Exercises

These exercises review the chapter as a whole. Some are numerical; others check whether you can read an experiment without overclaiming.

MATH-C10-C-001Exercise: Split arithmetic

A dataset has 200 examples. The train split has 140 examples and the validation split has 30 examples.

How many examples remain for the test split?

Compute it first, then check your number.

MATH-C10-C-002Exercise: Sample mean

Compute the mean of:

3, 5, 7, 93,\ 5,\ 7,\ 9

Compute it first, then check your number.

MATH-C10-C-003Exercise: Interval width

A confidence interval runs from 0.62 to 0.74.

What is its width?

Compute it first, then check your number.

MATH-C10-C-004Exercise: Cross-validation runs

In 4-fold cross-validation, how many validation runs are made?

Compute it first, then check your number.

MATH-C10-C-005Exercise: Bayesian score

A prior weight is 0.3 and a likelihood weight is 0.6.

What is the unnormalized posterior weight?

Compute it first, then check your number.

MATH-C10-C-006Exercise: Test-set leakage

Should a test split be checked repeatedly while choosing the model?

Answer it first, then check.

MATH-C10-C-007Exercise: Bias or variance

A model has high training error and high validation error.

Which word is the better first diagnosis: bias or variance?

Answer it first, then check.

MATH-C10-C-008Exercise: Likelihood overclaim

Does a higher likelihood prove that a model is the true explanation?

Answer it first, then check.

MATH-C10-C-009Exercise: Bootstrap replacement

In bootstrap resampling, can the same example appear more than once in one resampled dataset?

Answer it first, then check.

MATH-C10-C-010Exercise: Practical significance

A hypothesis test finds evidence of a difference between two models.

Does that automatically mean the difference is large enough to matter in deployment?

Answer it first, then check.

MATH-C10-C-011Exercise: Large but narrow sample

Enter 1 if a very large dataset can still be weak evidence for a population it does not cover well.

Compute it first, then check your number.

MATH-C10-C-012Exercise: Estimator luck

Enter 1 if a reasonable estimator can still give a misleading estimate on one unlucky sample.

Compute it first, then check your number.

MATH-C10-C-013Exercise: MLE and truth

Enter 1 if maximum likelihood can choose the best parameter among candidates without proving that the whole model family is true.

Compute it first, then check your number.

MATH-C10-C-014Exercise: Confidence interval target

Enter 1 if a confidence interval reports uncertainty in an estimate rather than promising the outcome of one future example.

Compute it first, then check your number.

MATH-C10-C-015Exercise: Cross-validation and final evidence

Enter 1 if cross-validation used to choose a model may still need a separate untouched test set for final reporting.

Compute it first, then check your number.

Next

Use the hints only after you have tried the exercises.