact equality row follows the stated comparison rule.threshold equality policyscore >= threshold -> class 1scorecomparison to 0decisionwhy-1score < threshold0below threshold0score = threshold1equality included1score > threshold1above thresholdscore=0 equals threshold -> class 1a stated 'score > threshold' policy would put only the equality row onthe other sidethreshold equality is a stated decision policy; not a claim of accuracy,calibration, training, generalization, or probability

The boundary row is included

The row with score 0 becomes class 1 because equality is included in the stated policy. No sigmoid decimal or probability value is computed.

0≥0⇒class 10\ge 0\Rightarrow\text{class }1
Threshold Equality Is a PolicyThe exact equality row follows the stated comparison rule.threshold equality policyscore >= threshold -> class 1scorecomparison to 0decisionwhy-1score < threshold0below threshold0score = threshold1equality included1score > threshold1above thresholdscore=0 equals threshold -> class 1a stated 'score > threshold' policy would put only the equality row onthe other sidethreshold equality is a stated decision policy; not a claim of accuracy,calibration, training, generalization, or probability

Boundary

A different stated policy, score > threshold, would put the zero row on the other side. This lesson pins the >= policy only: not a claim of accuracy, calibration, training, generalization, or probability.

stated policy, exact comparison only\text{stated policy, exact comparison only}
Threshold Equality Is a PolicyThe exact equality row follows the stated comparison rule.threshold equality policyscore >= threshold -> class 1scorecomparison to 0decisionwhy-1score < threshold0below threshold0score = threshold1equality included1score > threshold1above thresholdscore=0 equals threshold -> class 1a stated 'score > threshold' policy would put only the equality row onthe other sidethreshold equality is a stated decision policy; not a claim of accuracy,calibration, training, generalization, or probability