Question

(a) Give the definition of a nonconformity measure in the context of conformal prediction.[3 marks] (b) Define the conformal predictor for a given nonconformity measure. Make sure to include the definition of the prediction set at a given significance level.[5 marks] (c) Compare and contrast nonconformity measures and conformity measures.[4 marks] (d) In the context of conformal prediction, what is the minimal possible p-value for a training set of size n? (e) Define the average false p-value for a test set in the context of conformal prediction.[3 marks] (f) Consider the following binary classification problem with two features. The training set is: • positive samples: (0,0), (1,0), (0,1); .• negative samples: (4,4), (3,4), (4,3). The test set consists of two samples, (1, 1) and (3,3). i. Find the 1-Nearest Neighbour predictions for the test samples. ii. Using the distance to the nearest sample of the same class as non-conformity measure, compute all the p-values for the test samples. For each test sample, compute the point prediction, confidence, and credibility.[13 marks] iii. You are told that the true labels of the test samples (1, 1) and (3, 3) are+1 and -1, respectively. What is the average false p-value for the test set with these labels?[3 marks]

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