GATE DA Supervised Learning – Data Science & AI | Set 1

Original solution basis:
Recall = TP / (TP + FN), measuring the ratio of correctly predicted positive observations to all actual positives.

Deep Dive
Recall uses the actual positive class as its denominator. Among all truly positive examples, it counts the fraction correctly predicted positive: TP/(TP+FN). False negatives reduce recall. Recall is particularly important when missing a positive case is costly.

Key Points to Remember:
• Recall = TP/(TP+FN).
• Recall is also called sensitivity or true positive rate.
• A lower classification threshold often increases recall but may reduce precision.

Exam tip:
Identify the governing definition or theorem first, write the formula, substitute the given values, and check dimensions/signs before selecting the option.

Original solution basis:
Precision = TP / (TP + FP), measuring accuracy among predicted positive instances.

Deep Dive
Precision conditions on the model's positive predictions. Of all cases predicted positive, it measures the fraction that are truly positive: TP/(TP+FP). False positives reduce precision. Precision is important when false alarms or incorrect positive predictions are costly.

Key Points to Remember:
• Precision = TP/(TP+FP).
• False positives lower precision.
• Precision and recall measure different aspects and should be interpreted together.

Exam tip:
Identify the governing definition or theorem first, write the formula, substitute the given values, and check dimensions/signs before selecting the option.

Original solution basis:
F1-Score is the harmonic mean of Precision and Recall.

Deep Dive
The F1-score is the harmonic mean of precision P and recall R: F1=2PR/(P+R). The harmonic mean penalizes a low value more strongly than the arithmetic mean. If either precision or recall is zero, F1 is zero (when the denominator is defined).

Key Points to Remember:
• F1 = 2PR/(P+R).
• F1 balances precision and recall; it does not include true negatives directly.
• F1 is useful when both false positives and false negatives matter.

Exam tip:
Identify the governing definition or theorem first, write the formula, substitute the given values, and check dimensions/signs before selecting the option.

Original solution basis:
ROC-AUC plots TPR vs FPR across all thresholds. AUC equals the probability of correct pairwise ranking of a random positive vs random negative.

Deep Dive
The ROC curve plots true-positive rate against false-positive rate as the classification threshold varies. Its area summarizes ranking discrimination across thresholds. Equivalently, under the usual interpretation, ROC-AUC is the probability that a randomly selected positive example receives a higher score than a randomly selected negative example (with half credit for ties).

Key Points to Remember:
• ROC plots TPR versus FPR across thresholds.
• AUC=1 indicates perfect ranking; AUC=0.5 corresponds to random ranking in the usual balanced-rank interpretation.
• ROC-AUC is not the same as accuracy at a fixed threshold.

Exam tip:
Identify the governing definition or theorem first, write the formula, substitute the given values, and check dimensions/signs before selecting the option.

Original solution basis:
K-Fold CV partitions data into K folds, fitting K times with each fold serving once as validation set.

Deep Dive
Divide the dataset into K approximately equal folds. In each of K rounds, train on K-1 folds and evaluate on the remaining fold. Each observation is used for validation once and for training K-1 times. The K validation scores are commonly averaged to estimate generalization performance.

Key Points to Remember:
• Each round uses (K-1)/K of the data for training.
• Every fold serves once as validation data.
• Preprocessing and feature selection must be performed inside each training fold to avoid leakage.

Exam tip:
Identify the governing definition or theorem first, write the formula, substitute the given values, and check dimensions/signs before selecting the option.