Softmax Regression for Multiclass Classification Quiz

Answers and explanations appear as you take the quiz.

1. What constraint do softmax probabilities satisfy for one case across all modeled classes?
   • They sum to one for each case across modeled classes
   • They sum to one only when the highest-scoring class is correct
   • Their sum equals the number of classes
   • Each class score is converted independently without a shared denominator
2. A three-class model returns probabilities 0.6, 0.3 and 0.1. Which class is the usual top-probability prediction?
   • The first class, because it has the largest probability
   • The second class, because it has the largest probability
   • The third class, because it appears last
   • No class can be chosen until probabilities are converted to integer scores
3. Why does adding the same constant to every class logit leave softmax probabilities unchanged?
   • Adding a constant changes only the denominator
   • Adding a constant changes only the numerator
   • The common exponential factor cancels between numerator and denominator
   • Softmax is invariant only when every logit is multiplied by the same constant
4. What does the sum-to-one output assumption imply about the target setup?
   • Several labels may be true together and are modeled independently
   • The classes are ordered and their numeric gaps are meaningful
   • The output may omit probability normalization across classes
   • Each case belongs to one of the modeled mutually exclusive alternatives
5. A classifier has high overall accuracy but weak recall for a rare category. Which report helps expose this?
   • Overall accuracy and the number of examples in each class
   • Per-class recall or precision alongside a confusion matrix
   • Only aggregate training loss across all examples
   • The total number of model coefficients
6. Why check the class-label ordering associated with probability columns?
   • Probability columns are always sorted from largest to smallest
   • Each column follows the raw input-file row order
   • Each probability column must be matched to its documented class label
   • The first column always represents the positive class
7. Which training objective is commonly used for multinomial logistic regression?
   • Squared error between arbitrary integer class IDs
   • A hinge objective on the top two scores
   • Zero-one error as a smooth differentiable training loss
   • Multinomial cross-entropy or log loss
8. A model ranks the correct class first but often assigns it 0.99 when it is right only about 0.7 of the time. What issue is present?
   • Poor calibration: confidence exceeds the observed success frequency
   • Poor recall: the predicted class is not the most frequent class
   • A violation of mutual exclusivity because confidence is high
   • A probability-sum error, even if all class probabilities sum to one