软最大回归与评估指标

Softmax Regression and Evaluation Metrics

Precision, recall, and their combination

Softmax, metrics, and a bootstrap test

Compute the softmax weight for the largest logit when $\mathbf{z} = [2, 0, -1]$, that is $\exp(2) / (\exp(2) + \exp(0) + \exp(-1))$, and round to three decimals.

For the class of interest, a classifier records $10$ true positives and $4$ false positives. Compute precision and round to three decimals.

A class achieves precision $P = 0.5$ and recall $R = 0.4$. Compute $F_1 = \frac{2PR}{P+R}$ and round to three decimals.

A three-class triage system handles a rare storm class with 17 test items and a routine class with 100. Performance on the rare class matters as much as on the frequent one. Which averaging scheme fits, and what does the alternative do?

On a paired test set, system A beats system B by $\delta(x) = 0.1$ accuracy. The paired bootstrap resamples the test set and compares each resampled difference $\delta(x^{(i)})$ against a threshold that corrects for the bias the resamples inherit from the observed data. A resample counts toward the p-value when $\delta(x^{(i)}) \geq t$. What is $t$? Answer as a decimal.