Multinomial Logistic Regression and Maximum Entropy DATA-SCIENCE-OPTIMIZE Practice Questions (Page 1)

Questions 1–5

1. 1foundation · easy

   According to the maximum entropy principle, when selecting a probability distribution subject to known constraints, one should choose the distribution that:

   • AMinimizes the entropy to reduce uncertainty
   • BMinimizes the number of parameters used in the model
   • CMaximizes the entropy while satisfying the constraints
   • DMaximizes the likelihood of the training data without regard to constraints
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2. 2application · medium

   A data scientist is building a maximum entropy model for sentiment analysis (positive, negative, neutral). They have a feature that indicates whether the word 'excellent' appears in a review. In the training data, 80% of reviews containing 'excellent' are labeled positive. The model is trained with this feature. What constraint does this feature impose on the model's probability distribution?

   • AThe model must predict positive for all reviews containing 'excellent' to satisfy the constraint
   • BThe model must assign exactly 80% probability to the positive class for every review containing 'excellent'
   • CThe model must ignore the feature because it is a binary indicator and cannot impose a probabilistic constraint
   • DThe model's expected count of reviews containing 'excellent' that are predicted positive must match the observed count in the training data
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4. 3application · medium

   A data scientist is building a multinomial logistic regression model to predict which of four products a customer will purchase. The model uses customer demographics as features. After training, the data scientist wants to understand which features are most influential for distinguishing between the products. Which approach provides the most direct insight into feature importance?

   • ACompute the softmax output for a single customer and inspect the probabilities
   • BCount the number of times each feature appears in the training data
   • CLook at the gradient of the loss function at the final iteration
   • DExamine the learned weight coefficients for each feature across all four classes
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5. 4foundation · easy

   Which optimization method is commonly used to train a multinomial logistic regression model?

   • APrincipal component analysis
   • BK-means clustering
   • CDecision tree pruning
   • DGradient descent
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6. 5application · medium

   A data scientist is building a multinomial logistic regression model to classify customer feedback into three categories: Positive, Negative, and Neutral. The model uses TF-IDF features. After training, the data scientist wants to evaluate the model's calibration—how well the predicted probabilities match the actual frequencies. Which approach is most appropriate?

   • ACompute the overall accuracy of the model on the test set
   • BPlot the ROC curve for each class
   • CExamine the learned weight coefficients to see if they are large
   • DGroup predictions by their predicted probability (e.g., bins of 0-0.1, 0.1-0.2, etc.) and compare the average predicted probability in each bin to the actual fraction of positive outcomes
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