A3.1 - Performance Assessment: review quiz on probability and statistics - [LINFO2262] Machine Learning: classification and evaluation

A3.1 - Performance Assessment: review quiz on probability and statistics

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Question 1:

Let a decision tree model $M$ be used to classify 1000 independent test examples. We consider the following events:

$A$ : $M$ classifies the third test example as positive;
$B$ : $M$ classifies the third test example as negative.

The model $M$ is fixed and deterministic. In both cases $A$ and $B$ , we consider the same third test example.

Select all valid answers.

Two mutually exclusive events $A$ and $B$ cannot be independent provided that $P(A)>0$ and $P(B)>0$ .

Those events are random because the test examples should be considered to be drawn at random.

Those events are mutually exclusive because they cannot both occur.

Those events are not random because the decision model is deterministic, i.e. it always predicts the same class for a given test point.

Those events are not mutually exclusive because either of them can happen.

Those events are independent because the test examples are independent.

Mutually exclusive events are never independent.

Question 2:

A polynomial kernel SVM is estimated on a validation set to have a 80% classification accuracy. When this model is run to classify a stream of new test examples, what is the expected number of examples to be processed until the first classification error appears (include the first error in the total number of examples required)?

Question 3:

How do you expect this number to vary according to the actual set of test examples? Report the standard deviation of your estimator.

When rounding, give at least 3 decimals.

Question 4:

What is the expected number of examples to be processed until the 6-th classification error is observed (include all 6 errors in the total number of examples required)?

Auteur(s)	Pierre Dupont
Date limite	23/03/2025 23:00:00
Limite de soumission	Pas de limite

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